The main purpose of this paper is to derive unbiased Monte Carlo estimators of various sensitivity indices for an averaged asset price dynamics governed by the gamma Lévy process. The key idea is to apply a scaling property of the gamma process with respect to the Esscher density transform...

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2011.

With the rapid development of option markets throughout the world, option pricing has become an important field in financial engineering. Among a variety of option pricing models, volatility of underlying asset is associated with risk and uncertainty, and hence is treated as one of the key...

As is well known, the classic Black-Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second,...

We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of at-the-money and out-of-the-money options as the option maturity approaches zero. We show that these prices converge...

We consider the hedging of derivative securities when the price movement of the underlying asset can exhibit random jumps. Under a one factor Markovian setting, we derive a spanning relation between a long term option and a continuum of short term options. We then apply this spanning relation to...

The binomial model has been used to price a wide variety of equity and interest rate options for more than two decades. Originally developed by Cox, Ross, and Rubinstein to clarify the basic pricing principle of its continuous-time counterpart with reduced mathematical requirements, the approach...

In the past decades several versions of the binomial model for option pricing, originally introduced by Cox, Ross, and Rubinstein, have been discussed in the finance literature. Some of these approaches model an arbitrage-free market in the discrete setup whereas others attain this property only...

Three years after the seminal work of Black and Scholes on the pricing of European options, Scholes presented a paper in which the impact of taxation on the value of an option is analyzed. We restart this discussion in a simple binomial setting emphasizing the economic principles of replicating...

This thesis develops a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The pricing problem can be reduced to solving a partial integro-differential equation (PIDE). The Fourier Space Time-stepping...