An exact analytical solution for discrete barrier options

Finance and Stochastics

Volumn 10, Issue 1, 2006, Pages 1-26

  Fusai, Gianluca ^a,b   Abrahams, I David ^c   Sgarra, Carlo ^d  

^a UNIVERSITY OF EASTERN PIEDMONT   (Italy)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

^d POLITECNICO DI MILANO   (Italy)

Author keywords

Barrier options; Black Scholes; Discrete monitoring; Wiener Hopf equation; z transform

Indexed keywords

EID: 29144511551     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-005-0170-y     Document Type: Article

References (44)

1. Abate, J., Whitt, W.: Numerical inversion of probability generating functions. Oper. Res. Lett. 12, 245-251 (1992)
2. Abrahams I.D.: On the solution of Wiener-Hopf problems involving noncommutative matrix kernel decompositions. SIAM J. Appl. Math. 57, 541-567 (1997)
3. Abrahams I. D.: The application of Padé approximants to Wiener-Hopf factorization. IMA J. Appl. Math. 65, 257-281 (2000)
4. Ahn, D.-H., Figlewski, S., Gao, B.: Pricing discrete barrier options with an adaptive mesh model. J. Derivatives 7, 33-43 (1999)
5. Ait-Sahlia F., Lai, T.L.: Valuation of discrete barrier and hindsight options. J. Financial Eng.6, 169-77 (1997)
6. Andricopoulos, A.D., Widdicks, M., Duck P.W., Newton D.P.: Universal option valuation using quadrature methods. J. Financial Econ. 67, 441-411 (2003)
7. Baxter, G., Donkser M.D.: On the distribution of the supremum functional for processes with stationary independent increments. Transactions Am. Math. Soc. 85, 73-87 (1952)
8. Bertoldi M., Bianchetti M.: Monte Carlo simulation of discrete barrier options. Internal Report, Financial Engineering - Derivatives Modelling, Caboto SIM S.p.a., Banca Intesa Group, Milan, Italy (2003)
9. Borovkov K., Novikov, A.: On a new approach to calculating expectations for option pricing. J. Appl. Probab. 39, 889-895 (2002)
10. Boyarchenko S., Levendorskii S.: Non-Gaussian Merton-Black-Scholes Theory. 1st ed. Singapore: World Scientific Pub. Co., 2002
11. Boyle P.P., Tian Y.S.: An explicit finite difference approach to the pricing of barrier options. Appl. Math. Finance 5, 17-43 (1998)
12. Broadie M., Glasserman P., Kou S.: A continuity correction for discrete barrier options. Math. Finance 7, 325-349 (1997)
13. Broadie M., Glasserman P., Kou S.: Connecting discrete and continuous path-dependent options. Finance Stochast. 3, 55-82 (1999)
14. Chernoff H.: Sequential tests for the mean of a normal distribution IV (discrete case). Ann. Math. Statist. 36, 55-68 (1965)
15. Duan, J. C., Dudley, E., Gauthier, G., Simonato J-G.: Pricing discretely monitored barrier options by a Markov chain. J. Derivatives 10, 9-32 (2003)
16. Fusai G., Recchioni, M.C.: Numerical valuation of discrete barrier options. J. Econ. Dynamics Control (forthcoming)
17. Fusai G., Abrahams I. D., Sgarra, C.: An exact analytical solution for discrete barrier options. Quaderno SEMEQ, Universitá del Piemonte Orientale, n. 75 (2004)
18. Geman H., Yor, M.: Pricing and hedging double barrier options: a probabilistic approach. Math. Financce, 365-378 (1996)
19. Greenwood P.: Wiener-Hopf methods, decompositions, and factorization identities for maxima and minima of homogeneous random processes. Adv. Appl. Probab. 7, 767-785 (1975)
20. Haug, E. G.: Barrier put-call transformations, Tempus Financial Engineering Number 3/97, Norway, download at http://ssrn.com/abstract=150156 (1999)
21. Heynen R.C., Kat, H.M.: Lookback options with discrete and partial monitoring of the underlying price. Appl. Math. Finance 2, 273-284 (1995)
22. Hörfeit, P.: Extension of the corrected barrier approximation by Broadie, Glasserman, and Kou. Finance Stochast. 7, 231-243 (2003)
23. Hui, C.H., Lo, C.F., Yuen, P.H.: Comment on 'Pricing double barrier options using Laplace transforms' by Antoon Pelsser. Finance Stochast. 4, 105-107 (2000)
24. Kat, H., Verdonk, L.: Tree surgery. Risk 8, 53-56 (1995)
25. Kou, S.G.: On pricing of discrete barrier options. Statist. Sinica 13, 955-964 (2003)
26. Kuan G., Webber, N.: Valuing discrete barrier options on a Dirichlet lattice, FORC preprint 04-140, University of Warwick, (2004)
27. Kunitomo, N., Ikeda, M.: Pricing options with curved boundaries. Math. Finance 2, 275-298 (1992)
28. Noble, B., Methods based on the Wiener-Hopf Technique, 2nd ed. New York: Chelsea Press, 1988
29. Nguyen-Ngoc, L., Yor, M.: Lookback and barrier options under general Lévy processes. In: Aït-Sahalia and Hansen (eds.) Handbook of financial econometrics. http://www.elsevier.com/wps/find/bookdescription. cws_home/622467/description#description
30. Ohgren, A.: A remark on the pricing of discrete lookback options. J. Comput. Finance 4, 141-146 (2001)
31. Pelsser, A. : Pricing double barrier options using Laplace transforms. Finance Stochast. 4, 95-104 (2000).
32. Petrella, G., Kou S.G.: Numerical pricing of discrete barrier and lookback options via Laplace transforms. J. Comput. Finance 8, 1-37 (2004)
33. Polyanin, A.D., Manzhirov, A.V.: Handbook of integral equations. Boca Raton: CRC Press, 1998
34. Priestley H.A.: Introduction to integration. New York: Oxford Science Publication, 1997
35. Rich, D.R.: The mathematical foundations of barrier option pricing theory. Adv. Futures Options Res. 7, 267-311 (1994)
36. Rogers, L.C.G.: Evaluating first-passage probabilities for spectrally one-sided Lévy processes. J. Appl. Probab. 37, 1173-1180 (2000)
37. Rudin, W.: Real and complex analysis. New York: McGraw-Hill, 1987
38. Spitzer, F.: A combinatorial lemma and its application to probability theory. Transactions Am. Math. Soc. 82, 323-339 (1956)
39. Spitzer, F.: The Wiener-Hopf equation whose kernel is a probability density. Duke Math. J. 24, 327-343 (1957)
40. Strauss, W.A.: Partial differential equations: an introduction. New York: Wiley 1992
41. Sullivan, M.A.: Pricing discretely monitored barrier options. J. Comput. Finance 3, 35-52 (2000)
42. Wei, J.Z.: Valuation of discrete barrier options by interpolation. J. Derivatives 6, 51-73 (1998)
43. Wendel J.G.: Spitzer's formula: A short proof. Proc. Am. Math. Soc. 9, 905-908 (1958)
44. Wilmott, P., Dewynne, J.N., Howison, S.: Option pricing: mathematical models and computation. Oxford: Oxford Financial Press, 1993