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

Fuente: arXiv
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Autori principali: Kaplowitz, Brandon, Reddy, Siddharth G.
Natura: Preprint
Pubblicazione: 2012
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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