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BENCHOP–SLV : the BENCHmarking project in Option Pricing–Stochastic and Local Volatility problems

von Sydow, Lina ; Milovanović, Slobodan ; Larsson, Elisabeth ; In't Hout, Karel ; Wiktorsson, Magnus LU ; Oosterlee, Cornelis W. ; Shcherbakov, Victor ; Wyns, Maarten ; Leitao, Alvaro and Jain, Shashi , et al. (2019) In International Journal of Computer Mathematics
Abstract

In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE) formulation and the Partial Differential Equation (PDE) formulation of the problem, as well as Fourier methods making use of the characteristic function, were implemented to solve these problems. Comparisons are made with respect to time to reach a certain error level in the computed solution for the different methods. The implemented Fourier method was superior to all others for the two problems where it... (More)

In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE) formulation and the Partial Differential Equation (PDE) formulation of the problem, as well as Fourier methods making use of the characteristic function, were implemented to solve these problems. Comparisons are made with respect to time to reach a certain error level in the computed solution for the different methods. The implemented Fourier method was superior to all others for the two problems where it was implemented. Generally, methods targeting the PDE formulation of the problem outperformed the methods for the SDE formulation. Among the methods for the PDE formulation the ADI method stood out as the best performing one.

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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
65-02, 91G20, 91G60, benchmark problem, characteristic function, numerical methods, Option pricing, partial differential equation, stochastic and local volatility, stochastic differential equation
in
International Journal of Computer Mathematics
publisher
Taylor & Francis
external identifiers
  • scopus:85057570384
ISSN
0020-7160
DOI
10.1080/00207160.2018.1544368
language
English
LU publication?
yes
id
a2ff2532-2457-4100-958a-dea906b4ef8d
date added to LUP
2018-12-20 17:22:16
date last changed
2022-04-25 19:40:36
@article{a2ff2532-2457-4100-958a-dea906b4ef8d,
  abstract     = {{<p>In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE) formulation and the Partial Differential Equation (PDE) formulation of the problem, as well as Fourier methods making use of the characteristic function, were implemented to solve these problems. Comparisons are made with respect to time to reach a certain error level in the computed solution for the different methods. The implemented Fourier method was superior to all others for the two problems where it was implemented. Generally, methods targeting the PDE formulation of the problem outperformed the methods for the SDE formulation. Among the methods for the PDE formulation the ADI method stood out as the best performing one.</p>}},
  author       = {{von Sydow, Lina and Milovanović, Slobodan and Larsson, Elisabeth and In't Hout, Karel and Wiktorsson, Magnus and Oosterlee, Cornelis W. and Shcherbakov, Victor and Wyns, Maarten and Leitao, Alvaro and Jain, Shashi and Haentjens, Tinne and Waldén, Johan}},
  issn         = {{0020-7160}},
  keywords     = {{65-02; 91G20; 91G60; benchmark problem; characteristic function; numerical methods; Option pricing; partial differential equation; stochastic and local volatility; stochastic differential equation}},
  language     = {{eng}},
  publisher    = {{Taylor & Francis}},
  series       = {{International Journal of Computer Mathematics}},
  title        = {{BENCHOP–SLV : the BENCHmarking project in Option Pricing–Stochastic and Local Volatility problems}},
  url          = {{http://dx.doi.org/10.1080/00207160.2018.1544368}},
  doi          = {{10.1080/00207160.2018.1544368}},
  year         = {{2019}},
}