Inside Volatility Filtering: Secrets of the Skew, 2nd Edition

Chapter 2The Inference Problem

In applying option pricing models, one always encounters the difficulty that the spot volatility and the structural parameters are unobservable.

—Gurdip Bakshi, Charles Cao & Zhiwu Chen

Introduction

Regardless of which specific model we are using, it seems that we cannot avoid the issue of calibration. There are two possible sets of data that we can use for estimating the model parameters: options prices and historic stock prices.¹

Using options prices via a least square estimator (LSE) has the obvious advantage of guaranteeing that we will match the used option market prices within a certain tolerance. However, the availability of option data is typically limited, which would force us to use interpolation and extrapolation methods. These data manipulation approaches might deteriorate the quality and the smoothness of our inputs. More importantly, matching a set of plain-vanilla option prices does not necessarily mean that we would obtain the correct price for another more exotic derivative.

Using stock prices has the disadvantage of offering no guarantee of matching option prices. However supposing that the model is right, we do have a great quantity of data-input for calibration, which is a powerful argument in favor of this approach.

It is important however to note that in using historic stock prices we are assuming that our time-step is small ...