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International money and stock market contingent claims

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  • Gourieroux, C.
  • Monfort, A.
  • Sufana, R.

Abstract

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

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Bibliographic Info

Article provided by Elsevier in its journal Journal of International Money and Finance.

Volume (Year): 29 (2010)
Issue (Month): 8 (December)
Pages: 1727-1751

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Handle: RePEc:eee:jimfin:v:29:y:2010:i:8:p:1727-1751

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Web page: http://www.elsevier.com/locate/inca/30443

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Keywords: Quadratic term structure Exchange rates Stochastic volatility model Wishart process Futures Forward contract;

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Citations

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Cited by:
  1. Bertholon, H. & Monfort, A. & Pegoraro, F., 2008. "Econometric Asset Pricing Modelling," Working papers 223, Banque de France.
  2. Gourieroux, Christian & Sufana, Razvan, 2011. "Discrete time Wishart term structure models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 815-824, June.
  3. Alessandro Gnoatto & Martino Grasselli, 2011. "The explicit Laplace transform for the Wishart process," Papers 1107.2748, arXiv.org, revised Aug 2013.
  4. Gourieroux, C. & Monfort, A., 2013. "Linear-price term structure models," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 24-41.

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