Testing of an Arbitrage-free Volatility Surface

Tarr, Grant

Testing of an Arbitrage-free Volatility Surface

Master Thesis

2022

Abstract

The Ensemble Carr-Pelts surface, which is a weighted mixture of standard CarrPelts surfaces, is an arbitrage-free parameterization of an implied volatility surface proposed by Antonov, Konikov and Spector (2019). This dissertation aims to investigate the additional benefits provided by using the Ensemble Carr-Pelts surface as opposed to the standard Carr-Pelts surface. We also show its validity in comparison to stochastic volatility inspired Gatheral (2004) surface, which is widely used by practitioners. The approach adopted was done in three stages, with each stage calibrating to an increasingly complicated surface. Surfaces considered were a flat volatility surface, a surface changing with strike only, and a surface changing with both strike and maturity. Testing revealed that as complexity increased for the implied volatility surface, the Ensemble Carr-Pelts calibrated better than CarrPelts. When compared to the widely accepted stochastic volatility inspired surface; considering no-arbitrage was not enforced, the Ensemble Carr-Pelts performed adequately. However, the Ensemble Carr-Pelts takes significantly longer to calibrate.

Keywords

Mathematical Finance

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