How Cross-Currency Option Hedges Create Correlation Risk

Summary

The document considers the risks created when hedging a TRY/JPY call option with positions in other currency pairs. One answer observes that expressing the hedge through several currency spots introduces exposure to multiple currencies, and that the original cross-rate option already depends on the relationship between its component exchange rates. The option’s implied volatility therefore reflects correlation between those underlying currency pairs, even without a basket option in the portfolio.

A second answer points to cross-currency basis and currency-specific hedge demand as possible sources of residual profit and loss. The exchange does not fully resolve whether those exposures exhaust the meaning of correlation risk, nor does it derive hedge ratios or quantify the resulting sensitivities. The discussion is conceptual and tied to its particular currency example; it highlights that delta hedging a cross option can leave dependence and basis exposures that require separate analysis.

Key ideas

• A cross-currency option’s implied volatility depends on the correlation between its component exchange rates.
• Hedging a cross option with several spot pairs can create exposures to multiple currencies.
• Cross-currency basis and currency-specific hedge demand can contribute to residual profit and loss.
• Delta hedging does not by itself quantify or remove every correlation-related exposure.

Tags

# FX Correlation Risk from cross ccy pairs


# FX Correlation Risk from cross ccy pairs












Suppose you are long a TRYJPY call option. And lets say you can delta hedge using USDTRY, AUDJPY, and AUDUSD.

In this case I would delta hedge by buying USDTRY, selling AUDJPY, and buying AUDUSD.

If this were to be the case, I am creating correlation risk between these currency pairs?

Also, if we were to delta hedge using just USDTRY and USDJPY, would this eliminate the correlation risk?

This example is kind of odd to me as correlation risk is created without having any basket options on the book.

## Answer by Randor (score 2)

https://quant.stackexchange.com/a/47071

yes you have introduced correlation risk since you have introduced spot positions in different currencies. but also, you could think about your original option position as having already had correlation risk , since the implied vol of the TRYJPY cross depends on the correl of USDTRY and USDJPY

## Answer by hotsource (score 2)

https://quant.stackexchange.com/a/47072

The cross currency basis of the 3 pairs of hedging positioning are the sources of unhedged risks. The currency hedging demand in AUD, TRY and JPY will drive some Pnl in the book. Not sure if this is the only source of correlation risk here.

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