| The Levy jump models are considered to be an improvement over the traditional Black-Scholes model for derivative pricing, and there are a good number of papers that discuss their performance. However, most of them emphasize the performance in the relatively easy to price European call options market. American options especially put options, are overlooked. Our research attempts to fill this gap. We apply quadratic approximation methods to estimate the early exercise premium of the American option, and calibrate Levy models to S&P 100 index options prices. We compare the performance across models for different moneyness and maturity categories. We further calculate prices of American puts by Monte Carlo simulation, and again compare their performance. Our test results show that: (1) The multi-parameter Levy models are likely to overfit; (2) The CGMY model shows the best call-put consistency, with Black-Scholes coming second. |
