EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 2 (March-April 2025) ESAIM: M2AN, 59 2 (2025) 643-670 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
Page(s) 643 - 670
DOI https://doi.org/10.1051/m2an/2025003
Published online 11 February 2025
  1. Y. Achdou and O. Pironneau, Computational Methods for Option Pricing. Frontiers Appl. Math. Vol. 30. SIAM, Philadelphia (2005). [Google Scholar]
  2. G. Akrivis and C. Lubich, Fully implicit, linearly implicit and implicit–explicit backward difference formulae for quasi-linear parabolic equations. Numer. Math. 131 (2015) 713–735. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Avellaneda and A. Paras, Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model. Appl. Math. Finan. 3 (1996) 21–52. [CrossRef] [Google Scholar]
  4. M. Avellaneda, A. Levy and A. Parás, Pricing and hedging derivative securities in markets with uncertain volatilities. Appl. Math. Finan. 2 (1995) 73–88. [CrossRef] [Google Scholar]
  5. C. Baiocchi and M. Crouzeix, On the equivalence of A-stability and G-stability. Appl. Numer. Math. 5 (1989) 19–22. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Barles and H.M. Soner, Option pricing with transaction costs and a nonlinear Black–Scholes equation. Finan. Stoch. 2 (1998) 369–397. [CrossRef] [Google Scholar]
  7. F.S. Black and M. Scholes, The pricing of options and corporate liabilities. J. Political Econ. 81 (1973) 637–654. [CrossRef] [MathSciNet] [Google Scholar]
  8. L. Boen and K.J. in ’t Hout, Operator splitting schemes for American options under the two-asset Merton jump-diffusion model. Appl. Numer. Math. 153 (2020) 114–131. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Boen and K.J. in ’t Hout, Operator splitting schemes for the two-asset Merton jump-diffusion model. J. Comput. Appl. Math. 387 (2021) 112309. [CrossRef] [Google Scholar]
  10. P.P. Boyle and T. Vorst, Option replication in discrete time with transaction costs. J. Finan. 47 (1992) 271–293. [CrossRef] [Google Scholar]
  11. M. Briani, C. La Chioma and R. Natalini, Convergence of numerical schemes for viscosity solutions to integro-differential degenerate parabolic problems arising in financial theory. Numer. Math. 98 (2004) 607–646. [Google Scholar]
  12. R. Company, E. Navarro, J.R. Pintos and E. Ponsoda, Numerical solution of linear and nonlinear Black–Scholes option pricing equations. Comput. Math. Appl. 56 (2008) 813–821. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Company, L. Jódar and J.R. Pintos, Consistent stable difference scheme for nonlinear Black–Scholes equations modelling option pricing wiht transaction costs. Math. Model. Numer. Anal. 43 (2009) 1045–1061. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. R. Company, L. Jódar and J.R. Pintos, A numerical method for European Option Pricing with transaction costs nonlinear equation. Math. Comput. Model. 50 (2009) 910–920. [CrossRef] [Google Scholar]
  15. R. Company, L. Jódar, E. Ponsoda and C. Ballester, Numerical analysis and simulation of option pricing problems modeling illiquid markets. Comput. Math. Appl. 59 (2010) 2964–2975. [CrossRef] [MathSciNet] [Google Scholar]
  16. R. Company, L. Jódar and J.R. Pintos, A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets. Math. Comput. Simul. 82 (2012) 1972–1985. [CrossRef] [Google Scholar]
  17. R. Cont and P. Tankov, Financial Modelling with Jump Processes. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC (2003). [Google Scholar]
  18. R. Cont and E. Voltchkova, A finite difference scheme for option pricing in jump diffusion and exponential Lévy models. SIAM J. Numer. Anal. 43 (2005) 1596–1624. [CrossRef] [MathSciNet] [Google Scholar]
  19. J.M.T.S. Cruz and D. Ševčovič, Option pricing in illiquid markets with jumps. Appl. Math. Finan. 25 (2018) 395–415. [CrossRef] [Google Scholar]
  20. G. Dahlquist, G-stability is equivalent to A-stability. BIT. Numer. Math. 18 (1978) 384–401. [CrossRef] [Google Scholar]
  21. M.H. Davis, V.G. Panas and T. Zariphopoulou, European option pricing with transaction costs. SIAM J. Control Optim. 31 (1993) 470–493. [CrossRef] [MathSciNet] [Google Scholar]
  22. F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing. Math. Ann. 300 (1994) 463–520. [CrossRef] [MathSciNet] [Google Scholar]
  23. Y. d’Halluin, P.A. Forsyth and K.R. Vetzal, Robust numerical methods for contingent claims under jump diffusion processes. IMA J. Numer. Anal. 25 (2005) 87–112. [Google Scholar]
  24. D.J. Duffy, Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. John Wiley & Sons, Ltd. (2006). [CrossRef] [Google Scholar]
  25. B. Düring, M. Fournié and A. Jüngel, High order compact finite difference schemes for a nonlinear Black–Scholes equation. Int. J. Theor. Appl. Finan. 6 (2003) 767–789. [CrossRef] [Google Scholar]
  26. B. Düring, M. Fournié and A. Jüngel, Convergence of a high-order compact finite difference scheme for a nonlinear black-scholes equation. ESAIM. Math. Model. Numer. Anal. 38 (2004) 359–369. [CrossRef] [EDP Sciences] [Google Scholar]
  27. M. Ehrhardt and R. Valkov, An uncondtionally stable explicit finite difference scheme for nonlinear European option pricing problems. Report, BUW-IMACM (October, 2013). [Google Scholar]
  28. X.V. Eynde, J. Servais and M. Lamberigts, Surface oxide maturation and selfreduction: a new process to ensure trip steel hot dip galvanizing. Galvatech 4 (2004) 361–372. [Google Scholar]
  29. R. Frey, Market Illiquidity as a Source of Model Risk in Dynamic Hedging. Risk Publication, London (2000). [Google Scholar]
  30. R. Frey and P. Patie, Risk management for derivatives in illiquid markets: a simulation study, in Advances in Finance and Stochastics, edited by K. Sandmann and P. Schönbucher. Springer, Berlin (2002) 137–159. [Google Scholar]
  31. R. Frey and A. Stremme, Market volatility and feedback effects from dynamic hedging. Math. Finan. 7 (1997) 351–374. [CrossRef] [Google Scholar]
  32. J. Guo and W. Wang, An unconditionally stable, positivity-preserving splitting scheme for nonlinear Black–Scholes equation with transaction costs. Sci. World J. 2014 (2014) 525207. [Google Scholar]
  33. J. Guo and W. Wang, On the numerical solution of nonlinear option pricing equation in illiquid markets. Comput. Math. Appl. 69 (2015) 117–133. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Guyon and P. Henry-Labordére, Nonlinear Option Pricing. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC (2013). [Google Scholar]
  35. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics v.14, 2nd revised edition. Springer-Verlag, Berlin Heidelberg (2002). [CrossRef] [Google Scholar]
  36. P. Heider, Numerical methods for non-linear Black–Scholes equations. Appl. Math. Finan. 17 (2010) 59–81. [CrossRef] [Google Scholar]
  37. A. Hirsa, Computational Methods in Finance, English Photocopy Version. China Machine Press, Beijing (2016). [CrossRef] [Google Scholar]
  38. S. Hodges, Optimal replication of contingent claims under transactioncosts. Rev. Futures Market 8 (1989) 222–239. [Google Scholar]
  39. T. Hoggard, A.E. Whalley and P. Wilmott, Hedging option portfolios in the presence of tranaction costs. Adv. Futures Option Res. 7 (1994) 21–35. [Google Scholar]
  40. M. Jandačka and D. Ševčovič, On the risk-adjusted pricing-methodology-based valuation of vanilla options and explantion of the volatility smile. J. Appl. Math. 3 (2005) 235–258. [CrossRef] [Google Scholar]
  41. M.K. Kadalbajoo, L.P. Tripathi and A. Kumar, Second order accurate IMEX methods for option pricing under Merton and Kou jump-diffusion models. J. Sci. Comput. 65 (2015) 979–1024. [CrossRef] [MathSciNet] [Google Scholar]
  42. M.K. Kadalbajoo, A. Kumar and L.P. Tripathi, A radial basis function based implicit–explicit method for option pricing under jump-diffusion models. Appl. Numer. Math. 110 (2016) 159–173. [Google Scholar]
  43. M.K. Kadalbajoo, L.P. Tripathi and A. Kumar, An error analysis of a finite element method with IMEX-time semidiscretizations for some partial integro-differential inequalities arising in the pricing of American options. SIAM J. Numer. Anal. 55 (2017) 869–891. [Google Scholar]
  44. S.G. Kou, A jump-diffusion model for option pricing. Manage. Sci. 48 (2002) 1086–1101. [CrossRef] [Google Scholar]
  45. S.G. Kou and H. Wang, Option pricing under a double exponential jump diffusion model. Manage. Sci. 50 (2004) 1178–1192. [CrossRef] [Google Scholar]
  46. Y. Kwon and Y. Lee, A second-order finite difference method for option pricing under jump-diffusion models. SIAM J. Numer. Anal. 49 (2011) 2598–2617. [Google Scholar]
  47. H.E. Leland, Option pricing and replication with transactions costs. J. Finan. 40 (1985) 1283–1301. [CrossRef] [Google Scholar]
  48. T.J. Lyons, Uncertain volatility and the risk-free synthesis of derivatives. Appl. Math. Finan. 2 (1995) 117–133. [CrossRef] [Google Scholar]
  49. M.C. Mariani and I. SenGupta, Nonlinear problems modeling stochastic volatility and transaction costs. Quant. Finan. 4 (2012) 663–670. [CrossRef] [Google Scholar]
  50. M.C. Mariani, I. SenGupta and P. Bezdek, Numerical solutions for option pricing models including transaction costs and stochastic volatility. Acta Appl. Math. 118 (2012) 203–220. [CrossRef] [MathSciNet] [Google Scholar]
  51. A.M. Matache, T. von Petersdorff and C. Schwab, Fast deterministic pricing of options on Lévy driven assets. ESAIM: M2AN 38 (2004) 37–71. [CrossRef] [EDP Sciences] [Google Scholar]
  52. R.C. Merton, Theory of rational option pricing. Bell J. Econ. Manag. Sci. (1973) 141–183. [CrossRef] [Google Scholar]
  53. R.C. Merton, Option pricing when underlying stock returns are discontinuous. J. Finan. Econ. 3 (1976) 125–144. [CrossRef] [Google Scholar]
  54. O. Nevanlinna and F. Odeh, Multiplier techniques for linear multistep methods. Numer. Funct. Anal. Optim. 3 (1981) 377–423. [Google Scholar]
  55. D.M. Pooley, P.A. Forsyth and K.R. Vetzal, Numerical convergence properties of option pricing PDEs with uncertain volatility. IMA J. Numer. Anal. 23 (2003) 241–267. [CrossRef] [MathSciNet] [Google Scholar]
  56. K. Ronnie Sircar and G. Papanicolaou, General Black–Scholes models accounting for increased market volatility from hedging strategies. Appl. Math. Finan. 5 (1998) 45–82. [CrossRef] [Google Scholar]
  57. S. Salmi, J. Toivanen and L. von Sydow, An IMEX-scheme for pricing options under stochastic volatility models with jumps. SIAM J. Sci. Comput. 36 (2014) B817–B834. [CrossRef] [Google Scholar]
  58. D. Tavella and C. Randall, Pricing Financial Instuments: The Finite Difference Method. John Wiley & Sons, Chichester, UK (2000). [Google Scholar]
  59. W. Wang, Y. Chen and H. Fang, On the variable two-step IMEX BDF method for parabolic integro-differential equations with nonsmooth initial data arising in finance. SIAM J. Numer. Anal. 57 (2019) 1289–1317. [CrossRef] [MathSciNet] [Google Scholar]
  60. W. Wang, M. Mao and Z. Wang, An efficient variable step-size method for options pricing under jump-diffusion models with nonsmooth payoff function. ESAIM. Math. Model. Numer. Anal. 55 (2021) 913–938. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  61. W.S. Wang, M.L. Mao and Y. Huang, A posteriori error control and adaptivity for the IMEX BDF2 method for PIDEs with application to options pricing models. J. Sci. Comput. 93 (2022) 55. [CrossRef] [Google Scholar]
  62. P. Wilmott and P.J. Schönbucher, The feedback effect of hedging in illiquid markets. SIAM J. Appl. Math. 61 (2000) 232–272. [CrossRef] [MathSciNet] [Google Scholar]
  63. S. Zhou, W. Li, Y. Wei and C. Wen, A positivity-preserving numerical scheme for nonlinear option pricing models. J. Appl. Math. 2012 (2012) 205686. [CrossRef] [Google Scholar]
  64. S. Zhou, L. Han, W. Li, Y. Zhang and M. Han, A positivity-preserving numerical scheme for option pricing model with transaction costs under jump-diffusion process. J. Comput. Appl. Math. 34 (2015) 881–900. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you