The Mathematical Institute, University of Oxford, Eprints Archive

Structure of asymptotic expansions of put prices, Deltas and Gammas

Su, Quanrong (2014) Structure of asymptotic expansions of put prices, Deltas and Gammas. Masters thesis, Oxford University.

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Abstract

In this dissertation, we present the matched asymptotic expansions method for solving the arithmetic Asian rate put options. We first start with a simpler perturbation problem of vanilla European puts and demonstrate the method to derive the asymptotic solutions under the assumption of low volatility that ǫ2 = σ2/r ≪ 1. Such method is then extended to arithmetic Asian rate puts. Particular simple analytic forms involving polynomials are found in the solutions for the zero risk-neutral drift case, which turns the pricing problem to the problem of finding polynomial solutions of linear ordinary differential equations. The solutions are in closed form and can be computed efficiently. They make it possible to attain O(ǫn+1) accuracy by taking the first n terms of the asymptotic series.

Item Type:Thesis (Masters)
Subjects:H - N > Mathematics education
Research Groups:Mathematical and Computational Finance Group
ID Code:1851
Deposited By: Laura Auger
Deposited On:07 Aug 2014 06:43
Last Modified:29 May 2015 19:32

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