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Representing Foreign-Currency Forwards in Linear VaR Models

Article Quant Q&A · Author: Guess601
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Summary

The document asks why a foreign-currency forward can be treated as a linear instrument for value-at-risk analysis. The quoted textbook framing represents a forward to buy foreign currency as a long position in a foreign bond and a short position in a domestic bond. The questioner understands the component concepts but seeks the reasoning behind this decomposition, and suggests that the payoff’s linear response to the underlying at maturity may explain the classification.

No answer or derivation is included, so the document does not establish the bond-based representation or explain how it is used to calculate VaR. It mainly identifies a conceptual issue: a forward’s value depends on exchange rates and the relative values of the two currencies over the contract’s life, while its terminal payoff is linear in spot. Readers should treat the proposed intuition as a question posed for clarification rather than a demonstrated result.

Key ideas

  • The document asks why a foreign-currency forward is classified as linear for VaR.
  • The stated representation combines a long foreign bond position with a short domestic bond position.
  • The questioner proposes linearity of the terminal payoff as a possible explanation.
  • No derivation or answer is provided to resolve the question.

Tags

ForexRisk managementDerivatives pricing
Full text
# A forward contract to buy a foreign currency can be handled by a linear model


# A forward contract to buy a foreign currency can be handled by a linear model












In Hull's book, he says that: "An example of a derivative that can be handled by the linear model is a forward contract to buy a foreign currency." Then he continues with, "For the purposes of calculating VaR, the forward contract is therefore treated as a long position in the foreign bond combined with a short position in the domestic bond." I know what a linear model, forward contract, bonds, long/short position, and VaR mean by studying Hull's book. But I still cannot understand his reasoning. My intuition says that a forward contract can be handled by a linear model because a change in the price of the underlying asset translates linearly to the value of the contract at maturity.

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