Approximating option prices

In this thesis we consider the method of Kristensen and Mele (2011, J. of Financial Economics) to approximate European call option prices from the constant elasticity of variance (CEV) model, for which no closed-form solution is available. The method provides a closed-form approximation that allows for direct calibration of the CEV model on option price data. Through a simulation study we find a good performance of the approximation method, both in terms of accuracy and parameter estimation. We proceed by testing the model on European call options on the S&P 500 index. The CEV model is calibrated through its closed-form approximation on option price data, using a non-linear least squares method that minimizes the sum of squared errors between the cross-sectional option price and the corresponding option price from the approximation, on a daily basis. The calibrated closed-form approximation is then used to get in-sample and out-of-sample fits of the daily option prices. When these fits are compared with those from two benchmark models, namely the Heston model and the Practitioners Black-Scholes model, the CEV model is outperformed by both. We conclude that the poor option price performance of the CEV model is due to the inaccuracy of the applied approximation.