# How to price a strategy involving more than 2 different prices?

When pricing a spread option with two different prices, one can use Kirk's approximation combined with Margrabe's formula (https://en.wikipedia.org/wiki/Margrabe%27s_formula).

But what if I am pricing an option that involves 3 or 4 different prices ? Is there a closed form formula ? Else how can I price it ?

The payoff of my strategy looks like this:

$$\mathop{\mathbb{E}} \left[\left(\alpha K+\beta F_1(t_1) +\gamma F_1(t_2)+\zeta F_2(t_1) +\lambda F_2(t_2)\right)^+\right]$$ Where $K$ is the strike, $F_1$ and $F_2$ the price of two different assets.

For such problems, you may consider the moment matching approach. For example, you can approximate the combination of terms where the coefficients have the same sign by a log-normal random variable, and then use the approach you mentioned. If all coefficients have the same sign, you can approximate the whole combination by a shifted log-normal random variable. That is, \begin{align*} \beta F_1(t_1) +\gamma F_1(t_2)+\zeta F_2(t_1) +\lambda F_2(t_2) \approx A + B e^{C\xi}, \end{align*} where $A$, $B$ and $C$ are constants, and $\xi$ is a standard normal random variable. Here, the parameters $A$, $B$ and $C$ can be calibrated by matching the moments up to the third order. However, you need to solve a cubic equation. For simplicity, you can assume that $A=0$ to have a second order moment matching.