Pragmatic Volatility Calibration

Sammanfattning

In this work, grid selection in the Andreassen & Huge Algorithm (AHA) for calibrating Local Volatility was examined, providing the body of literature with a more detailed examination of the resilience of AHA to sparse grids. It was found that, if the goal is to calibrate a surface of European call option prices to marked price data, AHA is capable of preserving model accuracy under grids much more sparse than those used in previous research. Additionally, the plausibility of retrieving risk-neural densities (RND) of the underlying asset usng the AHA-derived call-surface was studied, which relies on a result from Breeden & Litzenberger [5]. These experiments, alongside the computations made when inverting call surfaces to Local Volatility surfaces, revealed that numrecal differentiation of AHA-derived call surfaces is unstable. This was shown to be resolvable by selecting denser grids. Grid selection in the AHA algorithm thus depends highly on the goal of the practitioner, as well as their computational resource constraints. Finally, a pricing scheme with quadrature integrals using the RND's and the AHA Local Volatility surface is proposed and evaluated against benchmark prices for the vanilla European call option in the Eurostoxx50 Index, and the digital European call option on the same underlying. The results suggest that this pricing scheme has some ability to accurately price instruments, while more research is neccessary to understand its capability to price a wider range of contracts.