Swing Options Valuation: A BSDE with Constrained Jumps Approach

Marie Bernhart; Huyên Pham; Peter Tankov; Xavier Warin

doi:10.1007/978-3-642-25746-9_12

Swing Options Valuation: A BSDE with Constrained Jumps Approach

Marie Bernhart
, Huyên Pham
, Peter Tankov
, Xavier Warin

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

Abstract

We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity A, the penalization parameter p > 0 and the time step. In particular, we obtain a convergence rate of the error due to penalization of order (Xp)^a~2 Va e (0, 1/2). Combining this approach with Monte Carlo techniques, we then work out the valuation problem.

Original language	English
Title of host publication	Numerical Methods in Finance
Pages	379-400
Number of pages	22
DOIs	https://doi.org/10.1007/978-3-642-25746-9_12
Publication status	Published - 1 Dec 2012
Externally published	Yes
Event	Workshop on Numerical Methods in Finance - Bordeaux, France Duration: 1 Jun 2010 → 2 Jun 2010

Publication series

Name	Springer Proceedings in Mathematics
Volume	12
ISSN (Print)	2190-5614
ISSN (Electronic)	2190-5622

Conference

Conference	Workshop on Numerical Methods in Finance
Country/Territory	France
City	Bordeaux
Period	1/06/10 → 2/06/10

Keywords

Backward stochastic differential equations with constrained jumps
Impulse control problems
Monte carlo methods
Swing options

Access to Document

10.1007/978-3-642-25746-9_12

Cite this

@inproceedings{5a9eaded9f6c4a4fbf37a692b65547e4,

title = "Swing Options Valuation: A BSDE with Constrained Jumps Approach",

abstract = "We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity A, the penalization parameter p > 0 and the time step. In particular, we obtain a convergence rate of the error due to penalization of order (Xp)a\textasciitilde{}2 Va e (0, 1/2). Combining this approach with Monte Carlo techniques, we then work out the valuation problem.",

keywords = "Backward stochastic differential equations with constrained jumps, Impulse control problems, Monte carlo methods, Swing options",

author = "Marie Bernhart and Huy{\^e}n Pham and Peter Tankov and Xavier Warin",

year = "2012",

month = dec,

day = "1",

doi = "10.1007/978-3-642-25746-9\_12",

language = "English",

isbn = "9783642257452",

series = "Springer Proceedings in Mathematics",

pages = "379--400",

booktitle = "Numerical Methods in Finance",

note = "Workshop on Numerical Methods in Finance ; Conference date: 01-06-2010 Through 02-06-2010",

}

TY - GEN

T1 - Swing Options Valuation

T2 - Workshop on Numerical Methods in Finance

AU - Bernhart, Marie

AU - Pham, Huyên

AU - Tankov, Peter

AU - Warin, Xavier

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity A, the penalization parameter p > 0 and the time step. In particular, we obtain a convergence rate of the error due to penalization of order (Xp)a~2 Va e (0, 1/2). Combining this approach with Monte Carlo techniques, we then work out the valuation problem.

AB - We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity A, the penalization parameter p > 0 and the time step. In particular, we obtain a convergence rate of the error due to penalization of order (Xp)a~2 Va e (0, 1/2). Combining this approach with Monte Carlo techniques, we then work out the valuation problem.

KW - Backward stochastic differential equations with constrained jumps

KW - Impulse control problems

KW - Monte carlo methods

KW - Swing options

U2 - 10.1007/978-3-642-25746-9_12

DO - 10.1007/978-3-642-25746-9_12

M3 - Conference contribution

AN - SCOPUS:84893556502

SN - 9783642257452

T3 - Springer Proceedings in Mathematics

SP - 379

EP - 400

BT - Numerical Methods in Finance

Y2 - 1 June 2010 through 2 June 2010

ER -

Swing Options Valuation: A BSDE with Constrained Jumps Approach

Abstract

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Keywords

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