Pricing of defaultable securities under stochastic interest

Nino Kordzakhia; Alexander Novikov

doi:10.1007/978-3-540-69532-5_14

Pricing of defaultable securities under stochastic interest

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We reduce a problem of pricing continuously monitored defaultable securities (barrier options, corporate debts) in a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. In the case when the interest rate is governed by a linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also find an estimation of the rate of convergence of the suggested approximation and illustrate results by numerical examples.

Original language	English
Title of host publication	Mathematical Control Theory and Finance
Editors	Andrey Sarychev, Albert Shiryaev, Manuel Guerra, Maria do Rosário Grossinho
Place of Publication	Berlin; London
Publisher	Springer, Springer Nature
Pages	251-263
Number of pages	13
ISBN (Electronic)	9783540695325
ISBN (Print)	9783540695318
DOIs	https://doi.org/10.1007/978-3-540-69532-5_14
Publication status	Published - 2008

Access to Document

10.1007/978-3-540-69532-5_14

Cite this

@inbook{f75f667efa6f4ebeb6f5be6c3df4da00,

title = "Pricing of defaultable securities under stochastic interest",

abstract = "We reduce a problem of pricing continuously monitored defaultable securities (barrier options, corporate debts) in a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. In the case when the interest rate is governed by a linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also find an estimation of the rate of convergence of the suggested approximation and illustrate results by numerical examples.",

author = "Nino Kordzakhia and Alexander Novikov",

year = "2008",

doi = "10.1007/978-3-540-69532-5_14",

language = "English",

isbn = "9783540695318",

pages = "251--263",

editor = "Andrey Sarychev and Albert Shiryaev and Manuel Guerra and Grossinho, {Maria do Ros{\'a}rio}",

booktitle = "Mathematical Control Theory and Finance",

publisher = "Springer, Springer Nature",

address = "United States",

}

Pricing of defaultable securities under stochastic interest. / Kordzakhia, Nino; Novikov, Alexander.
Mathematical Control Theory and Finance. ed. / Andrey Sarychev; Albert Shiryaev; Manuel Guerra; Maria do Rosário Grossinho. Berlin; London: Springer, Springer Nature, 2008. p. 251-263.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Pricing of defaultable securities under stochastic interest

AU - Kordzakhia, Nino

AU - Novikov, Alexander

PY - 2008

Y1 - 2008

N2 - We reduce a problem of pricing continuously monitored defaultable securities (barrier options, corporate debts) in a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. In the case when the interest rate is governed by a linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also find an estimation of the rate of convergence of the suggested approximation and illustrate results by numerical examples.

AB - We reduce a problem of pricing continuously monitored defaultable securities (barrier options, corporate debts) in a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. In the case when the interest rate is governed by a linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also find an estimation of the rate of convergence of the suggested approximation and illustrate results by numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=84895325800&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-69532-5_14

DO - 10.1007/978-3-540-69532-5_14

M3 - Chapter

AN - SCOPUS:84895325800

SN - 9783540695318

SP - 251

EP - 263

BT - Mathematical Control Theory and Finance

A2 - Sarychev, Andrey

A2 - Shiryaev, Albert

A2 - Guerra, Manuel

A2 - Grossinho, Maria do Rosário

PB - Springer, Springer Nature

CY - Berlin; London

ER -

Pricing of defaultable securities under stochastic interest

Abstract

Access to Document

Other files and links

Fingerprint

Cite this