0
$\begingroup$

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.

Improve this question
$\endgroup$
3
  • $\begingroup$ I might be misreading your tree data, however, I don't even see the terminal payoffs being equal for your two corner cases. The OTM case is clear, 0$ = 0€ always. The ITM case for a correlation of +1 would pay max[200-100, 0]$ times 0.5€ for every 1$, so 50€. For a correlation of -1, you'd have max[200-100,0]$ times 2€ for every 1$, so 200€? $\endgroup$
    – KevinT
    May 25, 2021 at 16:50
  • $\begingroup$ @KevinT that's because by definition in quanto options, the exchange rate for the final payoff is fixed at the beginning of the contract. In this case it is 1€ = 1$. $\endgroup$
    – qwerty_uiop
    Oct 26, 2021 at 4:26
  • $\begingroup$ If you consider the risk-neutral measure for a trader that thinks in \$, you should have a 1/3 change of ending up at \$200 in both cases. However, would the risk neutral measure/probabilities for a trader thinking in EUR be the same here? $\endgroup$
    – Marses
    Dec 28, 2022 at 17:41

1 Answer 1

Reset to default
1
$\begingroup$

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.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Does this correlation still interact if we consider options paying relative performance of an index : (Final value-Initial Value)/Initial Value ? $\endgroup$
    – Delepine
    May 25, 2021 at 11:39
  • $\begingroup$ Yes, if the accounting currency is not the natural currency of the payout (ie a quanto) then you have this effect. Your hedge instrument is still non-linear, being the product of the exchange rate and the index level. $\endgroup$
    – river_rat
    May 25, 2021 at 13:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.