Stochastic hyperbolic dynamics for infinite-dimensional forward rates and option pricing

Shin Ichi Aihara; Arunabha Bagchi

doi:10.1111/j.0960-1627.2005.00209.x

Stochastic hyperbolic dynamics for infinite-dimensional forward rates and option pricing

Shin Ichi Aihara, Arunabha Bagchi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

21 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	27-47
Number of pages	20
Journal	Mathematical finance
Volume	15
Issue number	1
DOIs	https://doi.org/10.1111/j.0960-1627.2005.00209.x
Publication status	Published - 2005

Keywords

European options
Stochastic hyperbolic systems
Option pricing
Completeness

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10.1111/j.0960-1627.2005.00209.x

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title = "Stochastic hyperbolic dynamics for infinite-dimensional forward rates and option pricing",

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.",

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AU - Bagchi, Arunabha

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AB - 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.

KW - European options

KW - Stochastic hyperbolic systems

KW - Option pricing

KW - Completeness

U2 - 10.1111/j.0960-1627.2005.00209.x

DO - 10.1111/j.0960-1627.2005.00209.x

M3 - Article

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VL - 15

SP - 27

EP - 47

JO - Mathematical finance

JF - Mathematical finance

IS - 1

ER -

Stochastic hyperbolic dynamics for infinite-dimensional forward rates and option pricing

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Keywords

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