Thesis (doctoral)--Universität St. Gallen, 2001.

Not available / text

Geometric Brownian Motion (GBM) and has been widely used in the Black Scholes option-pricing framework to model the return of assets. However, many empirical investigations show that market returns have higher peaks and fatter tails than GBM. Contrary to the Black Scholes model, an option-pricing model which contains jumps reflects the evolution of stock prices more accurately. Therefore, hedging a model under jump diffusion would be desirable. This thesis develops a simplified method for hedging jump diffusions. In order to hedge the jump risk, other instruments besides the underlying asset must be used in the hedging procedure. We start with a the Partial Integro Differential Equation (PIDE) that models contingent claims with jumps and consider a dynamic hedging strategy that uses a hedging portfolio with the underlying asset and liquidly traded options. We introduce a simple hedging method, where, at each rebalance time, we minimize the instantaneous jump risk by finding proper weights for the underlying asset and instruments. We use a simulation method to test our approach using a Truncated SVD method to solve the linear system of equations resulting from our minimization procedure. Our results indicate that the proposed dynamic hedging strategy provides sufficient protection against diffusion and jump risk. The method also provides a firm theoretical basis for a method which is used in practice.

In this thesis we discuss option pricing and hedging under regime switching models. To the standard model we add jumps of various types. In particular, we consider a jump that is synchronous with a change in the regime state. Thus, for example, we can define a process such that the stock price moves to a high volatility state and simultaneously has a large downward jump in returns. This type of model is consistent with market experience. We derive the compensator for our synchronous jumps and price options on such a price process using Fourier transforms. We also test the model on S&P futures options and show that it performs significantly better than a jump diffusion model. Furthermore, we look at the problem of hedging options under finitely many regime states and with finitely many possible jump sizes. We find risk-free hedge portfolios using the risk-free asset, the underlying asset, and finitely many options. Our risk-free trading strategy is consistent with any equivalent martingale measure, and so does not in itself specify which measure should be used to price options.

Zugl.: Augsburg, University, Diss., 2006.

Zugl.: Augsburg, Universiẗat, Diss., 2008.

Thesis (D.B.A.)--Victoria University (Melbourne, Vic.), 2007. / Includes bibliographical references.

Zugl.: Trier, Univ., Diss., 2007

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (M.Econ.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 31). Also available in print.