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Research Papers

Lookback option pricing using the Fourier transform B-spline method

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Pages 789-803 | Received 08 Nov 2012, Accepted 06 Jan 2014, Published online: 27 Mar 2014

References

  • AitSahlia, F. and Lai, T.L., Valuation of discrete barrier and hindsight options. J. Financ. Eng., 1997, 6, 169–177.
  • Atkinson, C. and Fusai, G., Discrete extrema of Brownian motion and pricing of exotic options. J. Comput. Finance, 2007, 10, 1–44.
  • Babbs, S., Binomial valuation of lookback options. Unpublished Working Paper, 1992.
  • Beckers, S., The constant elasticity of variance model and its implications for option pricing. J. Finance, 1980, 35, 661–673.
  • Black, F. and Scholes, M., The pricing of options and corporate liabilities. J. Polit. Econ., 1973, 81, 637–654.
  • Borovkov, K. and Novikov, A., On a new approach to calculating expectations for option pricing. J. Appl. Probab., 2002, 39, 889–895.
  • Boyle, P.P. and Tian, Y., Pricing lookback and barrier options under the CEV process. J. Financ. Quant. Anal., 1999, 34, 241–264.
  • Broadie, M., Glasserman, P. and Kou, S.G., Connecting discrete and continuous path-dependent options. Finance Stoch., 1999, 3, 55–82.
  • Broadie, M. and Yamamoto, Y., A double-exponential fast Gauss transform algorithm for pricing discrete path-dependent options. Oper. Res., 2005, 53, 764–779.
  • Cai, N. and Kou, S.G., Option pricing under a mixed-exponential jump diffusion model. Manage. Sci., 2011, 57, 2067–2081.
  • Carr, P.P., Geman, H., Madan, D.B. and Yor, M., The fine structure of asset returns: An empirical investigation. J. Bus., 2002, 75, 305–333.
  • Carr, P.P. and Madan, D., Option valuation using the fast Fourier transform. J. Comput. Finance, 1999, 2, 61–73.
  • Chourdakis, K., Option pricing using the fractional FFT. J. Comput. Finance, 2005, 8, 1–18.
  • Conze, A. and Viswanathan, R., Path dependent options: The case of lookback options. J. Finance, 1991, 46, 1893–1907.
  • De Boor, C., A Practical Guide to Splines, 2001 (Springer Verlag: New York).
  • Delbaen, F. and Schachermayer, W., A general version of the fundamental theorem of asset pricing. Math. Ann., 1994, 300, 463–520.
  • Dufresne, D., Garrido, J. and Morales, M., Fourier inversion formulas in option pricing and insurance. Methodol. Comput. Appl. Probab., 2009, 11, 359–383.
  • Eberlein, E., Application of generalized hyperbolic Lévy motion to Finance. In Lévy Processes Theory and Applications, edited by O.E. Barndorff-Nielsen, T. Mikosch, and S. Resnick, pp. 319–337, 2001 (Birkhauser: Basel).
  • Eberlein, E., Glau, K. and Papapantoleon, A., Analysis of Fourier transform valuation formulas and applications. Appl. Math. Finance, 2010, 17, 211–240.
  • Eberlein, E., Papapantoleon, A. and Shiryaev, A.N., On the duality principle in option pricing: Semimartingale setting. Finance Stoch., 2008, 12, 265–292.
  • Fang, F. and Oosterlee, C.W., A novel pricing method for European options based on Fourier-cosine series expansions. SIAM J. Sci. Comput., 2008, 31, 826–848.
  • Feng, L. and Linetsky, V., Computing exponential moments of the discrete maximum of a Lévy process and lookback options. Finance Stoch., 2009, 13, 501–529.
  • Forsyth, P.A., Vetzal, K.R. and Zvan, R., A finite element approach to the pricing of discrete lookbacks with stochastic volatility. Appl. Math. Finance, 1999, 6, 87–106.
  • Foufas, G. and Larson, M.G., Valuing European, barrier, and lookback options using the finite element method and duality techniques. Technical report, Citeseer, 2004.
  • Gaffney, P. and Powell, M., Optimal interpolation. Numer. Anal., 1976, 506, 90–99.
  • Goldman, M.B., Sosin, H.B. and Shepp, L.A., On contingent claims that insure ex-post optimal stock market timing. J. Finance, 1979a, 34, 401–413.
  • Goldman, M., Sosin, H.B. and Gatto, M.A., Path dependent options: “Buy at the low Sell at the High”. J. Finance, 1979b, 34, 1111–1127.
  • Green, R., Fusai, G. and Abrahams, I.D., THE Wiener-Hopf technique and discretely monitored path-dependent option pricing. Math. Finance, 2010, 20, 259–288.
  • Haslip, G.G. and Kaishev, V.K., A Fourier transform B-spline method for option pricing. J. Comput. Finance, forthcoming. Available at SSRN: http://ssrn.com/abstract=2269370.
  • Heynen, R.C. and Kat, H.M., Lookback options with discrete and partial monitoring of the underlying price. Appl. Math. Finance, 1995, 2, 273–284.
  • Hull, J.C. and White, A.D., Efficient procedures for valuing European and American path-dependent options. J. Deriv., 1993, 1, 21–31.
  • Ignatov, Z.G. and Kaishev, V.K., A probabilistic interpretation of multivariate B-splines and some applications. Serdica, 1989, 15, 91–99.
  • Jacod, J. and Shiryaev, A.N., Limit Theorems for Stochastic Processes, Vol. 288, 2003 (Springer-Verlag: Berlin).
  • Kaishev, V.K., Lévy processes induced by Dirichlet (B-) splines: Modelling multivariate asset price dynamics. Math. Finance, 2013, 23, 217–247.
  • Kaishev, V.K. and Dimitrova, D.S., Dirichlet bridge sampling for the variance gamma process: Pricing path-dependent options. Manage. Sci., 2009, 55, 483–496.
  • Kou, S.G., A jump-diffusion model for option pricing. Manage. Sci., 2002, 48, 1086–1101.
  • Kou, S.G. and Wang, H., Option pricing under a double exponential jump diffusion model. Manage. Sci., 2004, 50, 1178–1192.
  • Küchler, U. and Tappe, S., Bilateral gamma distributions and processes in financial mathematics. Stoch. Process. Appl., 2008, 118, 261–283.
  • Levendorskiĭ, S. and Xie, J., Fast pricing and calculation of sensitivities of out-of-the-money European options under Lévy processes. J. Comput. Finance, 2012, 15, 71–133.
  • Lewis, A.L., Option Valuation Under Stochastic Volatility With Mathematica Code, 2000 (Finance Press: Newport Beach, CA).
  • Lewis, A., A simple option formula for general jump-diffusion and other exponential Lévy processes. Unpublished Working Paper, 2001.
  • Lin, X.S. and Tan, K.S., Valuation of equity-indexed annuities under stochastic interest rates. N. Am. Actuar. J., 2003, 7, 72–91.
  • Linetsky, V., Lookback options and diffusion hitting times: A spectral expansion approach. Finance Stoch., 2004, 8, 373–398.
  • Lipton, A., Mathematical Methods for Foreign Exchange: A Financial Engineer’s Approach, 2001 (World Scientific: Singapore).
  • Lipton, A., Assets with jumps. Risk Mag., 2002a, 15, 149–153.
  • Lipton, A., The vol smile problem. Risk Mag., 2002b, 15, 61–66.
  • Lord, R., Fang, F., Bervoets, F. and Oosterlee, C.W., A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes. SIAM J. Sci. Comput., 2008, 30, 1678–1705.
  • Madan, D.B., Carr, P.P. and Chang, E.C., The variance gamma process and option pricing. Eur. Finance Rev., 1998, 2, 79–105.
  • Marsden, M.J., Quadratic spline interpolation. Am. Math. Soc., 1974, 80, 903–906.
  • Merton, R.C., Option pricing when underlying stock returns are discontinuous. J. Financ. Econ., 1976, 3, 125–144.
  • Micchelli, C.A., Rivlin, T.J. and Winograd, S., The optimal recovery of smooth functions. Numer. Math., 1976, 26, 191–200.
  • Öhgren, A., A remark on the pricing of discrete lookback options. J. Comput. Finance, 2001, 4, 141–147.
  • Petrella, G. and Kou, S.G., Numerical pricing of discrete barrier and lookback options via Laplace transforms. J. Comput. Finance, 2004, 8, 1–38.
  • Poppe, G.P.M. and Wijers, C.M.J., More efficient computation of the complex error function. ACM Trans. Math. Softw. (TOMS), 1990, 16, 38–46.
  • Spitzer, F., A combinatorial lemma and its application to probability theory. Trans. Am. Math. Soc., 1956, 82, 323–339.
  • Tse, W.M., Li, L.K. and Ng, K.W., Pricing discrete barrier and hindsight options with the tridiagonal probability algorithm. Manage. Sci., 2001, 47, 383–393.
  • Vandevender, W.H. and Haskell, K.H., The SLATEC mathematical subroutine library. ACM SIGNUM Newslett., 1982, 17, 16–21.
  • Wendel, J., Spitzer’s formula: A short proof. Proc. Am. Math. Soc., 1958, 9, 905–908.
  • Wilmott, P., Dewynne, J. and Howison, S., Option Pricing: Mathematical Models and Computation, 1993 (Oxford Financial Press: Oxford).
  • Wong, H.Y. and Lam, K.W., Valuation of discrete dynamic fund protection under Lévy processes. N. Am. Actuar. J., 2009, 13, 202–216.
  • Yamamoto, Y., Double-exponential fast Gauss transform algorithms for pricing discrete lookback options. Publ. Res. Inst. Math. Sci., 2005, 41, 989–1006.

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