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

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DOI: 10.4236/jmf.2015.53025 5,843 Downloads 6,801 Views

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E. R. Offen, E. M. Lungu

Affiliation(s)

University of Botswana, Gaborone, Botswana.

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

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

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