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Bonds and Options in Exponentially Affine Bond Models

Bermin, Hans-Peter LU (2012) In Applied Mathematical Finance 19(6). p.513-534
Abstract
In this article we apply the Flesaker–Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox–Ingersoll–Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that... (More)
In this article we apply the Flesaker–Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox–Ingersoll–Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that allows the yield curve to be inverted and is consistent with the CIR dynamics for the abstract short rate, thus giving rise to closed form bond option and swaption prices. (Less)
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
interest rates, yield curve, term structure, bonds, bond options, swaptions, square-root process, exponentially affine measure
in
Applied Mathematical Finance
volume
19
issue
6
pages
22 pages
publisher
Routledge
external identifiers
  • scopus:84867280118
ISSN
1350-486X
DOI
10.1080/1350486X.2011.646505
language
English
LU publication?
no
id
7ebcf490-5b31-47d9-a958-3c148f61d65a
date added to LUP
2017-01-21 16:46:36
date last changed
2017-04-02 04:34:25
@article{7ebcf490-5b31-47d9-a958-3c148f61d65a,
  abstract     = {In this article we apply the Flesaker–Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox–Ingersoll–Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that allows the yield curve to be inverted and is consistent with the CIR dynamics for the abstract short rate, thus giving rise to closed form bond option and swaption prices.},
  author       = {Bermin, Hans-Peter},
  issn         = {1350-486X},
  keyword      = {interest rates,yield curve,term structure,bonds,bond options,swaptions,square-root process,exponentially affine measure},
  language     = {eng},
  number       = {6},
  pages        = {513--534},
  publisher    = {Routledge},
  series       = {Applied Mathematical Finance},
  title        = {Bonds and Options in Exponentially Affine Bond Models},
  url          = {http://dx.doi.org/10.1080/1350486X.2011.646505},
  volume       = {19},
  year         = {2012},
}