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R: Data Analysis and Visualization by Ágnes Vidovics-Dancs, Kata Váradi, Tamás Vadász, Ágnes Tuza, Balázs Árpád Szucs, Julia Molnár, Péter Medvegyev, Balázs Márkus, István Margitai, Péter Juhász, Dániel Havran, Gergely Gabler, Barbara Dömötör, Gergely Daróczi, Ádám Banai, Milán Badics, Ferenc Illés, Edina Berlinger, Bater Makhabel, Hrishi V. Mittal, Jaynal Abedin, Brett Lantz, Tony Fischetti

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Exchange options

Exchange options grant the holder the right to exchange one risky asset to another risky asset at maturity. It is easy to see that simple options are special forms of exchange options where one of the risky assets is a constant amount of money (the strike price).

The pricing formula of an exchange option was first derived by Margrabe, 1978. The model assumptions, the pricing principles, and the resultant formula of Margrabe are very similar to (more precisely, the generalization of) those of Black, Scholes, and Merton. Now we will show how to determine the value of an exchange option.

Let's denote the spot prices of the two risky assets at time t by S1t and S2t. We assume that these prices under the risk neutral probability measure ...

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