A non-Gaussian option pricing model with skew

References

References

• Black , F and Scholes , M . 1973 . The pricing of options and corporate liabilities . J. Political Economy , 81 : 637 – 59 .
   Web of Science ®Google Scholar
• Merton , R C . 1973 . Theory of rational option pricing . Bell J. Economics Manage. Sci. , 4 : 143 – 82 .
   Google Scholar
• For a critique of the Black–Scholes model, see Bouchaud J P and Potters M 2001 Welcome to a non Black–Scholes world Quant. Finance 1 482 and [10]
   Google Scholar
• Dupire , B . 1994 . Pricing with a smile . Risk , 7 : 18 – 20 .
   Google Scholar
• Derman , E and Kani , I . 1994 . Riding on a smile . Risk , 7 : 32 – 9 .
   Google Scholar
• Hagan P S Kumar D Lesniewski A S Woodward D E 2002 Managing Smile Risk Wilmott pp 84–108
   Google Scholar
• Eberlein , E , Keller , U and Prause , K . 1998 . New insights into smile, mispricing and value at risk: the hyperbolic model . J. Business , 71 : 371
   Web of Science ®Google Scholar
• Boyarchenko S I Levendorskii S Z 2002 Non-gaussian Merton–Black–Scholes Theory Singapore World Scientific
   Google Scholar
• Cont R Tankov P 2004 Financial Modelling with Jump Processes Boca Raton FL CRC Press
   Google Scholar
• Bouchaud J-P Potters M 2004 Theory of Financial Risks and Derivative Pricing 2nd edn Cambridge Cambridge University Press
   Google Scholar
• Heston , S L . 1993 . A closed-form solution for options with stochastic volatility with applications to bond and currency options . Rev. Financial Studies , 6 : 327 – 4 .
   Web of Science ®Google Scholar
• Fouque J-P Papanicolaou G Sircar K R 2000 Derivatives in Financial Markets with Stochastic Volatility Cambridge Cambridge University Press
   Google Scholar
• Carr , P , Geman , H , Madan , D and Yor , M . 2003 . Stochastic volatility for Levy processes . Math. Finance , 13 : 345
   Web of Science ®Google Scholar
• Pochart , B and Bouchaud , J-P . 2002 . The skewed multifractal random walk with applications to option smiles Quant. Finance , 2 : 303
   Google Scholar
• Perello , J , Masoliver , J and Bouchaud , J-P . 2004 . Multiple time scales in volatility and leverage correlations: a stochastic volatility model . Appl. Math. Finance , 11 : 1 – 24 .
   Google Scholar
• Jarrow , R and Rudd , A . 1982 . Approximate option valuation for arbitrary stochastic processes . J. Financial Economics , 10 : 347
   Web of Science ®Google Scholar
• Corrado , C J and Su , T . 1997 . Implied volatility skews and stock index skewness and kurtosis implied by S&P 500 index option prices . J. Derivatives , XIX 8
   Google Scholar
• Backus D Foresi S Lai K Wu L 1997 Accounting for biases in Black–Scholes Working paper of NYU Stern School of Business
   Google Scholar
• Potters , M , Cont , R and Bouchaud , J-P . 1998 . Financial markets as adaptive systems . Europhys. Lett. , 41 : 239
   Google Scholar
• Gopikrishnan , P , Plerou , V , Nunes Amaral , L A , Meyer , M and Stanley , H E . 1999 . Scaling of the distribution of fluctuations of financial market indices . Phys. Rev. E , 60 : 5305
   PubMed Web of Science ®Google Scholar
• Borland , L . 2002 . A theory of non-Gaussian option pricing . Quant. Finance , 2 : 415 – 31 .
   Google Scholar
• Borland , L . 2002 . Option pricing formulas based on a non-Gaussian stock price model . Phys. Rev. Lett. , 89 : 098701
   PubMed Web of Science ®Google Scholar
• Borland , L . 1998 . Microscopic dynamics of the nonlinear Fokker–Planck equation: a phenomenological model . Phys. Rev. E , 57 : 6634
   Web of Science ®Google Scholar
• Tsallis , C and Bukman , D J . 1996 . Anomalous diffusion in the presence of external forces: exact time-dependent solutions and their thermostatistical basis . Phys. Rev. E , 54 : R2197
   PubMed Web of Science ®Google Scholar
• Tsallis C 1988 J. Stat. Phys. 52 479 Curado E M. F, Tsallis, C, 1991, J. Phys. A 24 L69; 1991 24 3187; 1992 25 1019
   Web of Science ®Google Scholar
• de Souza , A M C and Tsallis , C . 1997 . Student'st- andr-distributions: unified derivation from an entropic variational principle . Phyisca A , 236 : 52 – 7 .
   Google Scholar
• Chasseigne , E and Vazquez , J L . 2002 . Theory of extended solutions for fast diffusion equations in optimal classes of data. Radiation from singularities . Arch. Rat. Mech. Anal. , 164 : 133 – 87 .
   Web of Science ®Google Scholar
• Cox J C 1974 Unpublished working paper Cox J C, Ross, S A. 1976, The evaluation of options for alternative stochastic processes, J. Financial Economics, 3, 145–66
   Google Scholar
• Borland L Bouchaud J P Unpublished
   Google Scholar
• Musiela M Rutkowski M 1997 Martingale Methods in Financial Modelling Berlin Springer
   Google Scholar
• Shreve S Lectures on Finance prepared by P Chalasani and S Jha, www.cs.cmu.edu/~chal/shreve.html
   Google Scholar
• Equation (71) of [21] is an approximation
   Google Scholar
• Market-makers (anonymous) 2003 New York
   Google Scholar
• Osorio R Borland L Tsallis C 2003 Distributions of high-frequency stock-market observables Nonextensive Entropy: Interdisciplinary Applications ed C Tsallis and M Gell-Mann Oxford Santa Fe Institute Studies in the Science of Complexity
   Google Scholar
• Michael , F and Johnson , M D . 2003 . Financial market dynamics . Physica A , 320 : 525
   Web of Science ®Google Scholar
• Bouchaud , J-P , Matacz , A and Potters , M . 2001 . Leverage effect in financial markets: the retarded volatility model . Phys. Rev. Lett. , 87 : 228701
   PubMed Web of Science ®Google Scholar
• Potters , M , Bouchaud , J-P and Sestovic , D . 2001 . Hedged Monte-Carlo: low variance derivative pricing with objective probabilities . Physica A , 289 : 517
   Web of Science ®Google Scholar
• See also Albanese C and Campolieti G 2001 Extensions of the Black–Scholes formula Working paper
   Google Scholar