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Locally Complete Markets, Exchange Rates and Currency Options

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Abstract

This paper extends the Heath, Jarrow and Morton model (1992) to atwo country setup. In the presence of common shocks and country specificshocks, we retrieve each country's pricing kernel implied by itsterm structure dynamics and show that the pricing kernels impose a constrainton the exchange rate to be the ratio of the pricing kernels. Under therisk neutral measure, the drift of the exchange rate is the interest ratedifferential, and the volatility reflects the forward rate risk-premiumdifferential of the two countries. The result implies that the risk premiumwill enter the currency option pricing model through the volatility term.Under the assumption of non-stochastic forward rate drift and volatility,we are able to derive closed-form solutions for currency options.

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Authors and Affiliations

  1. Kenan-Flagler Business School, University of North Carolina-Chapel Hill, China

    Dong-Hyun Ahn (Associate Professor of Finance)

  2. Kenan-Flagler Business School, Universit y of North Carolina-Chapel Hill, China

    Bin Gao (Associate Professor of Finance)

  3. China Center for Financial Research, Tsinghua University, China

    Bin Gao (Associate Professor of Finance)

Authors
  1. Dong-Hyun Ahn
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  2. Bin Gao
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Ahn, DH., Gao, B. Locally Complete Markets, Exchange Rates and Currency Options. Review of Derivatives Research 6, 5–26 (2003). https://doi.org/10.1023/A:1022869920134

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