Pricing Dax index options with Heston’s stochastic volatility model

Abstract

The purpose of this thesis is to compare the pricing power of two different option pricing models on DAX Index data. The models included are Black-Scholes-Merton (BS) and Heston’s stochastic volatility (SV) model. The data covers a period from Dec 1st 2001 to Dec 29th 2001, where the pricing power of option pricing models could be tested is in the middle of a market turbulence. All options with moneyness ranging from -20% to +20% and maturity between 100 and 20 days were included. The prices were then categorized by their moneyness, using classes ATM (+6% to -6%) and ITM/OTM (-6% to -20% and +6% to +20%).

One hypothesis was formed in this study based on the findings in earlier studies. The more complex model should generate most accurate pricing results.

The empirical test was concluded by estimating a daily parameter vector for both models. The calibration was executed by inverting the parameters from observed option market prices. Obtained parameters were then used to price options on a following day with same parameters for all observations on volatility surface within 100 to 20 days range. The pricing error was calculated from the option prices for both models separately. The mean square root error was chosen for an error statistic. Even though one set of parameters were calibrated for several maturities, we found Heston’s (1993) stochastic volatility model to substantially outperform the Black-Scholes-Merton model in both absolute and relative terms. Both average pricing error and its standard deviation were reduced when mean squared pricing error was minimized. The best performance was reach when OTM options were priced.