STOCHASTIC HYPERBOLIC DYNAMICS FOR INFINITE‐DIMENSIONAL FORWARD RATES AND OPTION PRICING

Shin Ichi Aihara and Arunabha Bagchi

Mathematical Finance, 2005, vol. 15, issue 1, 27-47

Abstract: We model the term‐structure modeling of interest rates by considering the forward rate as the solution of a stochastic hyperbolic partial differential equation. First, we study the arbitrage‐free model of the term structure and explore the completeness of the market. We then derive results for the pricing of general contingent claims. Finally we obtain an explicit formula for a forward rate cap in the Gaussian framework from the general results.

Date: 2005
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