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Stochastic volatility models
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School of Business |
Master's thesis
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en
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51
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In 1973, when Fischer Black and Myron Scholes published their paper The Pricing of Options and Corporate Liabilities, they revolutionized the entire financial market and laid the foundation for the field of quantitative finance by introducing a framework for pricing financial derivatives. However, this framework, despite its enduring popularity, comes with several significant limitations. Most notably, the assumption of constant volatility and its inability to capture the negative correlation between the asset price and its volatility, called the leverage effect. This leads to something referred to as the volatility smile or the volatility skew, depending on the shape of the implied volatility curve when plotted against the strike price or the maturity. Hence, a more accurate framework is needed.
This thesis contributes to existing research on the leverage effect and the volatility smile/skew by demonstrating how the introduction of stochastic volatility into the Black-Scholes framework is able to more accurately account for these phenomena. The main research questions and motivation for the thesis are to demonstrate why it makes sense to model volatility as a stochastic process by analyzing stock price data, and how modelling volatility as a stochastic variable leads to more accurate models and prices. The thesis also serves as an introduction to stochastic calculus and risk-neutral pricing of derivatives. The thesis con-sists of six chapters and is structured so that every chapter builds on the previous one, and all the necessary mathematical tools are introduced as needed.