Glossary

Deferred payout option
A deferred payout option is a variation on Americanstyle options similar to a shout option. The holder of the option may exercise it at any time, for the value taken by the underlying at that time, but the payout is delayed until the expiration date. This term is also applied to certain digital options whose payout is not paid when triggered, but deferred until the final maturity.

Delayed reset swap
Also known as an inarrears swap. A swap in which floating payment is based on the future, rather than present, value of the reference rate. For sixmonth delayed Libor reset swaps, for example, instead of fixing Libor six months and two days before the payment date, the floatingrate borrower delays fixing until two days before payment. Such swaps are popular in a steep yield curve environment, when a fixedrate receiver may think rates will not rise as fast as the yield curve predicts.

Delta
The delta of an option describes its premium's sensitivity to changes in the price of the underlying. In other words, an option's delta will be the amount of the underlying necessary to hedge changes in the option price for small movements in the underlying. The delta of an option changes with changes in the price of the underlying. An atthemoney option will have a delta of close to 50%. It falls for outofthemoney options and increases for inthemoney options, but the change is nonlinear: it changes much faster when the option is closetothemoney. The rate of change of delta is an option's gamma.

Delta hedging
An option is said to be deltahedged if a position has been taken in the underlying in proportion to its delta. For example, if one is short a call option on an underlying with a face value of $1 million and a delta of 25%, a long position of $250,000 in the underlying will leave one deltaneutral with no exposure to small changes in the price of the underlying. Such a hedge is only effective instantaneously, however. Since the delta of an option is itself altered by changes in the price of the underlying, interest rates, the option_and_rsquo;s volatility and its time to expiry, changes in any of these factors will shift the net position away from deltaneutrality. In practice, therefore, a deltahedge must be rebalanced continuously if it is to be effective.

Derivative
A derivative instrument or product is one whose value changes with changes in one or more underlying market variables, such as equity or commodity prices, interest rates or foreign exchange rates. Basic derivatives include: forwards, futures, swaps, options, warrants and convertible bonds. In mathematical models of financial markets, derivatives are known as contingent claims.

Diffusion process
A continuoustime model of the behaviour of a random variable. An example of such a model is Generalised Brownian Motion (GBM), which is often used to model the behaviour of spot rates.

Digital option
Digital options pay a set amount if the underlying asset is above, or sometimes below, a certain level on a specific date. These options have only two possible outcomes: a set payout, or nothing at all. Thus, they are also known as binary or allornothing options.

Digital swap
A swap in which the fixed leg is only paid on each swap settlement date if the underlying has met certain trigger conditions over the period since the previous payment date. Nothing is paid if this is not the case. The premium for such a swap is amortised over the maturity of the swap and an instalment paid at each payment date.

Discrete barrier option
Barrier options where the trigger level is only active for part of the option's lifetime. This includes barrier options where the trigger is only valid on certain fixing dates, as well as cases where the trigger is valid for subintervals of the option's lifetime.

Distribution
The probability distribution of a variable describes the probability of the variable attaining a certain value. Assumptions about the distribution of the underlying are crucial to option models because the distribution determines how likely it is that the option will be exercised. Many models assume the logarithm of the relative return has a normal distribution, which can be described by two parameters. The first is the distribution's mean; the second its standard deviation (equivalent, if annualised, to volatility). In practice, most empirically observed asset distributions depart from normality. This departure can be described in terms of the skew (how much it tilts to one side or the other) and kurtosis, which describes how fat or thin are the tails at either side. Most markets tend to have fat tails (to be leptokurtic)rather than thin tails (platykurtic). This pushes up the price of outofthemoney options.

Double barrier option
This is an option with two barriers; one setting the upper limit of the price of the underlying and one setting the lower limit. If the underlying crosses either of these barriers the option is either activated (knockin) or deactivated (knockout).

Double notouch
A double notouch option pays a set amount as long as one of two specified barrier levels are not broken during the life of the option. This tool is popular for usage in relatively stable markets.

Downside risk
The risk the investor is exposed to if there is a fall in the value of the underlying.

Dual currency swap
Dual currency swaps are currency swaps that incorporate the foreign exchange options necessary to hedge the interest payments back into the principal currency for dual currency bonds.