# Three Typical Use Cases of the Implied Volatility Surface

Implied volatility surface describes implied volatility as a function of option strike price and option mature time. They are calibrated from option prices by famous Black Scholes formula. There are three typical use cases of implied volatility: exotic option pricing, option market making, and alpha research. Furthermore, option data is much noisier than stock price so we need data cleaning methods. Because the reason people using it is different, we can see great differences in the volatility surface building methodologies among them.

1. exotic option pricing

Sell-side, investment banks sell exotic options (or structure products) to investors and using stocks or vanilla options to delta hedge their shorting positions. The hedging strategy requires stable or slow-changing vol surface parameters. Also, sell-side will use implied volatility to build local volatility surface and run local volatility Monte Carlo to price exotic options. The instability in implied volatility surface will transfer to bad convergence of Monte Carlo and then great swing of position greeks, which makes hedging much more difficult. Then, sell-side wants to use the “real” bid-ask spread by option market maker, reducing the influence of short term supply and demand changing.

In summary, exotic option pricing using the price discovery of the implied volatility surface. Then stability is preferred than accuracy and fast. They want stability and like to sacrifices prediction ability so they “moving average” the surface. PnL is usually calculated daily so they do not need to calibrate very fast.

2. option market making:

Sell-side and some hedge fund. Fast is the most important requirement of option market making. Optimization in implied volatility requires nonlinear optimization with complex non-arbitrage constrains for hundreds of parameters. For the SVI curve model, there are 5 parameters for each curve and there might be 20 maturities to be considered, then a total of 100 parameters. For the option market making, the speed of calculation/ updating should be compatible with the speed of market updating. They want to use the information of supply and demand to make short term predictions then adjust their quote.

3. alpha research

Hedge funds find patterns in option prices. For example, option open interest, trading volume, and implied vol skew have prediction ability for stock prices, mainly predicting bad news (for example Johnson and So 2011). Deep out the money put can be seen as an alternative as a credit default swap. According to the principle of one price, there should be a strong correlation between CDS price and deep OTM put option price, which can be used for statistical arbitrage (Carr and Wu 2011). The building of the implied volatility surface depends on the signal types and signal frequency. One’s meat is another’s poison, and one’s noise is another’s signal.