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STOCHASTIC HYPERBOLIC DYNAMICS FOR INFINITE‐DIMENSIONAL FORWARD RATES AND OPTION PRICING
Author(s) -
Aihara Shin Ichi,
Bagchi Arunabha
Publication year - 2005
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2005.00209.x
Subject(s) - forward rate , term (time) , stochastic differential equation , mathematical economics , mathematics , arbitrage , rendleman–bartter model , econometrics , partial differential equation , short rate , economics , interest rate , heath–jarrow–morton framework , short rate model , yield curve , financial economics , mathematical analysis , volatility (finance) , physics , quantum mechanics , monetary economics
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.