Local volatility enhanced by a jump to default

Peter Carr, Dilip B. Madan

Research output: Contribution to journalArticle

Abstract

A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for General Motors and the Ford Motor Company over the period October 2004 to September 2007.

Original languageEnglish (US)
Pages (from-to)2-15
Number of pages14
JournalSIAM Journal on Financial Mathematics
Volume1
Issue number1
DOIs
StatePublished - 2010

Fingerprint

Volatility
Hazards
Jump
Swap
Equity
Hazard Rate Function
Hazard Rate
Stock Prices
Industry
Equity options
Hazard rate
Credit default swaps
Local volatility
Model
Volatility models
Stock prices
Option prices
General Motors

Keywords

  • Default adjusted drifts
  • Recovering default free option prices
  • Truncated power prices
  • Weibull distribution

ASJC Scopus subject areas

  • Applied Mathematics
  • Numerical Analysis
  • Finance

Cite this

Local volatility enhanced by a jump to default. / Carr, Peter; Madan, Dilip B.

In: SIAM Journal on Financial Mathematics, Vol. 1, No. 1, 2010, p. 2-15.

Research output: Contribution to journalArticle

Carr, Peter ; Madan, Dilip B. / Local volatility enhanced by a jump to default. In: SIAM Journal on Financial Mathematics. 2010 ; Vol. 1, No. 1. pp. 2-15.
@article{6f332660d4254b2a906ccdc32a5be980,
title = "Local volatility enhanced by a jump to default",
abstract = "A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for General Motors and the Ford Motor Company over the period October 2004 to September 2007.",
keywords = "Default adjusted drifts, Recovering default free option prices, Truncated power prices, Weibull distribution",
author = "Peter Carr and Madan, {Dilip B.}",
year = "2010",
doi = "10.1137/090750731",
language = "English (US)",
volume = "1",
pages = "2--15",
journal = "SIAM Journal on Financial Mathematics",
issn = "1945-497X",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - Local volatility enhanced by a jump to default

AU - Carr, Peter

AU - Madan, Dilip B.

PY - 2010

Y1 - 2010

N2 - A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for General Motors and the Ford Motor Company over the period October 2004 to September 2007.

AB - A local volatility model is enhanced by the possibility of a single jump to default. The jump has a hazard rate that is the product of the stock price raised to a prespecified negative power and a deterministic function of time. The empirical work uses a power of -1.5. It is shown how one may simultaneously recover from the prices of credit default swap contracts and equity option prices both the deterministic component of the hazard rate function and revised local volatility. The procedure is implemented on prices of credit default swaps and equity options for General Motors and the Ford Motor Company over the period October 2004 to September 2007.

KW - Default adjusted drifts

KW - Recovering default free option prices

KW - Truncated power prices

KW - Weibull distribution

UR - http://www.scopus.com/inward/record.url?scp=84871051304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871051304&partnerID=8YFLogxK

U2 - 10.1137/090750731

DO - 10.1137/090750731

M3 - Article

VL - 1

SP - 2

EP - 15

JO - SIAM Journal on Financial Mathematics

JF - SIAM Journal on Financial Mathematics

SN - 1945-497X

IS - 1

ER -