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

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 p...

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Published inMathematical finance Vol. 15; no. 1; pp. 27 - 47
Main Authors Aihara, Shin Ichi, Bagchi, Arunabha
Format Journal Article
LanguageEnglish
Published 350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK Blackwell Publishing, Inc 01.01.2005
Wiley Blackwell
Blackwell Publishing Ltd
SeriesMathematical Finance
Subjects
Capital market
completeness
European options
Financial economics
Forward deals
Interest rates
Mathematical economics
Methodology
Option pricing
Options trading
Partial differential equations
Prices
Statistical methods
stochastic hyperbolic systems
Stochastic models
Studies
Term structure
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Summary: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.
Bibliography:ArticleID:MAFI209
ark:/67375/WNG-TQDMK2WT-H
istex:1849208FF7347CC28E2B3567CFD2B739945CF15D
Manuscript received November 2002; final revision received February 2004.
This work was partially supported by the MEXT, Grants‐in‐Aid for Scientific Research 14550456(c).
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SourceType-Scholarly Journals-1
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ISSN:0960-1627
1467-9965
DOI:10.1111/j.0960-1627.2005.00209.x