Sunday, April 8, 2012

#1 usage of a volatility surface

I'd say end-of-day unrealized PnL is the most IMPORTANT usage. An integral part of it is mark-to-market. (However, For liquid option products with numerous "tight" market quotes, I don't know if we really need the vol surface for PnL.)

A more "fundamental" need for vol surface is the valuation of non-liquid volatility contracts, including structured, exotic, tailor-made contracts with optionality features. I prefer the words "contract" or "deal" rather than "instrument", "product", "security" or "asset". Contract means there are at 2 counter-parties. If they really do the deal, at contract termination each will end up with a realized PnL, potentially humongous. The estimate, risk-management and analysis of that realized PnL is often the biggest job in a trading desk.

In Equities and FX, vol surface is often the centerpiece (at least part thereof) of the valuation framework for such "contracts". In a valuation framework, most other factors are simpler compared to the volatility factor.

In a real London structured eq vol desk, such a valuation requires a Monte Carlo simulation which queries one or more vol  surfaces repeatedly. However, i don't think the valuation need to use the parameters (like skew, tail...). The surface is treated as a black box to query.


The vol surface must be constructed by taking into consideration a variety of observed market data. Therefore a good surface is consistent with a diverse variety of market data, including but not limited to
- dividend forecast,
- tax schedule on dividends,
- calendar convention,
- holiday schedules....

But the most important market data is the premium on the liquid instruments, which typically cover the first few years only. Long-dated instruments are much less liquid.

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