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Questions tagged [margrabes-formula]

Margrabe's formula prices an option to exchange one risky asset for another risky asset (an exchange option).

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Continuous flows Perpetual maturity cap on Exchange Options PDE Change of variable

Im trying to do a change of variable on the following PDE Using the following change of variable $$ V(P^1,P^2) = P^2 W(C), C=\frac{P^1}{P^2} $$ I get this for the homogeneous part of the equation: ...
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Why risk-free interest is needed for Margrabe's Formula?

The source code for Margarble's formula in QuantLib is here. The implementation requires a forward price be computed: ...
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Value of an option to exchange an asset for another

I'm working out the examples in the paper "Changes of Numeraire, Changes of Probability Measure and Option Pricing", corollary 3. An option of exchanging asset 2 against asset 1 at time T, its time-0 ...
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Who trades exchange options in practice (Margrabe's formula)?

I'm currently studying the pricing of the exchange option. https://en.wikipedia.org/wiki/Margrabe%27s_formula While I can appreciate the theory, who actually buys these options in practice? Are ...
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Margrabe option: change of numeraire versus conditioning and numerical integration

I am having a slight brain meltdown because I do not seem to be able to understand the following basic thing. Consider a BS economy, and two assets $X$ and $Y$ $$ dX = \sigma X dW $$ $$ dY = \nu Y dZ ...
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Changing numeraire in Margrabes formula

Consider a Black Scholes market with constant coefficients, a bond and two risky assets: $$dB_{t}=r B_{t}dt \\ dS_{t}^{i}=S_{t}^{i}(b_{i}dt+\sigma_{i,1}dW_{t}^{1}+\sigma_{i,2}dW_{t}^{2})$$ where $i=1,...