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Option Pricing in the Presence of Natural Boundaries and a Quadratic Diffusion Term

(by Sven Rady)

 

Finance and Stochastics 1(4), 1997, pp. 331-344

An earlier version of the paper, entitled "Option Pricing with a Quadratic Diffusion Term" and containing an application to exchange rate options, is available as LSE Financial Markets Group Discussion Paper No. 226.

[Download discussion paper version]

Abstract
This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios. An application to the pricing of bond options and certain interest rate derivatives illustrates the main results.

Keywords: Option Pricing, Bond Options, Change-of-Numeraire Technique, Diffusion Process, Quadratic Diffusion Term
JEL Classification: G13

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