Essays on pricing and applications of financial derivatives

Sandipan Mullick, Purdue University

Abstract

In the first essay, we propose a nonparametric testing methodology for jump diffusion models of asset prices with stochastic volatility. We test various parametric specifications against a nonparametric alternative. The test statistic is constructed using the transition densities of the asset prices. The asymptotic distribution of the proposed test statistic is derived. Our empirical analysis rejects most of the commonly used specifications for the asset prices. The specifications not rejected by our tests are highly nonlinear and are generalizations of the most popular specifications. Given the correct specification of the asset pricing model, a nonparametric contingent claim valuation methodology is proposed. We derive the limiting distribution of the derivative prices. Using our nonparametric pricing methodology, we obtain the prices of European call options for a particular day in our sample, for different maturities and strike prices. In the second essay, we propose a structural hazard rate model of credit risk where default is defined as the first jump of a Cox process. The intensity of default is a function of the equity value of the firm, defined as the difference between the market value of the assets and the liabilities. Both assets and liabilities are assumed to have interest rate sensitive and interest rate insensitive components. Using this formulation, we are able to explicitly factor in the duration gap which is an important determinant of the credit spreads. We use our credit risk framework to obtain the term structure of credit spreads for noncallable zero coupon bonds and do a factor and parameter sensitivity analysis for them. We also obtain the term structure of credit spreads for defaultable swaps when there is bilateral default risk. In the third essay, we model corporate payout policies in a barrier option framework. Managers use their "insider" valuation of the firm's stock to select the appropriate payout policy, in terms of a dividend increase, stock repurchase, or a dividend cut, with the objective of correcting any mispricing of the firm's equity by the market. The payout policies are viewed as exchange options for the managers, where they have the option to exchange the firm's existing stock for another stock, which reflects its true value. The choice of a payout policy depends on the "barriers" defined by the managers and the path of the stock prices over the life of the options. Assuming specifications for the underlying stochastic processes, we derive closed form solutions for the American options using a decomposition technique. Using these option values we determine the optimal announcement times for the payout policies.

Degree

Ph.D.

Advisors

Abrevaya, Purdue University.

Subject Area

Finance

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