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Stochastic PDEs and Quantitative Finance: The Black-Scholes-Merton Model of Options Pricing and Riskless Trading

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  • Brandon Kaplowitz
  • Siddharth G. Reddy
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    Abstract

    Differential equations can be used to construct predictive models of a diverse set of real-world phenomena like heat transfer, predator-prey interactions, and missile tracking. In our work, we explore one particular application of stochastic differential equations, the Black-Scholes-Merton model, which can be used to predict the prices of financial derivatives and maintain a riskless, hedged position in the stock market. This paper is intended to provide the reader with a history, derivation, and implementation of the canonical model as well as an improved trading strategy that better handles arbitrage opportunities in high-volatility markets. Our attempted improvements may be broken into two components: an implementation of 24-hour, worldwide trading designed to create a continuous trading scenario and the use of the Student's t-distribution (with two degrees of freedom) in evaluating the Black-Scholes equations.

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    File URL: http://arxiv.org/pdf/1212.1919
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1212.1919.

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    Date of creation: Dec 2012
    Date of revision: Jul 2013
    Handle: RePEc:arx:papers:1212.1919

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    Web page: http://arxiv.org/

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