Abstract
Gauss-Hermite quadrature together with a finite difference method is used to solve numerically jump-diffusion two-asset option pricing problem consisting in a partial integro-differential equation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Dover Books on Mathematics, New York (1961)
Barles, G., Soner, H.M.: Option pricing with transaction costs and a nonlinear Black-Scholes equation. Finance Stoch. 2, 369–397 (1998)
Clift, S.S., Forsyth, P.A.: Numerical solution of two asset jump diffusion models for option valuation. Appl. Numer. Math. 58, 743–782 (2008)
Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Finance Mathematical Series. Chapman & Hall/CRC, Boca Raton (2004)
Duffy, D.J.: Finite Difference Methods in Financial Engineering: A Partial Differential Approach. Wiley, Chichester (2006)
Dupire, B.: Arbitrage pricing with stochastic volatility. Technical Report, Banque Paribas Swaps and Options Research Team Monograph (1993)
Ehrhardt, M., Mickens, R.A.: A fast, stable and accurate numerical method for the Black–Scholes equation of American options. Int. J. Theor. Appl. Finance 11, 471–501 (2008)
Fakharany, M., Company, R., Jódar, L.: Positive finite difference schemes for partial integro-differential option pricing model. Appl. Math. Comput. 249, 320–332 (2014)
Fakharany, M., Company, R., Jódar, L.: Solving partial integro-differential option pricing problems for a wide class of infinite activity Lévy processes. J. Comput. Appl. Math. 296, 739–752 (2016)
Garabedian, P.R.: Partial Differential Equations. AMS Chelsea Pubs. Co., Providence, R.I. (1998)
Heston, S.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6, 327–343 (1993)
Kangro, R., Nicolaides, R.: Far field boundary conditions for Black–Scholes equations. SIAM J. Numer. Anal. 38(4), 1357–1368 (2000)
Rambeerich, N., Tangman, D.Y., Lollchund, M.R., Bhuruth, M.: High-order computational methods for option valuation under multifactor models. Eur. J. Oper. Res. 224, 219–226 (2013)
Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd edn. Clarendon Press, Oxford (1985)
Zvan, R., Forsyth, P.A., Vetzal, K.R.: Negative coefficients in two-factor option pricing models. J. Comput. Finance 7 (1), 37–73 (2003)
Acknowledgements
This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economía y Competitividad Spanish grant MTM2013-41765-P.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Jódar, L., Fakharany, M., Company, R. (2017). 2D Gauss-Hermite Quadrature Method for Jump-Diffusion PIDE Option Pricing Models. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 2. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59387-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-59387-6_14
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-59386-9
Online ISBN: 978-3-319-59387-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)