Johan Nykvist: Time Consistency in Option Pricing Models

Since the introduction of the famous Black- Scholes model (1973), several attempts have been made to construct option pricing models that allow for non- gaussian return distributions as well as varying volatilities. In this thesis, we examine the robustness of two of these models in terms of the time consistency, or possibly inconsistency, of the model parameters. We restrict our attention to the stochastic volatility model provided by Heston (1993) and the local volatility model introduced by Dupire (1994). We estimate the models daily in order to find parameters that match the current market prices as closely as possible, hence the calibration process constitutes a major part of the thesis. Our results show that both models are successful in explaining important characteristics of the implied volatility surface, when the market conditions are fairly stable. On the other hand, when the market is heavily fluctuating, both models reveal a high degree of time inconsistency, as they are unable to capture the current market conditions without large parameter variations. In addition, the use of principal component analysis shows that variations of the local volatility surface, to a large extent can be explained by three distinct movements.