Pricing a European Option in a Black-Scholes Quanto Market When  Stock Price is a Semimartingale

E. R. Offen; E. M. Lungu

doi:10.4236/jmf.2015.53025

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Journal of Mathematical Finance > Vol.5 No.3, August 2015

Pricing a European Option in a Black-Scholes Quanto Market When Stock Price is a Semimartingale ()

E. R. Offen, E. M. Lungu

University of Botswana, Gaborone, Botswana.

DOI: 10.4236/jmf.2015.53025 PDF HTML XML 6,073 Downloads 7,148 Views

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.

Keywords

Semimartingale, Hedging, Arbitrage, Contingent Claim

Share and Cite:

Offen, E. and Lungu, E. (2015) Pricing a European Option in a Black-Scholes Quanto Market When Stock Price is a Semimartingale. Journal of Mathematical Finance, 5, 286-303. doi: 10.4236/jmf.2015.53025.

Conflicts of Interest

The authors declare no conflicts of interest.

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