The square-root process and Asian options

Quantitative Finance

Volumn 6, Issue 4, 2006, Pages 337-347

  Dassios, Angelos ^a   Nagaradjasarma, Jayalaxshmi ^b  

^a LONDON SCHOOL OF ECONOMICS   (United Kingdom)

^b IFSC ^*  (Ireland)

Author keywords

DER P H; Quantitative Finance classification scheme

Indexed keywords

EID: 33747621669     PISSN: 14697688     EISSN: 14697696     Source Type: Journal    
DOI: 10.1080/14697680600724775     Document Type: Article

References (45)

1. Andreasen, J., The pricing of discretely sampled Asian and look-back options: a change of numeraire approach. J. Comput. Finance, 1998, 2, 5-30.
2. Bakshi, G., Cao, C. and Chen, Z., Empirical performance of alternative option pricing models. J. Finance, 1997, 52, 2003-2049.
3. Ball, C. and Roma, A., Stochastic volatility option pricing. J. Financ. Quant. Anal., 1994, 29, 584-607.
4. Beckers, S., The constant elasticity of variance model and its implications for option pricing. J. Finance, 1980, 35, 661-673.
5. Boyle, P.P. and Tian, Y., Pricing lookback and barrier options under the cev process. J. Financ. Quant. Anal., 1999, 34, 241-264.
6. Carverhill, A. and Clewlow, L., Flexible convolution. From Black Scholes to Black Holes, 1992, 1, 165-171.
7. Chen, R.R. and Scott, L., Pricing interest rate options in a two-factor Cox-Ingersoll-Ross model of the term-structure. Rev. Financ. Stud., 1992, 5, 613-636.
8. Cox, J.C., Notes on option pricing i: constant elasticity of variance diffusions. J. Portfolio Manag., 1996, 22, 15-17.
9. Cox, J.C., Ingersoll, J.E.J. and Ross, S.A., A theory of term structure of interest rates. Econometrica, 1985, 53, 385-407.
10. Cox, J.C. and Ross, S.A., The valuation of options for altervative stochastic processes. J. Financ. Econ., 1976, 3, 145-166.
11. Das, S.R. and Sundaran, R.K., Of smiles and smirks: a term-structure perspective. J. Financ. Quant. Anal., 1999, 34, 211-239.
12. Dassios, A. and Nagaradjasarma, J., Pricing average rate claims. Working Paper, 2003 (Department of Statistics, London School of Economics).
13. Davydov, D. and Linetsky, V., Pricing and hedging path-dependent options under the cev process. Manag. Sci., 2001, 47, 949-965.
14. Davydov, D. and Linetsky, V., Pricing options on scalar diffusions: an eigenfunction expansion approach. Operat. Res., 2003, 51, 185-209.
15. Duffie, D., Pan, J. and Singleton, K., Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 2000, 68, 1343-1376.
16. Dufresne, D., Laguerre series for asian and other options. Math. Finance, 2000, 10, 407-428.
17. Dufresne, D., The integral of the square-root process. Working Paper, 2001 (Centre for Actuarial Studies, University of Melbourne).
18. Eydeland, A. and Geman, H., Dominos effect. Risk, 1995, 8, 65-67.
19. Feller, W., Two singular diffusion problems. Ann. Math., 1951, 54, 173-182.
20. Fu, M.C., Madan, D. and Wang, T., Pricing continuous Asian options: a comparison of Monte Carlo and Laplace transform inversion methods. J. Comput. Finance, 1998, 2, 49-74.
21. Geman, H. and Yor, M., Quelques relations entre processus de bessel, options asiatiques et fonctions confluentes hypergeometriques. C. R. Acad. Sci. Paris, 1992, 314, 471-474.
22. Geman, H. and Yor, M., Bessel processes, Asian options and perpertuities. Math. Finance, 1993, 3, 349-375.
23. Gradshteyn, I.S. and Ryzhik, I.M., Table of Integrals, Series and Products, 1980 (Academic Press: New York).
24. Hauser, S. and Lauterbach, B., Test of warrant pricing models: the trading profits perspective. J. Derivatives, 1996, Winter, 71-79.
25. Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud., 1993, 6, 327-343.
26. Lamberton, D. and Lapeyre, B., An Introduction to Stochastic Calculus Applied to Finance, 1995 (Chapman and Hall: London).
27. Lamperti, J.W., Semi-stable Markov processes. Z. Wahrsch., 1972, 22, 205-225.
28. Linetsky, V., Exotic sprectra. Risk, 2000, April, 85-89.
29. Linetsky, V., Spectral expansions for Asian (average price) options. Operat. Res., 2004, 52, 856-867.
30. Lo, C.F., Yuen, P.H. and Hui, C.H., Pricing barrier options with square-root process. Int. J. Theoret. Appl. Finance, 2001, 4, 805-818.
31. Maghsoodi, Y., Solutions of the extended cir term structure and bond option valuation. Math. Finance, 1996, 6, 89-109.
32. Milevski, M.A. and Posner, S.E., Asian options, the sum of lognormals and the reciprocal gamma distribution. J. Financ. Quant. Anal., 1998, 33, 409-422.
33. Nagaradjasarma, J., Path-dependent functionals of constant elasticity of variance and related processes: distributional results and applications in finance. PhD thesis, London School of Economics, 2003.
34. Pan, J., The jump-risk premia implicit in options: evidence from an integrated time-series study. J. Financ. Econ., 2002, 63, 3-50.
35. Pitman, J.D., and Yor, M., Bessel processes and infinitely divisible laws. Stochastic Integrals, 1981, 851, 285-370.
36. Posner, S.E. and Milevski, M.A., Valuing exotic options by approximating the spd with higher moments. J. Financ. Eng., 1998, 7, 109-125.
37. Revuz, D. and Yor, M., Continuous Martingales and Brownian Motion, 1991 (Springer-Verlag: Berlin).
38. Rogers, L.C.G. and Shi, Z., The value of an Asian option. J. Appl. Probab., 1995, 32, 1077-1088.
39. Schroder, M., Computing the constant elasticity of variance option pricing formula. J. Finance, 1989, 4, 211-219.
40. Schröder, M., Analytical ramifications of derivatives valuation: Asian options and special functions. Working Paper, 2002 (University of Mannheim).
41. Shiga, T. and Watanabe, S., Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrsch, 1973, 27, 47-52.
42. Vecer, J., A new pde approach for pricing arithmetic average Asian options. J. Comput. Finance, 2001, 4, 105-113.
43. Vecer, J., and Xu, M., Pricing Asian options in a semimartingale model. Quant. Finance, 2004, 4, 170-175.
44. Yor, M., Exponential Functionals of Brownian Motion and Related Processes, 2001 (Springer-Verlag: New York).
45. Zvan, R., Forsyth, P. and Vetzal, K., Robust numerical methods for pde models of Asian options. J. Comput. Finance, 1997, 1, 39-78.