Exchange Option Numeraire - Quant Trader Interview Question
Difficulty: Hard
Category: Stochastic Calculus
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Topics: numeraire, exchange option, Margrabe's formula, stochastic calculus, option pricing
Problem Description
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?
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