Essays on option valuation: A quasi-parametric method for pricing options and testing the parametric option pricing models

This thesis includes two individual essays: Essay One presents a new methodology to calibrate the state price density (SPD) from observed market prices of options, and Essay Two investigates how the parametric option pricing models fit the market data.; Essay One presents a quasi-parametric method (QP method) as an alternative to overcome drawbacks of the three categories of nonparametric methods. The method is called quasi-parametric method because I construct a family of density functions in a nonparametric framework around a parametric prior. With the aid of a specific form of a family of density functions governed by a set of parsimonious parameters, the SPDs can be calibrated from the market prices of European options with a single maturity as well as with multiple maturities. The performance of the QP method is better than the existing method such as Buchen and Kelly (1996) in that it makes the results more stable due to its built-in mechanism to filter out the measurement errors. The other advantages are requirement of only substantially small data set, no data region restriction etc.; Essay Two investigates which parametric option pricing model is more compatible with the market data from the view point of the term structure of moments for the risk-neutral distributions (RND) of the underlying asset price returns. By comparing jump-diffusion (JD), CEV and GARCH models, I find that GARCH performs best in fitting term structures of moments of risk-neutral distributions. The CEV model can fit skewness and kurtosis better than GARCH model but it cannot fit annualized volatility. The JD model can generate too large negative skewness and positive kurtosis in short maturities but it goes back to normality too fast.