# future trading strategy

Jun 28th, 2015
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Academy of Art University
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Black and Scholes published their seminal work on option pricing in 1973 [3]. In it, they described a mathematical framework for calculating the fair price of a European option in which they used a no-arbitrage argument to derive a partial differential equation which governs the evolution of the option price with respect to the time to expiry, t, and the price of the underlying asset, S. As a starting point, we will briefly discuss options in general and we will work through the derivation of the Black-Scholes PDE, highlighting along the way some of the key assumptions that the model makes. We will then compare and contrast three of the primary numerical techniques that are currently used by financial professionals for determining the price of an option: Finite difference solution of the Black-Scholes PDE, The Binomial Method, and Monte-Carlo simulation.

Word Count: 7032
Showing Page: 1/22
Numerical Methods for Option PricingMark RichardsonMarch 2009Contents1 Introduction22 A brief introduction to derivatives and options23 The3.13.23.33.4Black-Scholes ModelAsset prices and Itos Lemma . . . .Derivation of the Black-Scholes PDEBoundary Conditions . . . . . . . . .Closed Form Solutions . . . . . . . .4 Numerical Methods4.1 Finite Difference Methods4.2 Risk-Neutral Valuation . .4.3 Binomial Tree Methods .4.4 Monte-Carlo Simulation .................................................................................................................22333........................................................................................44667....99910105 Pricing American Options5.1 Boundary Conditions and Early Exercise Criteria .5.2 Pricing American Options using a Binomial Tree .5.3 Pricing American Options using Finite Differences5.4 Comparing the Performance of the Two Methods .....................................................6 Conclusions117 Appendix7.1 MATLAB7.2 MATLAB7.3 MATLAB7.4 MATLAB7.5 MATLAB7.6 MATLAB7.7 MATLAB7.8 MATLAB7.9 MATLAB12121314141516181921codeco

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