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Hard · Stochastic Calculus · Quant Trader interview question · numeraire, exchange option, Margrabe's formula, stochastic calculus, option pricing
You are tasked with pricing an exchange option, which gives the holder the right, but not the obligation, to exchange one asset, $S_1$, for another asset, $S_2$, at a future time $T$. This is equivalent to a call option on $S_1$ with a strike price of $S_2$. When using the numeraire method to simplify the pricing problem, which asset is the most natural choice to use as the numeraire?