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Factor Models Of Domestic And Foreign Interest Rates With Stochastic Volatilities

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  • Antoine Frachot
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    Abstract

    We consider a two-country economy under the nonarbitrage assumption and where volatilities are stochastic. Assuming the existence of state variables, we show that, under some mild volatility assumptions, the model is actually fully specified. In particular, both term structure dynamics and the exchange rate process can be given endogeneously under the risk-neutral probability. We then derive the exact dependence of the zero-coupon bonds and the exchange rate on the underlying state variables. As a result, some closed-form solutions can be proposed for the derivative assets as futures and options written on foreign zero-coupon bonds. Copyright 1995 Blackwell Publishers.

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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 5 (1995)
    Issue (Month): 2 ()
    Pages: 167-185

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    Handle: RePEc:bla:mathfi:v:5:y:1995:i:2:p:167-185

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    Cited by:
    1. Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.
    2. Vincenzo Costa, 2004. "Risk neutral valuation and uncovered interest rate parity in a stochastic two-country-economy with two goods," Economics Bulletin, AccessEcon, vol. 3(43), pages 1-10.
    3. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc S., 2006. "Accurate Value-at-Risk forecast with the (good old) normal-GARCH model," CFS Working Paper Series 2006/23, Center for Financial Studies (CFS).
    4. Hartz, Christoph & Mittnik, Stefan & Paolella, Marc, 2006. "Accurate value-at-risk forecasting based on the normal-GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2295-2312, December.
    5. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.
    6. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
    7. Driessen, Joost & Melenberg, Bertrand & Nijman, Theo, 2003. "Common factors in international bond returns," Journal of International Money and Finance, Elsevier, vol. 22(5), pages 629-656, October.
    8. Thomas Kaiser, 1996. "One-Factor-GARCH Models for German Stocks - Estimation and Forecasting -," Econometrics 9612007, EconWPA.
    9. Samson Assefa, 2007. "Calibration and Pricing in a Multi-Factor Quadratic Gaussian Model," Research Paper Series 197, Quantitative Finance Research Centre, University of Technology, Sydney.

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