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International Money and Stock Market Contingent Claims

  • Economics
  • Mathematics


We develop a unified approach with closed-form solutions for pricing bonds, stocks,currencies and their derivatives. The specification assumes a fundamental risk factorrepresented by a stochastic positive definite matrix following a Wishart autoregressive(WAR) process. By assuming a volatility-in-mean specification for the domestic stockreturns and the relative changes of the exchange rates, and a domestic stochastic discountfactor exponential affine with respect to the fundamental risk, it is possible to deriveclosed form solutions for the term structures of interest rates and for the risk neutralprobabilities. In particular:i) The domestic and foreign termstructures are jointly affine and correspond toWishartquadratic term structures, which can ensure the positivity of interest rates;ii) In this framework where the stock price follows a model with stochastic volatilitywe obtain explicit or quasi-explicit formulas for futures and forward contracts, swaps andoptions; this extends results by Heston (1993) and Ball, Roma (1994).

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