Skip to content
All library documents

Pricing FX-Linked Equity Options: Quanto, Converted Underlying, and Payment Currency

Article Quant Q&A · Author: zuiqo
Read the original

Summary

The document distinguishes three contracts that can be described as an option on a foreign-currency stock but have different payoffs. If a USD payoff is converted at a predetermined exchange rate, the contract is a quanto. If the strike is in EUR while the stock price is in USD, valuation requires modeling the stock’s value in EUR, which brings in FX volatility and the correlation between the stock and exchange rate. If the option payoff remains in USD and the buyer simply pays in EUR, the suggested approach is to price in USD and convert at the current spot rate.

For the converted-underlying case, the answer suggests obtaining FX volatility from implied volatility in FX options and estimating correlation from time series, while noting that correlation is harder to source. A second answer mentions change of numeraire and put-call parity as possible pricing tools. The discussion is an introductory classification, not a full pricing derivation; it does not specify a model, calibration procedure, or market conventions.

Key ideas

  • A predetermined conversion rate on a foreign-currency payoff defines a quanto-style contract.
  • An option with a strike in one currency and an underlying quoted in another requires modeling the converted underlying.
  • FX option implied volatility can inform the exchange-rate volatility input.
  • The answer suggests time-series data for estimating stock–FX correlation and notes that this input is difficult to obtain.
  • When only the purchase price is converted, the option can be priced in its payoff currency and converted at spot.

Tags

OptionsForexVolatilityDerivatives pricing
Full text
# Price of a composite option


# Price of a composite option












how would you calculate the fair value of an option on a fx'ed underlying, e.g. a put on a USD-stock which is changed into EUR? How should I get, in practice, the fx spot vol/correl?

Purpose is to have a starting point when dealing with otc structuring desks.

Thanks!

## Answer by Mark Joshi (score 4, accepted)

https://quant.stackexchange.com/a/15722

it depends on how it's converted. There are three different possibilities.

- the pay-off is $(K-S_T)_+$ with $K$ and $S_T$ in USD but the pay-off is converted to EUR as a predetermined rate. This called a quanto and is widely discussed in books. (eg my book Concepts...)

- the pay-off is $(K-S_T)_+$ with $K$ in EUR and $S_T$ in USD. Then you have to model the dynamics of the EUR value of the stock. Which comes down to knowing the FX volatility and the correlation. The first you could get from implied vols of FX options. The second is harder and probably from time series.

- the pay-off is $(K-S_T)_+$ with $K$ and $S_T$ in USD but you want to buy it with EUR. In this case, just price in USD and convert with today's exchange rate.

## Answer by Student tea (score 0)

https://quant.stackexchange.com/a/15246

I guess the easiest would be to price a call option, and then use put-call parity. To price the call option you would have to do a change of numeraire. A good reference for this would probably be Brigo and Mercurio.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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