A non-Gaussian model of stock returns: Option smiles, credit skews, and a multi-time scale memory

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5848, Issue , 2005, Pages 55-65

  Borland, Lisa ^a  

^a Evnine Vaughan Associates Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COST EFFECTIVENESS; FINANCE; STATISTICAL METHODS;

CREDIT SKEWS; FEEDBACK MODEL; MULTI-TIME SCALE MEMORY; STOCK RETURNS;

INVENTORY CONTROL;

EID: 28444479843     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.610723     Document Type: Conference Paper

References (41)

1. F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, Journal of Political Economy 81, 637-659, (1973)
2. R.C. Merton, Theory of Rational Option Pricing, Bell Journal of Economics and Management Science 4, 143-182, (1973)
3. B. Dupire, Pricing with a Smile, Risk 7, 18-20, Jan 1994
4. E. Derman and I. Kani, Riding on a Smile, Risk 7, 32-39, Feb 1994
5. E. Eberlein, U. Keller, K. Prause, New insights into smile, mispricing and Value at Risk: the hyperbolic model, Journal of Business, 71, 371 (1998).
6. S. I. Boyarchenko, and S. Z. Levendorskii, Non-gaussian Merton-Black-Scholes Theory, World Scientific (2002)
7. R. Cont, P. Tankov, Financial modelling with jump processes, CRC Press, 2004.
8. J.-P. Bouchaud and M. Potters, Theory of Financial Risks and Derivative Pricing (Cambridge: Cambridge University Press), 2nd Edition 2004
9. S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. of Fin. Studies, 6, 327-343, 1993
10. J.-P. Fouque, G. Papanicolaou, G. and K. R. Sircar, Derivatives in financial markets with stochastic volatility, Cambridge University Press, 2000
11. P. Carr, H. Geman, D. Madan, M. Yor, Stochastic Volatility for Levy Processes, Mathematical Finance, 13, 345 (2003).
12. P.S. Hagan, D. Kumar, A.S. Lesniewski and D.E. Woodward, Managing Smile Risk, Wilmott, p. 84-108, Sept. 2002
13. B. Pochart, and J.-P. Bouchaud, The skewed multifractal random walk with applications to option smiles, Quantitative Finance, 2, 303 (2002).
14. J. Perello, J. Masoliver and J.-P. Bouchaud, Multiple time scales in volatility and leverage correlations: a stochastic volatility model, Applied Mathematical Finance, 11, 1-24 (2004).
15. A.L. Alejandro-Quiñones, K.E. Bassler, M. Field, J.L. McCauley, M. Nicol, I. Timofryev, A. Torok and G.H. Gunaratne, A Theory of Fluctuations in Stock Prices, cond-mat/0409375, (2004).
16. R. Jarrow, and A. Rudd, Approximate option valuation for arbitrary stochastic processes, Journal of Financial Economics, 10, 347 (1982)
17. C. J. Corrado, and T. Su, Implied volatility skews and stock index skewness and kurtosis implied by S&P 500 index option prices, The Journal of Derivatives, XIX, 8 (1997)
18. M. Potters, R. Cont, and J.-P. Bouchaud, Financial markets as adaptive systems, Europhysics letters, 41, 239 (1998)
19. L. Borland, A Theory of non-Gaussian Option Pricing, Quantitative Finance 2, 415-431, (2002)
20. L. Borland, Option Pricing Formulas based on a non-Gaussian Stock Price Model, Phys. Rev. Lett. 89 N9, 098701, (2002)
21. L. Borland and J.P. Bouchaud, A Non-Gaussian Option Pricing Model with Skew,Quantitative Finance 4, 499-514 (2004)
22. L. Borland, J. Evnine, and B. Pochart, A Merton-Like Approach to Pricing Debt based on a non-Gaussian Asset Model, to appear (2005)
23. P. Gopikrishnan, V. Plerou, L.A. Nunes Amaral, M. Meyer and H.E. Stanley, Scaling of the distribution of fluctuations of financial market indices, Phys. Rev. E 60, 5305, (1999)
24. L. Borland, Microscopic dynamics of the nonlinear Fokker-Planck equation; a phenomenological model, Phys. Rev. E 57, 6634, (1998)
25. C. Tsallis and D.J. Bukman, Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis, Phys. Rev. E 54, R2197, (1996)
26. Tsallis C., J. Stat. Phys. 52, 479, 1988;
27. Curado E.M.F. and Tsallis C., J. Phys. A 24 L69, 1991;
28. Curado E.M.F. and Tsallis C., J. Phys. A 24, 3187, 1991
29. Curado E.M.F. and Tsallis C., J. Phys. A 25 1019, 1992
30. E. Chasseigne and J. L. Vazquez, Theory of extended solutions for Fast Diffusion Equations in Optimal Classes of Data. Radiation from Singularities, Archive Rat. Mech. Anal. 164, 133-187, (2002)
31. A.M.C. de Souza and C. Tsallis, Student's t- and r-distributions: Unified derivation from an entropic variational principle, Phyisca A 236, 52-57, (1997)
32. J.-P. Bouchaud, A. Matacz, A. and M. Potters, Leverage effect in financial markets: the retarded volatility model, Physical Review Letters, 87, 228701, (2001)
33. J. C. Cox, unpublished working paper (1974);
34. J. C. Cox and S. A. Ross, The Evaluation of Options for Alternative Stochastic Processes, Journal of Financial Economics 3, 145-166, (1976)
35. 1-q/2(3-q), which can alternatively be seen as a redefinition of time.
36. A multi-time scale non-Gaussian model of stock returns, e-print cond-mat/0412526 (2004)
37. R.C. Merton, On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance 29, 449-470, (May 1974).
38. G. Zumbach, Volatility Processes and Volatility Forecast with Long Memory, Quantitative Finance, 4 70-86, (2004)
39. L. Borland, J.P. Bouchaud, J.F. Muzy and G. Zumbach, The dynamics of financial markets Mandelbrot's cascades and beyond, to appear in Wilmott Magazine, March 2005, cond-mat/0501292 (2005).
40. L. Borland and J.P. Bouchaud, work in progress (2005)
41. R. Osorio, L. Borland and C. Tsallis, Distributions of High-Frequency Stock-Market Observables, in Nonextensive Entropy: Interdisciplinary Applications ed C. Tsallis and M. Gell-Mann (Oxford:Santa Fe Institute Studies in the Science of Complexity, (2003)