How Correlation Affects the Value of a Spread Option

Summary

A spread call pays when the first asset’s terminal value exceeds the second asset’s value plus a strike. The note explains why increasing the correlation between the two assets tends to lower the option’s value: the payoff benefits when the first asset rises relative to the second, while assets moving together tend to reduce those relative moves.

It also connects this intuition to Kirk’s approximation, where correlation affects the spread’s equivalent volatility. The discussion is qualitative and gives no derivation, numerical example, or empirical evidence. Its explanation assumes the stated spread-call payoff and does not explore how contract details or other modeling assumptions might affect the result.

Key ideas

• A spread call gains value when the first asset outperforms the second by more than the strike.
• Higher correlation tends to reduce the relative movement that can produce a positive payoff.
• In Kirk’s approximation, correlation enters the equivalent volatility and affects the option value.

Tags

# Increasing the correlation of two asset reduce the value of spread option.


# Increasing the correlation of two asset reduce the value of spread option.












We know the payment function of Spread option is $$\max\{X_T - Y_T-K,0\}$$ here $$d X_t = (\mu_x - D_x)X_t dt + \sigma_xX_td W^x_t$$ $$d Y_t = (\mu_y - D_y)Y_t dt + \sigma_yY_td W^y_t$$ $$d W^x_td W^y_t = \rho dt$$ and we know the the increasing of $\rho$ will reduce the value of spread option, but how to explain this result without deducing the mathematical formula?

I know the `Kirk’s approximation formula,` $\rho$ only contribute to the equivalent volatility $$\sigma^2 = \sigma^2_x - 2\rho\sigma_x\sigma_z + \sigma^2_z$$ here $\sigma_z$ is a transformation of $\sigma_y$ which is fixed. Then increasing of $\rho$ will reduce the $\sigma,$ and will reduce the value of option.

## Answer by mbison (score 3)

https://quant.stackexchange.com/a/33448

the payoff is max(X-Y-K,0). so this option pays you the most if X goes up and Y goes down. So you need X and Y to move in opposite directions. The more X and Y move in the same direction (high rho) the less you get paid.

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