An empirical study on models of derivative pricing

This dissertation examines a new simulation estimator designed to estimate the volatility parameters in a stochastic differential equation.; The new estimator is based on the combination of the equivalent martingale measure, one of the most important innovations in theoretical finance in recent years, and the recently-developed asymptotic theory for simulation-based estimators in econometrics. The derivative pricing formula expressed as the conditional expectation of future payoffs of the derivative asset with respect to the equivalent martingale measure constitutes the moment condition for the generalized method of moments estimator. GMM is made operational by evaluating the intractable moment condition through a Monte Carlo simulation. The new estimator, therefore, fits into the framework of the method of simulated moments estimator very nicely.; Chapter 2 introduces the concept of the equivalent martingale measure and investigates the implications of the measure on the theory of derivative pricing and the empirical study in the dissertation.; In Chapter 3, I explore the possibility of introducing a statistical error term into the derivative pricing formula without discarding market completeness and the uniqueness of the equivalent martingale measure. The consistency and asymptotic normality of the new simulation estimator are established. The estimator is T -consistent and its asymptotic variance is inversely related to the accuracy of the simulation.; The first part of Chapter 4 examines the small sample properties of the new simulation estimator by taking advantage of a very convenient statistical structure of the geometric Brownian motion. The new estimator shows good small sample properties comparable to the maximum likelihood estimator. The second part of the Chapter illustrates two empirical examples using options on the S&P 500 Index and options on five foreign currencies. Popular forms of the diffusion function such as the geometric Brownian motion and constant elasticity of variance are rejected. Instead, the evidence favors a more flexible form of the diffusion function, extended constant elasticity of variance. In-sample and out-of-sample prediction analyses are also conducted.; Chapter 5 concludes by summarizing the findings of the dissertation.