I'm trying to solve this problem given:

The dividend yield for asset 1 (asset 2) is 0.05 (0.03), and it is also given the time zero stock prices, and both assets' Black-Scholes equation.

I need to find the time zero price of an asset which pays:

$[max(S_{3}^{1}-S_{3}^{2},0)]$ at T = 3.

Just wanted to get a hint on how to approach the problem?



Basically what you are after is an exchange option on the two assets, i.e., a zero-strike call option on the price difference between asset1 and asset2. Having the equations of motion for both asset prices, you are in a position to work out:

i) the forward prices for both assets at $T=3$;

ii) both assets' volatilities $\sigma_1$ and $\sigma_2$; AND

iii) the correlation coefficient $\rho_{1,2}$.

Having all of this, you can apply the Margrabe formula Margrabe's formula on Wikipedia


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