Glossary

Valueatrisk
Formally, the probabilistic bound of market losses over a given period of time (known as the holding period) expressed in terms of a specified degree of certainty (the confidence interval). Put more simply, the valueatrisk (VaR) is the worstcase loss expected over the holding period within the probability set out by the confidence interval. Larger losses are possible, but with a low probability. For instance, a portfolio whose VaR is $20 million over a oneday holding period, with a 95% confidence interval, would have only a 5% chance of suffering an overnight loss greater than $20 million. Calculation of VaR entails modelling the possible market moves over the holding period, incorporating correlations among market factors, calculating the impact of such potential market moves on portfolio positions, and combining the results to examine risk at different levels of aggregation. The three main approaches to this analysis are historical simulation, the analytical approach using a correlation matrix or empirical (Monte Carlo) simulation. Major trading houses expend considerable energies on their VaR methodologies and have lobbied regulators to recognise their efforts, with some success.

Vanilla option
Also known as a plain vanilla option. A vanilla option is a standard call or put option in its most basic form.

Vanna
The vega of an option is not constant. Vega changes as spot changes and as volatility changes. The vanna of an option measures the change in vega for a change in the underlying spot. As spot moves deeper outofthemoney for a vanilla option the vega is lower. If spot and volatility movements are positively correlated the holder of an option with positive vanna will be expected to profit from this correlation.

Variable notional option/swap
An option or swap where the notional value is linked to the underlying asset price or rate. Usually changes in the notional will be directly proportional to changes in the underlying price; ie, they both decrease or increase together. Such derivatives have two main uses. In an equity swap, the fixedrate receiver can opt to receive the return of either a fixed number of stocks, or the number of stocks that could be purchased for a fixed sum. The former case amounts to a variable notional amount for the swap. An example using an option is the case of a firm that sells more exports as exchange rates decline and its products therefore become cheaper abroad. Since it now has greater foreign currency revenue to hedge, it would purchase a variable notional currency option for this purpose.

Variance gamma model
A jump model that better captures the characteristics of the volatility smile for shorterdated options than stochastic volatility models.

Variance swap
The cash payout of a variance swap is equal to notional multiplied by the difference between the realised variance of the underlying index over the life of the swap and the strike variance.

Vasicek model
An interest rate model that incorporates mean reversion and a constant volatility for the short interest rate. It is a onefactor model from which discount bond prices and options on those bonds can be deduced. All have closedform solutions.

Vega
Measures the change in an option's price caused by changes in volatility. Vega is at its highest when an option is atthemoney. It decreases the more the market and strike prices diverge. Options closer to expiration have a lower vega than those with more time to run. Positions with positive vega will generally have positive gamma. To be long vega (to have a positive vega) is achieved by purchasing either put or call options. Positions that are long vega benefit from increases in implied volatility but also from actual volatility if the option is being delta hedged. They will also lose from reductions in volatility. Spread options can be an exception: a reduction in the volatility of one of the assets may actually increase the price of the option because the correlation between the two assets decreases. Vega is sometimes known as kappa or tau.

Vertical spread
Any option strategy that relies on the difference in premium between two options on the same underlying with the same maturity, but different strike prices. Thus put spreads and call spreads would both be vertical spreads. Volatility A measure of the variability (but not the direction) of the price of the underlying instrument. It is defined as the annualised standard deviation of the natural log of the ratio of two successive prices. Historical volatility is a measure of the standard deviation of the underlying instrument over a past period. Implied volatility is the volatility implied in the price of an option. All things being equal, higher volatility will lead to higher vanilla option prices. In traditional BlackScholes models, volatility is assumed to be constant over the life of an option. Since traders mainly trade volatility, this is clearly unrealistic. New techniques have been developed to cope with volatility's variability. The best known are stochastic volatility, Arch and Garch.

Volatility skew
The difference in implied volatility between outofthemoney puts and calls. In most equity option markets outofthe money calls have lower implied volatility than outofthemoney puts. This is mostly ascribed to the greater supply of volatility above, rather than below, the money since fund managers are happy to write calls and not so happy to write puts. Volatility skews can be very pronounced in the currency markets although whether puts or calls are favoured depends on market sentiment and demand and supply.

Volatility smile
A graph of the implied volatility of an option versus its strike (for a given tenor) typically describes a smileshaped curve  hence the term "volatility smile"This can be attributed to the belief that the underlying distribution is leptokurtic, since this tends to increase the value of outofthemoney options.

Volatility swap
The cash payout of a volatility swap is equal to notional multiplied by the difference between the realised volatility of the underlying index over the life of the swap and the strike volatility.

Volatility term structure
The term structure of volatility is the curve depicting the differing implied volatilities of options with differing maturities. Such a curve arises partly because implied volatility in short options changes much faster than for longer options. However, the volatility term structure also arises because of assumed mean reversion of volatility. The effect of changes in volatility on the option price is less the shorter the option. Most marketmakers take advantage of differing volatilities to hedge their books or to trade perceived anomalies in volatility. Such strategies have to be weighted because of the differing vega effects.

Volatility trading
A strategy based on a view that future volatility in the underlying will be more or less than the implied volatility in the option price. Option marketmakers are volatility traders. The most common way to buy/sell volatility is to buy/sell options, hedging the directional risk with the underlying. Volatility buyers make money if the underlying is more volatile than the implied volatility predicted. Sellers of volatility benefit if the opposite holds. Other methods of buying/selling volatility are to buy/sell combinations of options, the most usual being to buy/sell straddles or strangles. Other strategies take advantage of the difference between implied volatilities of differing maturity options, not between implied and actual volatility. For example, if implied volatility in shortterm options is high and in longer options low, a trader can sell shortterm options and buy longer ones.

Vomma
The vega of an option is not constant. Vega changes as spot changes and as volatility changes. The vomma of an option is defined as the change in vega for a change in volatility. Vomma measures the convexity of an option price with respect to volatility. Vega is to vomma (volatility gamma) as delta is to gamma for spot movements. Holders of options with a high vomma benefit from volatility of volatility.