Semianalytic Pricers

Tom Hyer

Chapter 14 in Derivatives Algorithms:Volume 1: Bones, 2015, pp 295-305 from World Scientific Publishing Co. Pte. Ltd.

Abstract: All our discussion so far has been centered on generic numerical pricing, where models and trades can communicate at arm's length. We now turn to specialized semianalytic methods, which use knowledge of both the trade and model to rapidly obtain the price, or a close approximation thereto.For example, a lognormal price diffusion with deterministic interest rate and dividend yield leads to the Black-Scholes pricing formula for equity options; and we need solve no PDE in the process. If the deterministic dividend yield is replaced by a set of discrete payments, or a richer parametrization of the dividend curve, then moment-matching methods can yield an inexact but quite accurate price.As the models grow richer, the semianalytic methods must be correspondingly more sophisticated and complex. This is the "high art" of the quant world. In this volume, we will focus more on the frame: how can we make these approximations available without sacrificing genericity?

Keywords: Derivatives; Quantitative; Numerical; Code Generation; C++; C++11; Algorithms; Coding; Protocols; Interfaces; Persistence; Indices; Underdetermined; Multiple Dispatch; Extensibility (search for similar items in EconPapers)
Date: 2015
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