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Applied
Math Seminar |
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We present a computational algorithm for computing the moments of the hedging error in a dynamic hedge. The algorithm applies to hedges that are affine in the value of the replicating portfolio, such as standard Black-Scholes or mean square optimal hedges. Specifically, we develop this algorithm for a derivative security written on an underlying asset (stock) modeled on a trinomial lattice. It is shown that the computation of moments reduces to the backward iteration of a matrix on the stock lattice. Hence, moments of the hedging error can be efficiently computed in a manner similar to lattice based pricing algorithms, providing important information about the accuracy of the hedge. We then briefly survey methods for estimating a probability density from moments, and for computing Value-at-Risk quantities. Finally, examples are provided where we examine the effect of non-continuous trading on the accuracy of hedges. |