Skew Brownian motion and pricing European options

European Journal of Finance

Volumn 13, Issue 6, 2007, Pages 523-544

  Corns, T R A ^a   Satchell, S E ^b  

^a Cantab Capital Partners   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Hedging; Non Gaussian; Options; Skew Brownian motion; Skew normal; Skew symmetric

Indexed keywords

EID: 34548583996     PISSN: 1351847X     EISSN: 14664364     Source Type: Journal    
DOI: 10.1080/13518470701201488     Document Type: Article

References (43)

1. Arellano-Valle, R. B. and del Pino, G. E. (2004) From symmetric to asymmetric distributions: a unified approach, in: M. G. Genton (Ed.) Skew-Elliptical Distributions and their Applications: A Journey Beyond Normality, pp. 113-130 (New York: Chapman and HaCRC).
2. Arellano-Valle, R. B. and Azzalini, A. (2006) On the unification of families of skew-normal distributions, Scandinavian Journal of Statistics, to appear.
3. Azzalini, A. (1985) A class of distribution which includes the normal ones, Scandinavian Journal of Statistics, 12, pp. 171-178.
4. Azzalini, A. (1986) Further results on a class of distributions which includes the normal ones, Statistica, XLVI, pp. 199-208.
5. Azzalini, A. and Capitanio, A. (1999) Statistical applications of the multivariate skew-normal distribution, Journal of the Royal Statistical Society Series B, 61, pp. 579-602.
6. Azzalini, A. and Della Valle, A. (1996) The multilvariate skew-normal distribution, Biometrika, 83, pp. 715-726.
7. Barlow, M., Burdzy, K., Kaspi, H. and Mandelbaum, A. (2000) Variably skewed Brownian motion, Electronic Communications in Probability, 5, pp. 57-66.
8. Bates, D. S. (1991) The crash of '87 - was it expected? The evidence from options markets, Journal of Finance, 46, pp. 1009-1044.
9. Bates, D. S. (1996) Jumps and stochastic volatility: exchange rate processes implicit in Deutsche Mark options, Review of Financial Studies, 9, pp. 69-107.
10. Bates, D. S. (2000) Post-'87 crash fears in the S&P 500 futures option market, Journal of Econometrics, 94, pp. 181-238.
11. Bingham, N. and Kiesel, R. (2001) Modelling asset returns with hyperbolic distributions, in: J. L. Knight and S. E. Satchell (Eds) Return Distributions in Finance, pp. 252-275.
12. Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities, Journal of Political Economy, 81, pp. 637-659.
13. Bodurtha, J. N. and Courtadon, G. R. (1987) Tests of an American option pricing model on the foreign currency options market, Journal of Financial, and Quantitative Analysis, 22, pp. 153-167.
14. Bookstaber, R. and McDonald, J. B. (1991) Option pricing for generalized distributions, Communications in Statistics, 20, pp. 4053-4068.
15. Borodin, A. N. and Salminen, P. (1996) Handbook of Brownian Motion-Facts and Formulae (Basel: Birkhauser).
16. Corrado, C. J. and Su, T. (1997) Implied volatility skews and stock index skewness and kurtosis implied by S&P 500 index option prices, Journal of Derivatives, Summer, pp. 8-19.
17. Cox, J. and Ross, S. (1976) The valuation of options for alternative stochastic process, Journal of Financial Economics, 3, pp. 145-166.
18. Eberlain, E. and Keller, U. (1995) Hyperbolic distributions in finance, Bernoulli, 1, pp. 281-299.
19. Eberlain, E., Keller, U. and Prause, K. (1998) New insights into smile, mispricing and value-at-risk, Journal of Business, 71, pp. 371-406.
20. Elliot, R. J. and van der Hoek, J. (2001) Fractional Brownian motion and financial modelling, in: Trends in Mathematics, pp. 140-151 (Basle: Birkhauser).
21. Genton, M. G. and Loperfido, N. (2005) Generalized skew-elliptical distributions and their quadratic forms, Annals of the Institute of Statistical Mathematics, to appear.
22. Gultekin, N. B., Rogalski, R. J. and Tinic, S. M. (1982) Option pricing model estimates: some empirical results, Financial Management, Spring, pp. 58-69.
23. Harrison, J. M. and Shepp, L. A. (1981) On skew Brownian. motion, Annals of Probability, 9(2), pp. 309-313.
24. Heston, S. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies, 6, pp. 327-344.
25. Hull, J. and White, A. (1987) The pricing of options on assets with stochastic volatilities, Journal of Finance, 2, pp. 281-300.
26. Itô, K. and McKean, H. P. (1965) Diffusion Processes and Their Sample Paths (New York: Springer).
27. Knight, J. L. and Satchell, S. E. (2001) Pricing derivatives written on assets with arbitrary skewness and kurtosis, in: J. L. Knight and S. E. Satchell (Eds) Return Distributions in Finance, pp. 252-275.
28. Knight, J. L., Satchell, S. E. and Tran, K. C. (1995) Statistical modelling of asymmetric risk in asset returns, Applied Mathematical Finance, 2, pp. 155-172.
29. Ma, Y and Genton, M. G. (2004) A flexible class of skew-symmetric distributions, Scandinavian Journal of Statistics, 31(3), pp. 459-468.
30. MacBeth, J. D. and Merville, L. J. (1979) Tests of the Black-Scholes and Cox call option valuation models, Journal of Finance, 50, pp. 87-129.
31. McDonald, J. B. (1996) Probability distributions for financial models, in: G. S. Maddala and C. R. Rao (Eds) Statistical Methods in Finance, Vol. 14 of Handbook of Statistics, pp. 427-461 (Amsterdam: Elsevier).
32. Merton, R. C. (1973) The theory of rational option pricing, Bell Journal of Economics and Management Science, 4, pp. 141-183.
33. Nadarajah, S. and Kotz, S. (2003) Skewed distributions generated by the normal kernel, Statistics and Probability Letters, 65, pp. 269-277.
34. Ouknine, Y. (1987) Skew-Brownian motion and derived processes, Theory of Probability and Its Applications, 35(1), pp. 163-169.
35. Portenko, N. I. (1976) Generalized diffusion processes, in: Lecture Notes in Mathematics 550, pp. 500-523 (New York: Springer).
36. Rogers, L. C. G. (1997) Arbitrage with fraction Brownian motion, Mathematical Finance, 7, pp. 95-105.
37. Rogers, L. C. G. and Satchell, S. E. (2000) Does the behaviour of the asset tell us anything about the option price formula? Applied Financial Economics, 10, pp. 37-39.
38. Rogers, L. C. G. and Williams, D. (2000) Diffusions, Markov Processes and Martingales, Volume 2: Itô Calculus (Cambridge: Cambridge University Press).
39. Rubinstein, M. (1985) Nonparametric test of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE options classes from August 23, 1976 through August 3, 1978, Journal of Finance, 56, pp. 455-480.
40. Scott, L. (1987) Option pricing when the variance changes randomly: theory, estimation and application, Journal of Financial and Quantitative Analysis, 4, pp. 419-438.
41. Walsh, J. B. (1978) A Diffusion with a discontinuous local time, Atérisque, 52/53, pp. 37-45.
42. Wang, J., Boyer, J. and Genton, M. G. (2004) A skew-symmetric representation of multivariate distributions, Statistica Sinica, 14(4), pp. 1259-1270.
43. Wiggins, J. (1987) Options values under stochastic volatility: theory and empirical estimates, Journal of Financial Economics, 19, pp. 351-372.