Local and Stochastic Volatility Models: An Investigation into the Pricing of Exotic Equity Options
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Date
2006-10-27T12:55:11Z
Authors
Majmin, Lisa
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Abstract
The assumption of constant volatility as an input parameter into the Black-Scholes option pricing formula is deemed primitive and highly erroneous when one considers the terminal distribution of the log-returns of the underlying process. To account for the `fat tails' of the distribution, we consider
both local and stochastic volatility option pricing models. Each class of models, the former being a special case of the latter, gives rise to a parametrization of the skew, which may or may not re°ect the correct dynamics of the skew. We investigate a select few from each class and derive the results presented in the corresponding papers. We select one from each class, namely the implied trinomial tree (Derman, Kani & Chriss 1996) and the SABR model (Hagan, Kumar, Lesniewski &
Woodward 2002), and calibrate to the implied skew for SAFEX futures. We also obtain prices for both vanilla and exotic equity index options and compare the two approaches.
Description
Faculty of Science;
School of Computational and Applied Maths;
MSC Thesis
Keywords
Black-Scholes, SABR model, SAFEX