Barrier option pricing for exchange rates under the Levy–HJM processes
In this paper, we present closed-forms for the valuation of the barrier option whose underlying is exchange rate under the multi-dimensional Levy process, including stochastic interest rates and stochastic assets. Instantaneous forward interest rates are assumed under the Heath et al. [1992. Econometrica 60, 77–105] framework, and the analytic formulas of the exchange rate barrier option are obtained when the Levy process is restricted in a double exponential process.
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- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- C. H. Hui & C. F. Lo, 2006. "Currency barrier option pricing with mean reversion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(10), pages 939-958, October.
- Paul Glasserman & S. G. Kou, 2003. "The Term Structure of Simple Forward Rates with Jump Risk," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 383-410.
- Johnson, Gordon & Schneeweis, Thomas, 1994. "Jump-Diffusion Processes in the Foreign Exchange Markets and the Release of Macroeconomic News," Computational Economics, Society for Computational Economics, vol. 7(4), pages 309-29.
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