American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison

Journal of Empirical Finance (Impact Factor: 0.84). 06/2011; 18(5). DOI: 10.2139/ssrn.1875847


This paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results indicate that, while the differences in performance are small overall, for in the money options the continuous time SV models do generally perform better than the discrete time GARCH specifications.

Download full-text


Available from: Lars Stentoft,
23 Reads
  • Source
    • "Among these models, Engle and Ng's (1993) nonlinear asymmetric GARCH model (NGARCH) has proven to be a strong contestant for tting stock returns, pricing options, and predicting volatility. Bollerslev and Mikkelsen (1996), Hsieh and Ritchken (2005), Christoersen et al. (2010), and Stentoft (2011), among others, all show that non ane GARCH models (such as the NGARCH) dominate ane models for both tting returns and option valuation. GARCH models also perform well in forecasting volatility. "
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper proposes an improved estimation and calibration method to a family of GARCH models. The suggested method xes one parameter such that the unconditional kurtosis of the model matches the sample kurtosis. The method can be used to estimate the model on historical returns, or calibrate it on observed option prices. An empirical analysis using Engle and Ng's (1993) NGARCH(1,1) model shows that the method dominates previous estimation methods on multiple aspects. When estimating on historical returns, the processing time is cut in half, and the out of sample t is improved. When calibrating on observed option prices, the optimization is simplied and the processing time is reduced by 50%, without aecting the quality of the t. Results are robust to various samples and selection of initial values.
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper investigates the weak convergence of general non-Gaussian GARCH models together with an application to the pricing of European style options determined using an extended Girsanov principle and a conditional Esscher transform as the pricing kernel candidates. Applying these changes of measure to asymmetric GARCH models sampled at increasing frequencies, we obtain two risk neutral families of processes which converge to different bivariate diffusions, which are no longer standard Hull–White stochastic volatility models. Regardless of the innovations used, the GARCH implied diffusion limit based on the Esscher transform can be obtained by applying the minimal martingale measure under the physical measure. However, we further show that for skewed GARCH driving noise, the risk neutral diffusion limit of the extended Girsanov principle exhibits a non-zero market price of volatility risk which is proportional to the market price of the equity risk, where the constant of proportionality depends on the skewness and kurtosis of the underlying distribution. Our theoretical results are further supported by numerical simulations and a calibration exercise to observed market quotes.
    European Journal of Operational Research 06/2015; 247(3). DOI:10.1016/j.ejor.2015.06.046 · 2.36 Impact Factor