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Hedging Correlation Risk in Dual Digital FX Options

Article Quant Q&A · Author: fwd_T
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Summary

The document presents a dual digital option whose payoff depends on two foreign exchange rates crossing specified thresholds at maturity. Because the payoff requires both conditions to hold, its value is sensitive to the correlation between the rates. The question asks how trading desks measure and hedge that correlation exposure.

The answer points to dispersion trading as a way to mitigate correlation risk and refers to a multicurrency option pricing framework. It also notes that digital payoffs can be approximated with call or put spreads, smoothing the sharp payoff around a threshold. These are brief suggestions rather than a detailed hedge construction: the document gives no sensitivity formula, hedge ratios, market calibration method, or evidence about hedge effectiveness. Practical implementation would depend on the relevant option markets and the precise payoff configuration.

Key ideas

  • A dual digital payoff depends jointly on two FX rates satisfying threshold conditions.
  • Correlation between the underlying exchange rates affects the option's value.
  • Dispersion trading is cited as a possible way to reduce correlation exposure.
  • Call or put spreads can approximate a digital payoff with a smoother transition near its barrier.

Tags

ForexOptionsVolatilityRisk management
Full text
# How to hedge a dual digital option


# How to hedge a dual digital option












Let us assume we have two FX rates: $ 1 EUR = S_t^{(1)} USD$ and $ 1 GBP=S_t^{(2)} USD $. Let $K_1>0, K_2>0$ be strictly positive values and a payoff at some time $ T>0 $ (called maturity) defined by: $ V_T=1_{ \{ \kappa_1\cdot S_T^{(1)}<\kappa_1\cdot K_1 \} } \cdot 1_{\{\kappa_2\cdot S_T^{(2)}<\kappa_2\cdot K_2\}} , \kappa_1,\kappa_2\in\{-1,+1\}$. We know that this product is dependent on the correlation between the two FX rates. HJow do trading desks measure the exposure to this correlation parameter? How do they hedge such options?

## Answer by Chiu-Tzu-Hsuan (score 2)

https://quant.stackexchange.com/a/75108

Dispersion trading is a way to mitigate correlation risk. The book "Foreign Exchange Option Pricing A Practitioners Guide" (Chapter 10 Multicurrency Options) introduces an analysis framework. Last, people use the gap to smooth out the barrier regarding digital options. i.e. using call/put spreads to replicate digital payoffs.

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.