Date of Award
Master of Science (MS)
Mathematics and Statistics
Much research has been done on options pricing. Black and Scholes  set the benchmark in 1973 with their model for arbitrage-free, risk-neutral options valuation. Arbitrage-free refers to a market environment where prices are such that trading opportunities with no risk do not exist and risk-neutral commodities earn a risk free interest rate. Since then the literature has seen a multitude of models improving the fit of the traditional Black -Scholes (BS) model. A brief overview of options and these models is given. A derivation and discussion of BS is followed by a derivation and discussion of the Extended Black-Scholes (EBS) model by Modisett and Powell  which augments BS with the addition of a small drift parameter. A solution to both BS and EBS is the n given. A bootstrap method is used to test whether EBS is a significant improvement over BS using S&P500 options data. It is concluded that not only does EBS significantly improve BS for the given data, but that EBS is arguably the most parsimonious model choice for such an improvement. This suggests that mark et price setters who are presumably using BS maybe doing something in addition to BS which is equivalent to fitting a drift parameter.
Bush, Bradley Thomas, "Black-Scholes and Extended Black-Scholes Models: A Comparative Statistical Analysis" (2007). All Graduate Plan B and other Reports. 1285.
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