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Course Summary of Computational Methods of Financial Mathematics Public

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<P>Most realistic financial derivatives models are too complex to allow explicit analytic solutions. The computational techniques used to implement those models fall into two broad categories: finite difference methods for the solution of partial differential equations (PDEs) and Monte Carlo simulation. Accordingly, the course consists of two sections.<P> <P>The first half of the course focuses on finite difference methods. The following topics are discussed; Parabolic PDEs, Black-Scholes PDE for European and American options; binomial and trinomial trees; explicit, implicit and Crank- Nicholson finite difference methods; far boundary conditions, convergence, stability, variance bias; early exercise and free boundary conditions; parabolic PDEs arising from fixed income derivatives; implied trees for exotic derivatives, adapted trees for interest rate derivatives.<P> <P>The second half of the course focuses on Monte Carlo. The following topics are discussed; Random number generation and testing; evaluation of expected payoff by Monte Carlo simulation; variance reduction techniques—antithetic variables, importance sampling, martingale control variables; stratification, low-discrepancy sequences and quasi-Monte Carlo methods; efficient evaluation of sensitivity measures; methods suitable for multifactor and term-structure dependent models.<P> <P>Computational Methods of Financial Mathematics is taught by Marcel Blais, a professor at Worcester Polytechnic Institute.<P>

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  • English
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  • etd-050509-105426
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  • 2009
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  • 2009-05-05
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