Pricing Options in Jump-Diffusion Models: An Extrapolation Approach

Published Online:https://doi.org/10.1287/opre.1070.0419

References

  • Amin K. I. Jump diffusion option valuation in discrete-time. J. Finance (1993) 48:1833–1863CrossrefGoogle Scholar
  • Andersen L., Andreasen J. Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing. Rev. Derivatives Res. (2000) 4:231–262CrossrefGoogle Scholar
  • Asmussen S., Rosinski J. Approximations of small jumps of Lévy processes with a view towards simulation. J. Appl. Probab. (2001) 38:482–493CrossrefGoogle Scholar
  • Bader G., Deuflhard P. A semi-implicit mid-point rule for stiff systems of ordinary differential equations. Numerische Mathematik (1983) 41:373–398CrossrefGoogle Scholar
  • Bates D. Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options. Rev. Financial Stud. (1996) 9(1):69–107CrossrefGoogle Scholar
  • Bates D. Post-'87 crash fears in the S&P 500 futures option market. J. Econometrics (2000) 94:181–238CrossrefGoogle Scholar
  • Bensoussan A., Lions J. L.Impulse Control and Quasi-Variational Inequalities (1984) (Gauthier-Villars, Paris, France) Google Scholar
  • Broadie M., Detemple J. American option valuation: New bounds, approximations, and a comparison of existing methods. Rev. Financial Stud. (1996) 9(4):1211–1250CrossrefGoogle Scholar
  • Broadie M., Kaya O. Exact simulation of stochastic volatility and other affine jump diffusion processes. Oper. Res. (2006) 54(2):217–231LinkGoogle Scholar
  • Broadie M., Yamamoto Y. Application of the fast Gauss transform to option pricing. Management Sci. (2003) 49(8):1071–1088LinkGoogle Scholar
  • Broadie M., Yamamoto Y. A double-exponential fast Gauss transform for pricing discrete path-dependent options. Oper. Res. (2005) 53(5):764–779LinkGoogle Scholar
  • Carr P., Hirsa A. Why be backward? Forward equations for American options. Risk (2003) 16(1):103–107Google Scholar
  • Carr P., Madan D. Option valuation using the fast Fourier transform. J. Comput. Finance (1999) 2(4):61–73CrossrefGoogle Scholar
  • Ciarlet P. G.The Finite Element Method for Elliptic Problems (1978) (North-Holland, Amsterdam, The Netherlands) Google Scholar
  • Cont R., Tankov P.Financial Modeling with Jump Processes (2004) (Chapman & Hall/CRC, Boca Raton, FL) Google Scholar
  • Cont R., Voltchkova E. A finite-difference scheme for option pricing in jump diffusion and exponential Lévy processes. SIAM J. Numer. Anal. (2005) 43(4):1596–1626CrossrefGoogle Scholar
  • Davis P.Circulant Matrices (1994) 2nd ed.(Chelsea Publishing Company, New York) Google Scholar
  • Deuflhard P. Recent progress in extrapolation methods for ordinary differential equations. SIAM Rev. (1985) 27(4):505–535CrossrefGoogle Scholar
  • Deuflhard P., Bornemann F.Scientific Computing with Ordinary Differential Equations (2002) (Springer, Berlin, Germany) CrossrefGoogle Scholar
  • d'Halluin Y., Forsyth P. A., Labahn G. A penalty method for American options with jump diffusion processes. Numerische Mathematik (2004) 97(2):321–352CrossrefGoogle Scholar
  • d'Halluin Y., Forsyth P. A., Vetzal K. R. Robust numerical methods for contingent claims under jump diffusion processes. IMA J. Numer. Anal. (2005) 25:87–112CrossrefGoogle Scholar
  • Duffie D., Pan J., Singleton K. Transform analysis and asset pricing for affine jump-diffusions. Econometrica (2000) 68(6):1343–1376CrossrefGoogle Scholar
  • Eraker B., Johannes M., Polson N. The impact of jumps in volatility and returns. J. Finance (2003) 58(3):1269–1300CrossrefGoogle Scholar
  • Eydeland A. A fast algorithm for computing integrals in function spaces: Financial applications. Comput. Econom. (1994) 7(4):277–285CrossrefGoogle Scholar
  • Feng L., Linetsky V. Pricing discretely monitored barrier options and defaultable bonds in Lévy process models: A Hilbert transform approach. Math. Finance. (2007) . ForthcomingGoogle Scholar
  • Glasserman P., Merener N. Numerical solution of jump-diffusion LIBOR market models. Finance Stochastics (2003) 7:1–27CrossrefGoogle Scholar
  • Hairer E., Wanner G.Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (1996) 2nd ed.(Springer, Berlin, Germany) CrossrefGoogle Scholar
  • Heston S. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. (1993) 6(2):327–343CrossrefGoogle Scholar
  • Hilber H., Matache A.-M., Schwab C. Sparse wavelet methods for option pricing under stochastic volatility. J. Comput. Finance (2005) 8(4):1–42CrossrefGoogle Scholar
  • Hirsa A., Madan D. B. Pricing American options under variance gamma. J. Comput. Finance (2003) 7(2):63–80CrossrefGoogle Scholar
  • Horn R. A., Johnson C. R.Topics in Matrix Analysis (1994) (Cambridge University Press, Cambridge, UK) Google Scholar
  • Hundsdorfer W., Verwer J. G.Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations (2003) (Springer, Berlin, Germany) CrossrefGoogle Scholar
  • Ibanez A. Robust pricing of the American put option: A note on Richardson extrapolation and the early exercise premium. Management Sci. (2003) 49(9):1210–1228LinkGoogle Scholar
  • Johnson C.Numerical Solution of Partial Differential Equations by the Finite Element Method (1987) (Cambridge University Press, Cambridge, UK) Google Scholar
  • Kangro R., Nicolaides R. Far field boundary conditions for Black-Scholes equations. SIAM J. Numer. Anal. (2000) 38(4):1357–1368CrossrefGoogle Scholar
  • Kou S. G. A jump-diffusion model for option pricing. Management Sci. (2002) 48(8):1086–1101LinkGoogle Scholar
  • Kou S. G., Wang H. First passage times of a jump diffusion process. Adv. Appl. Probab. (2003) 35:504–531CrossrefGoogle Scholar
  • Kou S. G., Wang H. Option pricing under a double exponential jump-diffusion model. Management Sci. (2004) 50:1178–1192LinkGoogle Scholar
  • Larsson S., Thomée V.Partial Differential Equations with Numerical Methods (2003) (Springer, Berlin, Germany) Google Scholar
  • Madan D. B., Milne F. Option pricing with V. G. Martingale components. Math. Finance (1991) 1(4):39–55CrossrefGoogle Scholar
  • Madan D. B., Seneta E. The variance gamma (V. G.) model for share market returns. J. Bus. (1990) 63(4):511–524CrossrefGoogle Scholar
  • Madan D. B., Carr P., Chang E. The variance gamma process and option pricing. Eur. Finance Rev. (1998) 2:79–105CrossrefGoogle Scholar
  • Marcozzi M. On the approximation of optimal stopping problems with application to financial mathematics. SIAM J. Sci. Comput. (2001) 22(5):1865–1884CrossrefGoogle Scholar
  • Matache A.-M., Nitsche P.-A., Schwab C. Wavelet Galerkin pricing of American options on Lévy driven assets. Quantitative Finance (2005a) 5(4):403–424CrossrefGoogle Scholar
  • Matache A.-M., Schwab C., Wihler T. P. Linear complexity solution of parabolic integro-differential equations. Numerische Mathematik (2006) . ForthcomingCrossrefGoogle Scholar
  • Matache A.-M., Schwab C., Wihler T. P. Fast numerical solution of parabolic integro-differential equations with applications in finance. SIAM J. Sci. Comput. (2005b) 27(2):369–393CrossrefGoogle Scholar
  • Matache A.-M., von Petersdorff T., Schwab C. Fast deterministic pricing of options on Lévy driven assets. Math. Model. Numer. Anal. (2004) 38(1):37–72CrossrefGoogle Scholar
  • Merton R. Option pricing when underlying stock returns are discontinuous. J. Financial Econom. (1976) 3:125–144CrossrefGoogle Scholar
  • Petrella G., Kou S. G. Numerical pricing of discrete barrier and lookback options via Laplace transforms. J. Comput. Finance (2004) 8:1–37CrossrefGoogle Scholar
  • Quarteroni A., Valli A.Numerical Approximation of Partial Differential Equations (1997) (Springer, Berlin, Germany) Google Scholar
  • Tavella D., Randall C.Pricing Financial Instruments: The Finite Difference Method (2000) (Wiley, New York) Google Scholar
  • Thomée V.Galerkin Finite Element Methods for Parabolic Problems (1997) (Springer, Berlin, Germany) CrossrefGoogle Scholar
  • Van Loan C.Computational Frameworks for the Fast Fourier Transform (1992) (SIAM, Philadelphia, PA) CrossrefGoogle Scholar
  • Vogel C. R.Computational Methods for Inverse Problems (2002) (SIAM, Philadelphia, PA) CrossrefGoogle Scholar
  • Zhang X.-L. Numerical analysis of American option pricing in a jump-diffusion model. Math. Oper. Res. (1997) 22(3):668–690LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.