Simple Statistical Tests to Identify Model Limitation or Accuracy of Lattice Approximation for Deterministic Volatility Models

概要

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In this research we investigate both the model limitation of the fitting to the market price and the accuracy of the approximation in a Lattice Construction method over Deterministic Volatility Models (DVM) using simple statistical tests. Li (2000/2001) proposed the Lattice Construction method which can express the market price flexibly using appropriate DVMs. However, this method has the implicit influence of approximation caused by recombining which is visible for DVM Lattice and is not common for Black-Scholes Lattice model. As a novelty approach we propose a new verification methodology to identify the model limitation or accuracy of lattice approximation for DVMs. It is difficult to discuss about the approximation issue in DVMs because they don't have closed-form solutions like Black-Scholes model. The presented statistical tests use the option model price distribution generated by Monte Carlo simulation technique which doesn't include the approximation of recombining. This specific characteristic of Monte Carlo method is used for capturing the influence of approximation caused by recombining in the DVMs. In that way we can verify whether the estimated models have model limitation of fitting to the market price or (and) whether there is a problem regarding the accuracy of lattice approximation in reproducing the market price.
2011-01-26