Volatility in the Black-Scholes equation

[1] A. Awasthi and T. Riyasudheen, An accurate solution for the generalized Black-Scholes equations governing option pricing, AIMS Math. 5 (2020), no. 3, 2226–2243.

[2] A. Baxter, A. Martin and A. Rennie, Financial Calculus: An introduction to derivative Pricing, Cambridge University Press, Cambridge, England, 1996.

[3] F. Black and M. Scholes, The Pricing of Options and Corporate Liabilities, J. Politic. Econ. 81 (1973), no. 3, 637–654.

[4] Z. Brzezniak and T. Zastawniak, Basic Stochastic Processes, Springer-Verlag, Heidelberg, 1998.

[5] G. Caginalp and D. Balenovich, Asset flow and momentum: Deterministic and stochastic equations, Phil. Trans. Royal Soc. London. Ser. A: Math. Phys. Engin. Sci. 357 (1999), 2119-2133.

[6] G. Caginalp and M. Desantis, Multi-group asset flow equations and stability, Discrete Cont. Dyn-B 16 (2011), 109–150.

[7] G. Caginalp, B. Ermentrout, A kinetic thermodynamics approach to the psychology of fluctuations in financial markets, Appl. Math. Lett. 3 (1990), 17–19.

[8] O. Calin, Deterministic and stochastic topics in computational finance, World Scientific, Singapore, 2017.

[9] N. Champagnat, M. Deaconu, A. Lejay, N. Navet and S. Boukherouaa, An empirical analysis of heavy-tails behavior of financial data: The case for power laws, HAL archives-ouvertes, 2013.

[10] J. Cohen, George Church and company on genomic sequencing, blockchain, and better drugs, Science (2018).

[11] R.D. Cohen, The relationship between the equity risk premium, duration and dividend yield, Wilmott Magazine 2002 (2002), 84–97.

[12] M. Desantis and D. Swigon, Slow-fast analysis of a multi-group asset flow model with implications for the dynamics of wealth, PLoS ONE 13 (2018).

[13] I. Glauche, A classical Approach to the Black and Scholes Formula and its Critiques, Discretization of the model, Working paper at Duke University, April, 2001.

[14] J. Huang and Z.D. Cen, Cubic spline method for a generalized Black-Scholes equation, Math. Prob. Eng. 2014 (2014).

[15] J. Hull, Options, Futures and Other Derivatives, Pearson Education India, 2003.

[16] M.K. Kadalbajoo, L.P. Tripathi and P. Arora, A robust nonuniform B-spline collocation method for solving the generalized Black–Scholes equation, IMA J. Numer. Anal. 34 (2014), 252–278.

[17] M.K. Kadalbajoo, L.P. Tripathi and A. Kumar, A cubic B-spline collocation method for a numerical solution of the generalized Black–Scholes equation, Mathe. Comput. Modell. 55 (2012), 1483–1505.

[18] F. Klebaner, Fima C, Introduction to stochastic calculus with Applications, Imperial College Press, London, 1999.

[19] J.R. Liang, J. Wang, W.J. Zhang, W.Y. Qiu and F.Y. Ren, Option pricing of a bi-fractional Black–Merton–Scholes model with the Hurst exponent H in [12, 1], Appl. Math. Lett. 23 (2010), 859–863.

[20] R. Mohammadi, Quintic B-spline collocation approach for solving generalized Black–Scholes equation governing option pricing, Comput. Math. Appl. 69 (2015), 777–797.

[21] C.S. Rao, Numerical solution of generalized Black–Scholes model, Appl. Math. Comput. 321 (2018), 401–421.

[22] M.K. Salahuddin, M. Ahmed and S.K. Bhowmilk, A note on numerical solution of a linear Black-Scholes model, GANIT: J. Bangladesh Math. Soc. 33 (2013), 103–115.

[23] S. Ross, S An Introduction to Mathematical Finance, Cambridge, England: Cambridge University Press, 1999.

[24] R.H. De Staelen and A.S. Hendy, Numerically pricing double barrier options in a time-fractional Black–Scholes model, Comput. Math. Appl. 74 (2017), 1166–1175.

[25] R. Valkov, Fitted finite volume method for a generalized Black–Scholes equation transformed on finite interval, Numer. Algorithms 65 (2014), 195–220.

[26] P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives, Cambridge University Press, Cambridge, 1997.

[27] M. L. Zheng, F. W. Liu, I. Turner and V. Anh, A novel high order space-time spectral method for the time fractional Fokker–Planck equation, SIAM J. Sci. Comput. 37 (2015), 701–724.