How Correlation Affects Quanto Option Valuation and Hedging

Summary

The document explores why correlation between a foreign underlying asset and the exchange rate matters for a quanto option, whose payoff is fixed in the holder’s currency. The questioner compares extreme positive and negative correlation cases in a simple two-outcome tree and concludes that the average payoff appears identical in both cases. This prompts a question about whether the option’s present value can therefore be independent of correlation.

The response locates the effect in replication and hedging rather than in the payoff formula alone. A quanto exposure combines the foreign security with currency conversion, so the hedge ratio depends on how the security and exchange rate move together. The example is an intuition prompt, not a complete pricing derivation: it does not specify a full probability model, discounting assumptions, or a calibrated valuation. It therefore highlights where correlation enters the valuation framework without quantifying its impact or establishing a general numerical result.

Key ideas

• A quanto option fixes its payoff in a currency different from the underlying asset’s currency.
• The option’s payoff formula does not explicitly contain the correlation between the asset and exchange rate.
• Correlation affects the replication and hedging of the quanto exposure.
• The appropriate hedge ratio depends on the joint behavior of the foreign security and exchange rate.
• The simple extreme-case example motivates the issue but does not provide a full pricing model.

Tags

# Correlation effect in Quanto options


# Correlation effect in Quanto options












My question will probably be stupid but here it is. I try to understand the effect of the correlation between exchange rate and underlying in a quanto option. And to have a non-precise understanding of this effect, I will consider a simple binomial tree. Suppose I have one underlying valuing 100 \$ & current exchange rate 1€=1\$. The quanto option pays at maturity max(S-100,0) paid in €. I consider now two extreme cases (correlation=+/- 1):

- At maturity, S=200\$, 1€=2\$ or S=50\$, 1€=0.5\$

- At maturity, S=50 \$, 1€=2\$ or S=200\$, 1€=0.5 \$

In both cases, the final payoff will be 50€=0.5 * 100€+0.5 * 0€ , whatever the correlation between underlying and exchange rate is. Therefore, the current value of the option would be the NPV in € of 100 € and is independent of the correlation between exchange rate and underlying.

Where is the error in this simulation?

PS: By the way, we can use multistep binomial trees. The evolution of the underlying does not depend on the exchange rate.

## Answer by river_rat (score 1)

https://quant.stackexchange.com/a/64203

The correlation comes into the replication (and thus hedging) of a quanto and not explicitly in the final payoff. In a sense you are trying to hedge a linear payoff with a linear hedging instrument (exchange rate) and a non-linear hedging instrument (foreign security converted into local currency) and the correct hedge ratio depends on the correlation.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.