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...

We present a derivative pricing and estimation methodology for a class of stochastic volatility models that exploits the observed 'bursty' or persistent nature of stock price volatility. Empirical analysis of high-frequency S&P 500 index data confirms that volatility reverts slowly to its mean...

There has been an on-going debate about choices of the most suitable model amongst a variety of model specifications and parameterizations. The first dissertation essay investigates whether asymmetric leptokurtic return distributions such as Hansen's (1994) skewed tdistribution combined with...

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...

In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal...

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