Derivatives Explained
The key to understanding derivatives is the notion of a
premium. Some derivatives are compared to insurance. Just as you pay an
insurance company a premium in order to obtain some protection against a
specific event, there are derivative products that have a payoff contingent
upon the occurrence of some event for which you must pay a premium in advance.
When one buys a cash instrument, for example 100 shares of
ABC Inc., the payoff is linear (disregarding the impact of dividends). If we
buy the shares at $50 and the price appreciates to $75, we have made $2500 on a
mark-to-market basis. If we buy the shares at $50 and the price depreciates to
$25, we have lost $2500 on a mark-to-market basis. Instead of buying the shares in the cash market, we could have bought a 1 month call option on ABC stock with a strike price of $50, giving us the right but not the obligation to purchase ABC stock at $50 in 1 month's time. Instead of immediately paying $5000 and receiving the stock, we might pay $700 today for this right. If ABC goes to $75 in 1 month's time, we can exercise the option, buy the stock at the strike price and sell the stock in the open market, locking in a net profit of $1800.
If the ABC stock price goes to $25, we have only lost the premium of $700. If ABC trades as high as $100 after we have bought the option but before it expires, we can sell the option in the market for a price of $5300. The option in this case gives us a great deal of positional flexibility with a different risk/reward profile.
Mark-to-market is a way of accounting for financial products in which an inventory of financial products is revalued a pre-set interval (usually at the end-of-business on a daily basis) at current market rates. The combination of realized and unrealized profit and loss is booked to the profit-and-loss account. Mark-to-market accounting is a good practice for the management of any financial portfolio.
It is mandatory for financial institutions to report their financial accounts in this fashion. In the near future, initiatives like the Financial Accounting Standards Board Statement No. 133 will require mark-to-market accounting from non-institutional end-users, as well.
Notional Amounts
Another aspect of financial derivatives is the fact that
they are carried off-balance sheet, generally. When we speak of the size of a
particular derivative contract, we refer to the notional amount. The notional
amount is the amount used to calculate the payoff. For example, in our options
example above, the notional amount was 100 shares. However, the potential
payoff and the potential loss were both different from the value of 100 shares.
Because the payoffs of derivative products differ from the payoffs that their
notional amounts might suggest if they were cash instruments, they are kept off
balance sheet. Otherwise, the balance sheet could be distorted and inflated by
even a relatively small derivatives portfolio. Finally, in terms of the regulatory appeal of derivative products, there are a number of different ways of looking at this issue. Derivative products, because of their off-balance sheet nature, can be used to clear up the balance sheet. A mutual fund manager who is restricted from taking currency plays by regulatory requirements can buy a structured note whose coupon is tied to the performance of a particular currency pair.
The Two Types of Derivatives
There are two types of derivatives: linear derivatives and
non-linear derivatives. A linear derivative is one whose payoff function is a
linear function. For example, a futures contract has a linear payoff in that
every one-tick movement translates directly into a specific dollar value per
contract. A non-linear derivative is one whose payoff changes with time and
space. Space in this case is the location of the strike with respect to the actual cash rate (or spot rate). One example of a non-linear derivative with a convex payoff profile at some point before the option's maturity is a simple plain vanilla option. As the option becomes progressively more in-the-money, the rate at which the position makes money increases until it asymptotically approaches the linear payoff of the future. Similarly, as the option becomes progressively more out-of-the-money, the rate at which the position loses money decreases until that rate becomes zero.
"Delta"
With non-linear derivatives, therefore, it is possible to
capture gains from volatility by hedging a portion of the option's value. This
is called the "delta", given by a mathematical formula derived from
the formula used to determine price, and rebalancing the hedge as spot moves
around and the delta changes. In the ABC Inc. example from above, we could have purchased a 1-month $50 call option on ABC giving us the right to purchase 100 shares. With the spot price at $50, the option is said to be at-the-money. At-the-money options have a delta of 50%, so to "delta-hedge" the option, we would have sold short 50 shares. If the ABC price proceeded to $25 the next week, we could buy back some of the 50 shares we were short (realizing a $25 profit on those shares).
Any move back to $50 subsequently and we could sell more shares short again. If the ABC price went to $75 the next week, we could sell more shares short. This would enable us to buy these shares back if the ABC price went lower before maturity. The more times we can delta-hedge the option (or "dynamically hedge" the option), the more profit we will realize.
Every time we realize a profit, we help to pay for the option. If you own an option and you delta hedge it, you will make money if the stock price goes up. You will also make money if the stock price goes down. You have to delta-hedge consistently in order to realize that profit, though. At the end of the day, you will only make money if you have realized delta-hedging profits that are greater than the premium you paid away for the option.
The more the stock prices moves up and down, the more likely you are to realize delta-hedging profits. Conversely, if you sell an option and delta hedge it, you will lose money if the stock price goes up and you will lose money if the stock price goes down. Each time that you delta-hedge, you are realizing a loss. At the end of the day, you will only make money if your delta-hedging losses are less than the option premium you earned to sell the option in the first place.
If you can understand delta hedging, then you can understand the way options are priced and what it means to determine good value in a premium. If we buy an option, then we are arguing that we will make more money dynamically hedging around it than we will pay in premium. If we sell an option, then we are arguing that we will make more money in premium than we will lose in dynamically hedging the option. One of the prime determinants of the price of an option is the volatility.
Volatility
Volatility is the measure of how much the spot rate is
expected to move around. Obviously, in a high volatility environment, the spot
rate will be expected to move around aggressively and options premiums are very
high. In a low volatility environment, the spot rate is expected to move around
very little and options premiums are very low. One of the key factors in making
money in options is to understand the nature of volatility. There are two important characteristics of volatility one needs to understand. First, volatility is not constant. It changes over the course of time. There might be specific events that will cause volatility to spike higher. For example, the 1992 European Exchange Rate Crisis, triggered by votes on the Maastricht Treaty, turned a relatively stable environment into a savagely volatile one. Second, volatility is statistically persistent. That is a fancy way of saying that volatility trends. If it's volatile today, then it should continue to be volatile. If it's calm today, then it should continue to be calm.
Making money in options often means realizing that the trend in volatility has changed from calm to volatile (in which case you buy options at the beginning of the volatile period when options volatilities are still low compared to what you expect actual volatility will turn out to be) or selling options when the trend changes from volatile to calm (and option volatilities are higher than what you expect them to be). In subsequent articles, we will elaborate on determining good value in options and we will focus on the other key element in making money in options: understanding the behavioral characteristics of derivative products. The biggest single problem with the use of derivative products today is the lack of knowledge about these two factors.
Credit Derivatives:
A credit derivative is a financial instrument used to
mitigate or to assume specific forms of credit risk by hedgers and speculators.
These new products are particularly useful for institutions with widespread
credit exposures. Some observers suggest that credit derivatives may herald a
new form of international banking in which banks resemble portfolios of
globally diversified credit risk more than purely domestic lenders.
CREDIT SWAPS
Corporate bonds trade at a premium to the risk-free yield curve in the same currency. US Corporate Bonds trade at a premium (called a credit spread) to the US Treasury curve. The credit spread is volatile in and of itself and it may be correlated with the level of interest rates. For example, in a declining, low interest rate environment combined with strong domestic growth, we might expect corporate bond spreads to be smaller than their historical average. The corporate who has issued the bond will find it easier to service the cash flows of the corporate bond and investors will be hungry for any kind of premium they can add to the risk-free rate.
Imagine the fund manager who specializes in corporate bonds who has a view on the direction of credit spreads on which he would like to act without taking a specific position in an individual corporate bond or a corporate bond index.
One way for the fund manager to take advantage of this view is to enter into a credit swap.
Let's say that the fund manager believes that credit spreads are going to tighten and that interest rates are going to continue to decline.
This is an off-balance sheet transaction and the swap will typically have zero value at inception.
If corporate yields continue to fall (i.e. through a combination of a lower risk-free rate and a lower corporate credit spread than the one he locked in with the swap), he will make money. If corporate yields rise, he will lose money.
1998 was a dynamic year for corporate bond spreads with the backup in interest rates in the aftermath of the Russian devaluation-inspired liquidity crisis concentrated mainly in corporate yields. The volatility of these spreads was extreme when compared to their historical movement. Credit swaps would have been an excellent way to play this spread volatility.
Moreover, credit swaps (particularly ones based on a spread index) are clean structures without the messy difficulty of finding individual corporate bond supply, etc.
Another example of a credit swap might be the exchange of fixed flows (determined by the yield on a corporate bond at inception) against paying floating rate flows tied to the risk-free Treasury rate for the corresponding maturity.
Naturally, swaps are flexible in their design. If you can imagine a cash flow exchange, you can structure the swap. There might be a cost associated with it but you can certainly put it on the books.
CREDIT DEFAULT SWAPS
A credit default swap is a swap in which one counterparty receives a premium at pre-set intervals in consideration for guaranteeing to make a specific payment should a negative credit event take place.
One possible type of credit event for a credit default swap is a downgrade in the credit status of some preset entity.
Consider two banks: First Chilliwack Bank and Banque de Bas.
De Bas now has exposure to Churchill, a position they could not take directly because they are not part of Churchill's lending syndicate.
OPTIONS ON CREDIT RISKY BONDS
Finally, our fund manager from the first example could use an options position to take advantage of his view on the level of the corporate yield.
If he believed that corporate yields were set to fall through some combination of lower risk-free interest rates and tighter corporate bond spreads, then he could just buy a call on a corporate bond of the appropriate maturity.
These are just a few of the examples of credit derivatives. Institutional investors often use credit derivatives when positioning themselves in emerging markets for the ease of transaction in the same way that they might use equity swaps. Fund managers can use credit derivatives to hedge themselves against adverse movements in credit spreads. Corporates can use credit swaps to hedge near-term issues of corporate bonds. Banks and other financial institutions can use credit derivatives to optimize the employment of their capital by diversifying their portfolio-wide credit risk.
Intro to Exotic Options:
This is to provide a brief overview of exotic options. We
have already talked about so-called "plain vanilla options" in
“Derivatives Explained”, the simple puts and calls that are priced in the
exchange-traded markets and the over-the-counter markets for equities, fixed
income, foreign exchange and commodities. Exotic options are either variations
on the payoff profiles of the plain vanilla options or they are wholly
different kinds of products with optionality embedded in them. The exotic
options market is most developed in the foreign exchange market so we will
restrict ourselves here to using foreign exchange examples, although we could
easily talk about any of the other asset classes.
Barrier Options
A barrier option is like a plain vanilla option but with
one exception: the presence of one or two trigger prices. If the trigger price
is touched at any time before maturity, it causes an option with pre-determined
characteristics to come into existence (in the case of a knock-in option) or it
will cause an existing option to cease to exist (in the case of a knock-out
option). There are single barrier options and double barrier options. A double barrier option has barriers on either side of the strike (i.e. one trigger price is greater than the strike and the other trigger price is less than the strike). A single barrier option has one barrier that may be either greater than or less than the strike price. Why would we ever buy an option with a barrier on it? Because it is cheaper than buying the plain vanilla option and we have a specific view about the path that spot will take over the lifetime of the structure.
Intuitively, barrier options should be cheaper than their plain vanilla counterparts because they risk either not being knocked in or being knocked out. A double knockout option is cheaper than a single knockout option because the double knockout has two trigger prices either of which could knock the option out of existence. How much cheaper a barrier option is compared to the plain vanilla option depends on the location of the trigger.
First, let us think of the case where the barrier is out-of-the-money with respect to the strike. Consider the example of a plain vanilla 1.55 US dollar Call/Canadian dollar put that gives the holder the right to buy USD against Canadian dollars at a rate of 1.55 for 1 month's maturity. Spot is currently trading at 1.54. Consider now the 1.55 US dollar call/Canadian dollar put expiring in 1 month that has a knockout trigger at 1.50. The knockout option will be cheaper than the plain vanilla option because it might get knocked out and the holder of the option should be compensated for this risk with a lower up front premium. However, it is not very likely that 1.50 will trade, so the difference in price is not that great. If we move the trigger to 1.53, the knockout option becomes considerably cheaper than the plain vanilla option because 1.53 is much more likely to trade in the next month.
Note that for a given trigger, we would expect the difference in price between the plain vanilla price and the knockout price to increase with moves higher in implied volatility. A higher implied volatility means that spot is more likely to trade at the trigger than if spot were less volatile. A greater likelihood of trading at the trigger means a greater likelihood of getting knocked out.
The reverse logic applies to knock-in options. The knock-in 1 month 1.55 US dollar call with a trigger of 1.53 will be more expensive than the 1 month 1.55 US dollar call with a knock-in trigger of 1.50 because 1.53 is more likely to trade. If we own the 1 month 1.55 US dollar call/Canadian dollar put that knocks out at 1.53 and we also own the 1 month 1.55 US dollar call/Canadian dollar put that knocks in at 1.53, the combined position is equivalent to owning the plain vanilla 1 month 1.55 US dollar call.
Now, turn to the case where the barrier is in-the-money with respect to the strike. Imagine that the spot US dollar/Canadian dollar exchange rate is trading at 1.54. Consider the price of a 1 month 1.50 US dollar call/Canadian dollar put. This option has quite a bit of intrinsic value to it, already. Its premium will be at least 0.04 Canadian dollar cents/US dollar notional. The price of a 1 month 1.50 US dollar call/Canadian dollar put that knocks out at 1.56 is much cheaper than the plain vanilla 1 month 1.50 US dollar call because of the likelihood of spot trading as high as 1.56. In the blink of an eye, 0.06 Canadian dollar cents/US dollar notional worth of intrinsic value could be knocked out if spot were to trade at 1.56. A knock out option in which the barrier is in-the-money with respect to the strike is called a reverse knockout option. A knock-in option in which the barrier is in-the-money with respect to the strike is called a reverse knockin option.
How do we make money with this position? We buy the cheaper 1 month 1.50 US dollar call/Canadian dollar put that knocks out at 1.56 if we believe that spot will be contained within a narrow range around the current spot. Ideally, spot drifts higher very slowly, ending up just under 1.56 at expiry (say at 1.5580) without ever trading that level. We exercise the option, buying our US dollars against Canadian dollars at 1.50 and sell them simultaneously in the spot market, locking in 0.5580 Canadian dollar cents/US dollar notional. The higher the implied volatility at the time the option is priced, the cheaper the knock out option with the in-the-money trigger will be, compared to the similar plain vanilla option.
Higher implied volatilities suggest a greater probability of triggering the barrier and knocking out the option. The reverse is true of the reverse knockin option. It will still be cheaper than the plain vanilla option but not by very much. The higher the implied volatility, the less of a difference there will be in price between the reverse knockin option and the corresponding plain vanilla option. If we own a reverse knock-out option and a reverse knock-in option with the same maturity, strike and trigger, holding the combined position is equivalent to owning the corresponding plain vanilla option.
Managing reverse barrier options can be a difficult proposition, especially if as it gets close to maturity spot trades near the barrier. A double barrier option is like a more complicated version of a reverse barrier option. Asian options contrary to what one might think on the face of it, the term Asian option refers to options whose payoff is contingent upon the path that spot takes over the lifetime of the option. With our previous examples of cash positions and plain vanilla positions, the payoff of these structures followed a "ramp-style" payoff. That is to say, their payoff was determined by the location of spot at expiry with respect to the strike. If the option is in-the-money, take the difference and multiply it by the notional amount to determine its final value. Here, the payoff depends on the path that spot took over the life of the option.
The payoff of average rate options is calculated by taking the difference between the average for a pre-set index over the life of the option and the strike price and then multiplying this difference by the notional amount. Because an average of a spot price is less volatile than a spot price, average rate options are naturally cheaper than the corresponding plain vanilla options. The payoff of lookback options depends on the best rate that spot traded over the life of the option.
A lookback call gives the owner the right to buy the underlying at expiry at a strike price equal to the lowest price that spot traded over the life of the option. A lookback put gives the owner the right to sell the underlying at expiry at a strike price equal to the highest price that spot traded over the life of the option.
Lookbacks are expensive. Anything that gives you the right to pick the top or the bottom is going to be costly. As a general rule of thumb, some people like to think that lookback prices are in the ballpark if they are roughly twice the price of an at-the-money straddle.
Compound Options
A compound option is an option-on-an-option. It could be a
call-on-a-call giving the owner the right to buy in 1 month's time a 6 month
1.55 US dollar call/Canadian dollar put expiring 7 months from today (or 6
months from the expiry of the compound). The strike price on the compound is
the premium that we would pay in 1 month's time if we exercised the compound
for the option expiring 6 months from that point in time. It could be a
put-on-a-call giving the owner the right to sell in 1 month's time a 6 month
1.55 US dollar call/Canadian dollar put expiring 7 months from today. These types of products are often used by corporations to hedge the foreign exchange risk involved with overseas acquisitions when the success of the acquisition itself is uncertain. Why buy a vanilla hedge or enter into a forward contract until you are sure that you will be buying the foreign company? Sophisticated speculators use compound options to speculate on the volatility of volatility.
Structured Notes:
Structured notes are financial products that appear to be
fixed income instruments, but contain embedded options and do not necessarily
reflect the risk of the issuing credit. These options may be 'plain vanilla' or
they may be highly leveraged exotic options. Due to the fact that each one is
unique, the risks inherent in any one structured note may not be obvious.
Plain vanilla structures include callable, puttable, retractable and extendible bonds. These types of structures are fairly common and most investors do not consider them to be structured notes in the sense of derivative exposure.
Structured notes may be used prudently to mitigate the risks to a portfolio of a systemic shock. An example would be to insulate against the effect on the Canadian dollar of a win in a referendum on sovereignty by Quebec Separatists. A structured note could be purcahsed with an embedded Canadian dollar put versus the US dollar. It would be prudent to hedge the currency risk of this event with a structured note along these lines. The premium would be considered insurance, as opposed to speculation.
Structured notes may also be used by investors to expose their portfolios to asset classes or markets in which they can not directly invest due to investment mandates and regulatory restrictions. Due to the fact that the note looks, and smells like a bond, with a credit exposure that makes it appear a solid credit, many investors utilize them to get involved with asset classes and markets outside of their general scope of business.
For example, let's say that Uncle Pipeline issues a structured product, the FinPipe 16.50% Six-Month Note. The investor takes the credit risk of a major financial institution (the stalwart Financial Pipeline!), giving the note a AA(H) credit rating. The investor actually owns a leveraged exposure to the equity of a TSE 300 basket of stocks.
The concept underlying the note is that in a time of market uncertainty the investor may realize a cash benefit from the high premiums for options on individual stocks or a basket of stocks. The payoff is either 16.50%, or common stock if the stock is at or below a certain level. If, however, the market rallies, the coupon payoff decreases significantly.
Many of these notes can cause the investor to lose part or their entire principal. Many investors are not aware of the inherent risks when buying a structured product. Structured notes have grown in popularity as investors find it increasingly difficult to utilize derivatives overtly in their portfolios. As with any product with derivative exposure, the investor must understand the costs, cash flows and risks inherent in the product before making any purchase decision.
Hedging Swaps:
Dealers at commercial banks do most of the market making
that is done in the interest rate swap and currency swap markets. In addition
to making markets to their customers, these traders will also make prices to
other financial institutions in the wholesale or interbank market, often in
transactions facilitated by interbank brokers. In any given day, the dealer at
the bank may engage in several transactions or several dozen transactions, all
of which are added to his general position. The combination of all of the
different swaps and bond trades and futures trades that the dealer has
conducted constitutes a portfolio.
While it may be easier for us to understand intuitively the
way in which the dealer manages the risk of an individual swap transaction, in
practice this is prohibitively difficult and it does not take advantage of the
natural hedges within the portfolio. Therefore, the swaps dealer will manage
the risks of his position using portfolio management techniques that are
similar to but more sophisticated than the portfolio management techniques used
for a simple cash position in fixed income or equities.In portfolio hedging, the dealer's objective is to construct a portfolio of hedges using swaps, forward rate agreements (FRAs), futures and bonds the changes in value of which offsets the change in value of the underlying swap portfolio for a given set of fluctuations in interest rates, currency rates or basis between the futures and the bonds.
Identifying the risk of the swaps portfolio
The first necessary step in hedging the swaps portfolio is to measure the risk of the swaps portfolio. Namely, the dealer must answer a series of questions. How much will the portfolio lose on a mark-to-market basis if interest rates move up in a parallel fashion (i.e. all interest rates increase by the same amount) by 50 basis points? How much will the portfolio lose on a mark-to-market basis if interest rates fall in a parallel fashion by 50 basis points? How much will the portfolio lose if the spread between the 30-year government bond and the 2-year government note increases by 25 basis points? How will the position's sensitivity to interest rates change if the level of interest rates change?
After reading the earlier articles on "Measuring Risk" and "An Introduction to the Hedging Greeks", the reader will recognize that the greeks are one useful way for measuring these kinds of sensitivities.
One way of looking at the delta is just the fixed income instrument with a term to maturity equal to the average maturity for the interval in question that is as sensitive in profit and loss terms to small changes in the interest rate for that bucket as the swaps portfolio is for that bucket.
Similarly, the gamma is an expression of the changes in the position size (i.e. the changes in the delta) for changes in the level of interest rates.
Vega is the sensitivity of the portfolio to changes in implied volatilities for at-the-money options associated with the maturity bucket in question. This may be important, for example, if the portfolio contains swaptions.
In categorizing the risk of the swaps portfolio, the dealer must look at different types of yield curve risk including parallel shifts in the yield curve, non-parallel shifts in the yield curve and changes in swap spreads. Sophisticated dealers may incorporate some assumptions about the correlation between swap spreads and interest rates in doing their scenario analysis. It may be reasonable to believe that swap spreads will widen out if interest rates back up because of degrading credit conditions, for example.
The dealer will then take this analysis of the behavioural characteristics of the swap portfolio and he will construct a hedging portfolio using one or more financial instruments in order to offset those aspects of the risk that he is unhappy carrying. Note that the dealer will not close out all of the aspects of the risk.
Why will the dealer only partially hedge the swaps portfolio?
Hedging costs money. The main benefit of hedging activity is to reduce the risk of the portfolio. This benefit must be compared to the hedging cost. If the marginal benefit of reducing the risk with an individual transaction is less than its marginal cost, it is not worthwhile to hedge that risk.
Another reason for not completely hedging the swaps portfolio is the fact that the dealer may carry a proprietary position in one or more aspects of the risk. If, for example, he thinks that interest rates are going to fall in the 2-year to 3-year bucket, he may be happy to continue received fixed interest payments for that period. If he is correct, he will make money on a mark-to-market basis that he can realize by hedging the position at a preferable level.
Floating rate cash flow management
One of the more difficult aspects of managing a swap portfolio is managing the short-term cash flows or the floating rate cash flows. There are two problems that confront the dealer.
First, there may be mismatches in the timing of short-term cash flows.
Consider a hedge that was entered into two years ago to hedge a two year fixed-floating plain vanilla interest rate swap where the hedge transaction took place a week after the initial customer transaction. Unless the dealer matched the dates precisely at the time he conducted the hedge transaction, there will be a one-week mismatch of flows. Matching the dates may have cost extra money in terms of the market prices at the time of transaction making it too expensive to match the timing of the cash flows. Some people might argue that one week is not very much of a difference. That is no way to run a business. To paraphrase an old saying, ten grand here and one hundred grand there and pretty soon you're talking about some real money.
Second, there may be mismatches in the type of index used to hedge.
Consider a swap in which the floating rate index is the 3-month US Bankers' Acceptance rate. If the best swap available at the time is the 3-month US LIBOR (London Interbank Offered Rate for US dollars), then there is an index mismatch risk. If the correlation between these two indices changes (and correlation between financial indices is rarely stable), then the swap portfolio is exposed to refunding risk.
One way for the commercial bank to hedge its floating rate cash flows is to establish a separate book dedicated to hedging such risks, one which participates actively in the futures markets such as the IMM Eurodollar market and one which takes aggressive positions in short-term interest rates.
An alternative might be to pay the hedging costs necessary for closing out the mismatches. This can get expensive. With the increased commoditization of global derivatives markets, dealers are losing much of their pricing edge, a phenomenon that makes paying for outside hedging more difficult.
By giving an appreciation for the way swaps dealers manage their combined portfolio risk, this article has identified some of the key types of risk in interest rate swaps and interest rate products, generally.
Derivatives Concepts A-Z:
This paper presents a glossary of derivatives-related terminology that will hopefully make the other chapters easier to understand. It is not an exhaustive list. We will be updated from time to time. One of the characteristics of new financial products is the proliferation of different terms used to describe the same instrument, as each financial institution tries to brand its product name onto the financial community's awareness.
A
Actuals (see also Cash; Physicals; Underlying)
Financial instruments that exist in one of the four main
asset classes: interest rates, foreign exchange, equities or commodities.
Typically, derivatives are used to hedge actual exposure or to take positions
in actual markets.
All or Nothings (see also Binary; Digital)
An option whose payout is fixed at the inception of the
option contract and for which the payout is only made if the strike price is
in-the-money at expiry. If the strike price is out-of-the-money at expiry,
there is no payout made to the option holder.
American Style Option
An option that can be exercised at any time from inception
as opposed to a European Style option which can only be exercised at expiry.
Early exercise of American options may be warranted by arbitrage. European
Style option contracts can be closed out early, mimicking the early exercise
property of American style options in most cases.
Accreting Swap (see also Interest Rate Swap)
An exchange of interest rate payments at regular intervals
based upon pre-set indices and notional amounts in which the notional amounts
decrease over time.
Arbitrage (see also Correlation)
The act of taking advantage of differences in price between
markets. For example, if a stock is quoted on two different equity markets,
there is the possibility of arbitrage if the quoted price (adjusted for
institutional idiosyncrasies) in one market differs from the quoted price in
the other. The term has been extended to refer to speculators who take
positions on the correlation between two different types of instrument,
assuming stability to the correlation patterns. Many funds have discovered that
correlation is not as stable as it is assumed to be.
Asset-Liability Management
Closing out exposure to fluctuations in interest rates by
matching the timing of cashflows associated with assets and liabilities. This
is a technique commonly used by financial institutions and large corporations.
At-the-Market (see also Market Order)
A type of financial transaction in which the order to buy
or sell is executed at the current prevailing market price.
At-the-Money Spot
An option whose strike price is equal to the current,
prevailing price in the underlying cash spot market.
At-the-Money Forward
An option whose strike price is equal to the current,
prevailing price in the underlying forward market.
Average Rate Options
An option whose payout at expiry is determined by the
difference between its strike and a calculated average market rate where the
period, frequency and source of observation for the calculation of the average
market rate are specified at the inception of the contract. These options are
cash settled, typically.
Average Strike Options
An option whose payout at expiry is determined by the
difference between the prevailing cash spot rate at expiry and its strike,
deemed to be equal to a calculated average market rate where the period,
frequency and source of observation for the calculation of the average market
rate are specified at the inception of the contract. These options are cash
settled, typically.
B
Backwardation (see also Contango)
A term often used in commodities or futures markets to
refer to markets where shorter-dated contracts trade at a higher price than
longer-dated contracts. Plotting the prices of contracts against time, with
time on the x-axis, shows the commodity price curve as sloping downwards as
time increases.
Barrier Options (see also Knock-In Options,
Knock-Out Options)
An option contract for which the maturity, strike price and
underlying are specified at inception in addition to a trigger price. The
trigger price determines whether or not the option actually exists. In the case
of a knock-in option, the barrier option does not exist until the trigger is
touched. For a knock-out option, the option exists until the trigger is
touched.
Basis (see also Index)
The difference in price or yield between two different
indices.
Benchmarking
A benchmark is a reference point. Benchmarking in financial
risk management refers to the practice of comparing the performance of an individual
instrument, a portfolio or an approach to risk management to a pre-determined
alternative approach.
Black-Scholes
A closed-form solution (i.e. an equation) for valuing plain
vanilla options developed by Fischer Black and Myron Scholes in 1973 for which
they shared the Nobel Prize in Economics.
C
Call Option
A call option is a financial contract giving the owner the
right but not the obligation to buy a pre-set amount of the underlying
financial instrument at a pre-set price with a pre-set maturity date.
Cap
A cap is a financial contract giving the owner the right
but not the obligation to borrow a pre-set amount of money at a pre-set
interest rate with a pre-set maturity date.
Cash Settlement
Some derivatives contracts are settled at maturity (or
before maturity at closeout) by an exchange of cash from the party who is
out-of-the-money to the party who is in-the-money.
Chooser Option
An option that gives the buyer the right at the choice date
(before the option's expiry) to choose if the option is to be a call or a put.
Collar (see also Range Forward; Risk Reversal)
A combination of options in which the holder of the
contract has bought one out-of-the money option call (or put) and sold one (or
more) out-of-the-money puts (or calls). Doing this locks in the minimum and
maximum rates that the collar owner will use to transact in the underlying at
expiry.
Commodity Swap
A contract in which counterparties agree to exchange
payments related to indices, at least one of which (and possibly both of which)
is a commodity index.
Contango (see also Backwardation)
A term often used in commodities or futures markets to
refer to markets where shorter-dated contracts trade at a lower price than
longer-dated contracts. Plotting the prices of contracts against time, with
time on the x-axis, shows the commodity price curve as sloping upwards as time
increases.
Convexity
A financial instrument is said to be convex (or to possess
convexity) if the financial instrument's price increases (decreases) faster
(slower) than corresponding changes in the underlying price.
Correlation (see also Arbitrage)
Correlation is a statistical measure describing the extent
to which prices on different instruments move together over time. Correlation
can be positive or negative. Instruments that move together in the same
direction to the same extent have highly positive correlations. Instruments
that move together in opposite direction to the same extent have highly
negative correlations. Correlation between instruments is not stable.
Covered Call Option Writing
A technique used by investors to help fund their underlying
positions, typically used in the equity markets. An individual who sells a call
is said to "write" the call. If this individual sells a call on a
notional amount of the underlying that he has in his inventory, then the
written call is said to be "covered" (by his inventory of the
underlying). If the investor does not have the underlying in inventory, the
investor has sold the call "naked".
Credit Risk
Credit risk is the risk of loss from a counterparty in
default or from a pejorative change in the credit status of a counterparty that
causes the value of their obligations to decrease.
Currency Swap (see also Interest Rate Swap)
An exchange of interest rate payments in different
currencies on a pre-set notional amount and in reference to pre-determined
interest rate indices in which the notional amounts are exchanged at inception
of the contract and then re-exchanged at the termination of the contract at
pre-set exchange rates.
D
Delta
The sensitivity of the change in the financial instrument's
price to changes in the price of the underlying cash index.
Documentation Risk
The risk of loss due to an inadequacy or other unforeseen
aspect of the legal documentation behind the financial contract.
Duration
A weighted average of the cash flows for a fixed income
instrument, expressed in terms of time.
E
Embedded Derivatives (see also Structured Notes)
Derivative contracts that exist as part of securities.
Equity Swap (see also Interest Rate Swap)
A contract in which counterparties agree to exchange
payments related to indices, at least one of which (and possibly both of which)
is an equity index.
European Style Option
An option that can be exercised only at expiry as opposed
to an American Style option that can be exercised at any time from inception of
the contract. European Style option contracts can be closed out early,
mimicking the early exercise property of American style options in most cases.
Exchange Traded Contracts
Financial instruments listed on exchanges such as the
Chicago Board of Trade.
Exercise Price (see also Strike Price)
The exercise price is the price at which a call's (put's)
buyer can buy (or sell) the underlying instrument.
Exotic Derivatives
Any derivative contract that is not a plain vanilla
contract. Examples include barrier options, average rate and average strike
options, lookback options, chooser options, etc.
F
Floor (see also Cap; Collar)
A floor is a financial contract giving the owner the right
but not the obligation to lend a pre-set amount of money at a pre-set interest
rate with a pre-set maturity date.
Forward Contracts
An over-the-counter obligation to buy or sell a financial
instrument or to make a payment at some point in the future, the details of
which were settled privately between the two counterparties. Forward contracts
generally are arranged to have zero mark-to-market value at inception, although
they may be off-market. Examples include forward foreign exchange contracts in
which one party is obligated to buy foreign exchange from another party at a
fixed rate for delivery on a pre-set date. Off-market forward contracts are
used often in structured combinations, with the value on the forward contract
offsetting the value of the other instrument(s).
Forward or Delayed Start Swap (see also Interest
Rate Swap)
Any swap contract with a start that is later than the
standard terms. This means that calculation of the cash flows does not begin
straightaway but at some pre-determined start date.
Forward Rate Agreements (FRAs) (see also Interest
Rate Swap)
A forward rate agreement is a cash-settled obligation on
interest rates for a pre-set period on a pre-set interest rate index with a
forward start date. A 3x6 FRA on US dollar LIBOR (the London Interbank Offered
Rate) is a contract between two parties obliging one to pay the other the
difference between the FRA rate and the actual LIBOR rate observed for that
period. An Interest Rate Swap is a strip of FRAs.
Futures Contracts
An exchange-traded obligation to buy or sell a financial
instrument or to make a payment at one of the exchange's fixed delivery dates,
the details of which are transparent publicly on the trading floor and for
which contract settlement takes place through the exchange's clearinghouse.
G
Gamma (see also Delta)
Gamma (or convexity) is the degree of curvature in the
financial contract's price curve with respect to its underlying price. It is
the rate of change of the delta with respect to changes in the underlying
price. Positive gamma is favourable. Negative gamma is damaging in a
sufficiently volatile market. The price of having positive gamma (or owning
gamma) is time decay. Only instruments with time value have gamma.
H
Hedge
A transaction that offsets an exposure to fluctuations in
financial prices of some other contract or business risk. It may consist of
cash instruments or derivatives.
Historical Volatility
A measure of the actual volatility (a statistical measure
of dispersion) observed in the marketplace.
Hybrid Security
Any security that includes more than one component. For
example, a hybrid security might be a fixed income note that includes a foreign
exchange option or a commodity price option.
I
Implied Volatility
Option pricing models rely upon an assumption of future
volatility as well as the spot price, interest rates, the expiry date, the
delivery date, the strike, etc. If we are given simultaneously all of the
parameters necessary for determining the option price except for volatility and
the option price in the marketplace, we can back out mathematically the
volatility corresponding to that price and those parameters. This is the
implied volatility.
In-The-Money Spot (see also Intrinsic Value;
At-The-Money; Out-of-The-Money)
An option with positive intrinsic value with respect to the
prevailing market spot rate. If the option were to mature immediately, the
option holder would exercise it in order to capture its economic value. For a
call price to have intrinsic value, the strike must be less than the spot
price. For a put price to have intrinsic value, the strike must be greater than
the spot price.
In-The-Money-Forward (see also Intrinsic Value;
At-The-Money; Out-of-The-Money)
An option with positive intrinsic value with respect to the
prevailing market forward rate. If the option were to mature immediately, the
option holder would exercise it in order to capture its economic value. For a
call price to have intrinsic value, the strike must be less than the spot
price. For a put price to have intrinsic value, the strike must be greater than
the spot price.
Index-Amortizing Swaps (see also Interest Rate
Swaps; Accreting Swaps)
An interest rate swap in which the notional amount for the
purposes of calculating cash flows decreases over the life of the contract in a
pre-specified manner.
Interest Rate Swap (see also Forward Rate
Agreements; Index-Amortizing Swaps; Accreting Swaps)
An exchange of cash flows based upon different interest
rate indices denominated in the same currency on a pre-set notional amount with
a pre-determined schedule of payments and calculations. Usually, one
counterparty will received fixed flows in exchange for making floating
payments.
International Swaps Dealers' Association (ISDA) Agreements
(see also Legal Risk)
In order to minimize the legal risks of transacting with
one another, counterparties will establish master legal agreements and sidebar
product schedules to govern formally all derivatives transactions into which
they may enter with one another.
Intrinsic Value
The economic value of a financial contract, as distinct
from the contract's time value. One way to think of the intrinsic value of the
financial contract is to calculate its value if it were a forward contract with
the same delivery date. If the contract is an option, its intrinsic value
cannot be less than zero.
K
Knock-in Option (see also Knock-Out Option; Trigger
Price)
An option the existence of which is conditional upon a
pre-set trigger price trading before the option's designated maturity. If the
trigger is not touched before maturity, then the option is deemed not to exist.
Knock-out Option
An option the existence of which is conditional upon a
pre-set trigger price trading before the option's designated maturity. The
option is deemed to exist unless the trigger price is touched before maturity.
L
Legal Risk (see also International Swap Dealers'
Association Agreements)
The general potential for loss due to the legal and
regulatory interpretation of contracts relating to financial market
transactions.
LIBOR London
The rate of interest paid on offshore funds in the
Eurodollar markets.
Liquidity Risk
The risk that a financial market entity will not be able to
find a price (or a price within a reasonable tolerance in terms of the
deviation from prevailing or expected prices) for one or more of its financial
contracts in the secondary market. Consider the case of a counterparty who buys
a complex option on European interest rates. He is exposed to liquidity risk
because of the possibility that he cannot find anyone to make him a price in
the secondary market and because of the possibility that the price he obtains
is very much against him and the theoretical price for the product.
Look-Back Options
An option which gives the owner the right to buy (sell) at
the lowest (highest) price that traded in the underlying from the inception of
the contract to its maturity, i.e. the most favourable price that traded over
the lifetime of the contract.
M
Margin
A credit-enhancement provision to master agreements and
individual transactions in which one counterparty agrees to post a deposit of
cash or other liquid financial instruments with the entity selling it a
financial instrument that places some obligation on the entity posting the
margin.
Mark to Market Accounting
A method of accounting most suited for financial
instruments in which contracts are revalued at regular intervals using
prevailing market prices. This is known as taking a "snapshot" of the
market.
Market Risk
The exposure to potential loss from fluctuations in market
prices (as opposed to changes in credit status).
Market-Maker
A participant in the financial markets who guarantees to
make simultaneously a bid and an offer for a financial contract with a pre-set
bid/offer spread (or a schedule of spreads corresponding to different market
conditions) up to a pre-determined maximum contract amount..
N
Naked Option Writing
The act of selling options without having any offsetting
exposure in the underlying cash instrument.
Netting
When there are cash flows in two directions between two
counterparties, they can be consolidated into one net payment from one
counterparty to the other thereby reducing the settlement risk involved.
O
OCC
The Office of the Comptroller of the Currency (US).
OSFI
Office of the Superintendent of Financial Institutions (
Open Interest
Exchanges are required to post the number of outstanding
long and short positions in their listed contracts. This constitutes the open
interest in each contract.
Operational Risk
The potential for loss attributable to procedural errors or
failures in internal control.
Option
The right but not the obligation to buy (sell) some
underlying cash instrument at a pre-determined rate on a pre-determined
expiration date in a pre-set notional amount.
Out-of-The-Money Spot (see also At-The-Money;
In-The-Money)
An option with no intrinsic value with respect to the
prevailing market spot rate. If the option were to mature immediately, the
option holder would let it expire. For a call price to have intrinsic value,
the strike must be less than the spot price. For a put price to have intrinsic
value, the strike must be greater than the spot price.
Out-of-The-Money-Forward (see also At-The-Money;
In-The-Money)
An option with no intrinsic value with respect to the
prevailing market forward rate. If the option were to mature immediately, the
option holder would let it expire. For a call price to have intrinsic value, the
strike must be less than the spot price. For a put price to have intrinsic
value, the strike must be greater than the spot price.
Over-the-Counter
Any transaction that takes place between two counterparties
and does not involve an exchange is said to be an over-the-counter transaction.
P
Path-Dependent Options (see also Knock-In Options;
Knock-Out Options; Average Rate Options; Average Strike Options; Lookback
Options)
Any option whose value depends on the path taken by the
underlying cash instrument.
Potential Exposure
An assessment of the future positive intrinsic value in all
of the contracts outstanding with an individual counterparty who may choose (or
may be unable) to make their obligated payments.
Premium
The cost associated with a derivative contract, referring
to the combination of intrinsic value and time value. It usually applies to
options contracts. However, it also applies to off-market forward contracts.
Put Option (see also Call Option)
A put option is a financial contract giving the owner the
right but not the obligation to sell a pre-set amount of the underlying
financial instrument at a pre-set price with a pre-set maturity date.
Put-Call Parity Theorem
A long position in a put combined with a long position in
the underlying forward instrument, both of which have the same delivery date
has the same behavioral properties as a long position in a call for the same
delivery date. This can be varied for short positions, etc.
Q
Quanto Option
An option the payout for which is denominated in an index
other than the underlying cash instrument.
R
Regulatory Risk
The potential for loss stemming from changes in the
regulatory environment pertaining to derivatives and financial contracts, the
utility of these instruments for different counterparties, etc.
Rho
The sensitivity of a financial contract's value to small
changes in interest rates.
RiskMetrics (see also Value-at-Risk)
A parametric methodology for calculating Value-at-Risk
using data conditioned by JP Morgan's spinoff company RiskMetrics that is most
useful for assessing portfolios with linear risks.
S
Settlement Risk
The risk of non-payment of an obligation by a counterparty
to a transaction, exacerbated by mismatches in payment timings.
Speculation
Taking positions in financial instruments without having an
underlying exposure that offsets the positions taken.
Spot
The price in the cash market for delivery using the
standard market convention. In the foreign exchange market, spot is delivered
for value two days from the transaction date or for the next day in the case of
the Canadian dollar exchanged against the US dollar.
Spread
The difference in price or yield between two assets that
differ by type of financial instrument, maturity, strike or some other factor.
A credit spread is the difference in yield between a corporate bond and the
corresponding government bond. A yield curve spread is the spread between two
government bonds of differing maturity.
Standard Deviation (see also Volatility; Implied
Volatility)
In finance, a statistical measure of dispersion of a time
series around its mean; the expected value of the difference between the time
series and its mean; the square root of the variance of the time series.
Stress Testing
The act of simulating different financial market conditions
for their potential effects on a portfolio of financial instruments.
Strike Price
The price at which the holder of a derivative contract
exercises his right if it is economic to do so at the appropriate point in time
as delineated in the financial product's contract.
Structured Notes
Fixed income instruments with embedded derivative products.
Swap Spread (see also Plain Vanilla Interest Rate
Swap)
The difference between the swap yield curve and the
government yield curve for a particular maturity, referring to the market
prices for the fixed rate in a plain vanilla interest rate swap.
Swaptions (see also Plain Vanilla Interest Rate
Swap)
Options on swaps.
T
Theta
The sensitivity of a derivative product's value to changes
in the date, all other factors staying the same.
Time Value (see also Intrinsic Value; Premium)
For a derivative contract with a non-linear value
structure, time value is the difference between the intrinsic value and the
premium.
V
Value at Risk or VaR (see also RiskMetrics)
The caculated value of the maximum expected loss for a
given portfolio over a defined time horizon (typically one day) and for a
pre-set statistical confidence interval, under normal market conditions
Value of a Basis Point
The change in the value of a financial instrument
attributable to a change in the relevant interest rate by 1 basis point (i.e.
1/100 of 1%).
Vega
The sensitivity of a derivative product's value to changes
in implied volatility, all other factors staying the same.
Volatility (see also Standard Deviation; Implied
Volatility)
In finance, a statistical measure of dispersion of a time
series around its mean; the expected value of the difference between the time
series and its mean; the square root of the variance of the time series.
Y
Yield Curve
For a particular series of fixed income instruments such as
government bonds, the graph of the yields to maturity of the series plotted by
maturity.
Yield Curve Risk
The potential for loss due to shifts in the position or the
shape of the yield curve.
Z
Zero Coupon Instruments
Fixed income instruments that do not pay a coupon but only
pay principal at maturity; trade at a discount to 100% of principal before
maturity with the difference being the interest accrued.
Zero Coupon Yield Curve
For zero coupon bonds, the graph of the yields to maturity of the series plotted by maturity.
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