Stochastic PDEs and Quantitative Finance: The Black-Scholes-Merton Model of Options Pricing and Riskless Trading
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2012
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| _version_ | 1866915577509969920 |
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| author | Kaplowitz, Brandon Reddy, Siddharth G. |
| author_facet | Kaplowitz, Brandon Reddy, Siddharth G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1212_1919 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Stochastic PDEs and Quantitative Finance: The Black-Scholes-Merton Model of Options Pricing and Riskless Trading Kaplowitz, Brandon Reddy, Siddharth G. Pricing of Securities 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. |
| title | Stochastic PDEs and Quantitative Finance: The Black-Scholes-Merton Model of Options Pricing and Riskless Trading |
| topic | Pricing of Securities |
| url | https://arxiv.org/abs/1212.1919 |