Volatility surface management - Part 2

Volatility surface is a 3d object with option volatilities, option strikes and option expiries on the 3 axes.
The volatility at any point on the surface is used in pricing an option with the corresponding strike and expiry. Rather than have a simple grid of these points, a more intutive and flexible approach is to manage the grid by using parameteric surfaces. i.e.The volatiliy surface is represented by some graphical parameters(specifications) which will plot the values.  This way, its easier to tweak just one meaningful parameter and it will reflect the new values for a set of strikes or expiries. Eg. If 'Skew' is a parameter, then increasing this value for a particular volatiliy curve(Vol vs Strikes for a particular expiry) will increment the vol values for all the ITM call options.

A number of volatility functions can be defined, each of them behaving differently in varied market scenarios.  Few of the criterion are

• Using parameters that can be easily conceptualised into surface dynamics.  Eg. Skew, Kurtosis, Smile etc
• Each parameter can be further defined to have a specific economic meaning Eg The long term skew might be the debt to asset ratio of the corporate [ofcourse you don't make up such things, you mathematically prove them..:)]
• Orthogonality - how change in one parameter affects the other. 

At the end of the day, it boils down to using the model that makes most sense to the trader.  Every trader(or desk) will have his/her own philosophy of the market.  The vol model that helps him visualise the market most intutively, helps him price his options the best.

In liquid markets(like Equities), you have the advantage of using the market bids and asks to formulate your implied volatility curve.  This way you always follow the market and quote your prices within the market bid-ask spread.  Today all insitutions components that automatically fit the volatility surface to the market bids and asks. Easier said than done, as this will need to filter out all the noise in the market and keep our assumptions data up-to-date. Not a trivial thing, considering how dynamic the enviroment can be with corporate actions, acquisitions, algo engine quotes etc.

A few more advanced features into this functionality can be

• to avoid market volatility moves due to your own firm market quotes
• analyse the tick by tick vol data to identify arbitrage opportunities and trade against them
  

Assuming your volatility surfaces are well managed and are accurate enough, another angle to its use can be in the the risk side of things. The data can run through stressing engines, which can churn our VAR numbers.