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Pricing a European Option in a Black-Scholes Quanto Market When Stock Price is a Semimartingale
University of Botswana, Gaborone, Botswana
University of Botswana, Gaborone, Botswana
- 1 University of Botswana, Gaborone, Botswana
- 2 University of Botswana, Gaborone, Botswana
Journal of Mathematical Finance·Volume 05 (2015)·Pages 286–303·Published 7 July 2015·DOI10.4236/jmf.2015.53025
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Abstract
We look at the price of the European call option in a quanto market defined on a filtered probability space when the exchange rate is being modeled by the process where H t is a semimartingale. Precisely we look at an investor in a Sterling market who intends to buy a European call option in a Dollar market. The market consists of a Dollar bond, Sterling bond and and Sterling risky asset. We first of all convert the Sterling assets by using the exchange rate E t and later on derive an integro-differential equation that can be used to calculate the price on the option.
KeywordsSemimartingaleHedgingArbitrageContingent Claim
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