Unraveling Volatility Surface Mysteries on Wilmott Forums

Have you ever found yourself lost in a sea of financial formulas on online forums like Wilmott, trying to make sense of volatility surfaces, risk reversals, and butterflies? If so, this blog post is for you.

Volatility Surface Basics

Volatility surfaces are graphical representations of implied volatilities for options with different strike prices and expiration dates. They play a crucial role in options pricing and risk management. Wilmott Forum members often discuss the intricacies of these surfaces, including the behavior of risk reversals and butterflies.

Risk Reversals and Butterflies

Risk reversals measure the difference between implied volatilities for out-of-the-money call and put options with the same expiration date. Butterflies, on the other hand, involve the combination of a bull spread (long call at a lower strike price and short call at a higher strike price) and a bear spread (long put at a higher strike price and short put at a lower strike price) with the same expiration date.

A Volatility Surface Puzzle

A Wilmott Forums user, Satriani, posed a question about whether certain formulas for calculating risk reversals and butterflies also apply to different delta levels. The ensuing discussion involved other members, including Cemil and Mutley, who helped clarify the original question and offered insights into the accuracy of various approximations.

Approximating Volatility Surfaces

Woodsdevil, a senior member, suggested that Satriani's formula is a reasonable first-order approximation but becomes less accurate with larger risk reversals. Unfortunately, Woodsdevil could not point to any specific papers on this topic. The discussion continued with Satriani seeking advice on interpolating implied volatilities for various delta levels when calculating option prices.

Interpolation Techniques and Portfolio Implications

Guclu, another forum member, offered guidance on appropriate interpolation methods that respect non-arbitrage conditions in the delta space. The discussion also touched upon iteratively searching for market deltas (not Black-Scholes deltas) to estimate model volatilities for given strikes.

Practical Insights for Volatility Surface Analysis

When analyzing volatility surfaces, consider these takeaways:

1. Accuracy of approximations: Be aware that first-order approximations may not be accurate for large risk reversals. 2. Interpolation methods: Choose appropriate interpolation techniques that respect non-arbitrage conditions in the delta space. 3. Market deltas: When estimating model volatilities, iteratively search for market deltas (not Black-Scholes deltas) for given strikes.