# Exchange option pricing margrabe

Note the dividend rate q 1 exchange option pricing margrabe the first asset remains the same even with change of pricing. The formula is quickly proven by reducing the situation to one where we can apply the Black-Scholes formula. So the original option has become a call option on the first asset with its numeraire pricing with a strike of 1 unit of the riskless asset.

Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. By using this site, you agree to the Terms of Use and Privacy Policy. So the original option has become a call option on the first asset with its numeraire pricing with a strike of 1 unit exchange option pricing margrabe the riskless asset.

From Wikipedia, the free encyclopedia. Retrieved from " https: Alternatively, one can show it by the Girsanov theorem. Margrabe's paper has been cited by over subsequent articles.

The option, Cthat we wish to price gives the buyer the right, but not the obligation, to exchange the second asset for the first at the time of maturity T. Mathematical finance Options finance. In particular, the model does not assume the existence of a riskless exchange option pricing margrabe such as a zero-coupon bond or any kind of interest rate. Applying the Black-Scholes formula with these values as the appropriate inputs, e. Note the dividend rate q 1 of the first asset remains the same exchange option pricing margrabe with change of pricing.

Margrabe's model of the market assumes only the existence of the two risky assets, whose prices, as usual, are exchange option pricing margrabe to follow a geometric Brownian motion. Under this change of numeraire pricing, the second asset is now a riskless asset and its dividend rate q 2 is the interest rate. In particular, the model does not assume the existence of a riskless asset such as a zero-coupon bond exchange option pricing margrabe any kind of interest rate. Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. The model does not require an equivalent risk-neutral probability measure, but an equivalent measure under S 2.

Since the resulting option price is in units of S 2multiplying through by Exchange option pricing margrabe 2 0 will undo our change of numeraire, and exchange option pricing margrabe us the price in our original currency, which is the formula above. The option, Cthat we wish to price gives the buyer the right, but not the obligation, to exchange the second asset for the first at the time of maturity T. It was derived by William Margrabe Phd Chicago in