Calibration of the temporally varying volatility and interest rate functions

References

• I. Arregui and J. Ráfales, A stochastic local volatility technique for TARN options, Int. J. Comput. Math. 97 (2020), pp. 1133–1149.
   Web of Science ®Google Scholar
• F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), pp. 637–654.
   Web of Science ®Google Scholar
• H.M. Chen and C.H. Huang, An inverse European option problem in estimating the time-dependent volatility function with statistical analysis, Int. J. Syst. Sci. 36 (2005), pp. 103–111.
   Web of Science ®Google Scholar
• J. Daněk and J. Pospíšil, Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models, Int. J. Comput. Math. 97 (2020), pp. 1268–1292.
   Web of Science ®Google Scholar
• A. Elettra and A. Rossella, A generalization of the Geske formula for compound options, Math. Soc. Sci. 45 (2013), pp. 75–82.
   Web of Science ®Google Scholar
• L.A. Grzelak, The collocating local volatility framework – a fresh look at efficient pricing with smile, Int. J. Comput. Math. 96 (2019), pp. 2209–2228.
   Web of Science ®Google Scholar
• L.A. Grzelak and C.W. Oosterlee, On the Heston model with stochastic interest rates, SIAM J. Financ. Math. 2 (2011), pp. 255–286.
   Web of Science ®Google Scholar
• C. Guardasoni, Semi-analytical method for the pricing of barrier options in case of time-dependent parameters (with matlab@@@ codes), Comun. Appl. Ind. Math. 9 (2018), pp. 42–67.
   Web of Science ®Google Scholar
• X.J. He and W. Chen, A closed-form pricing formula for European options under a new stochastic volatility model with a stochastic long-term mean, Math. Financial Econ. 15 (2021), pp. 381–396.
   Web of Science ®Google Scholar
• S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Rev. Financ. Stud. 6 (1993), pp. 327–343.
   Web of Science ®Google Scholar
• F.A. Ko and R.J.A. David, A numerical scheme for the Black–Scholes equation with variable interest rate using spectral collocation and backward-differences, in Proceedings of the International MultiConference of Engineers and Computer Scientists 1, 2015, pp. 401–403.
   Google Scholar
• Y. Liang and C. Xu, An efficient conditional Monte Carlo method for European option pricing with stochastic volatility and stochastic interest rate, Int. J. Comput. Math. 97 (2020), pp. 638–655.
   Web of Science ®Google Scholar
• S. Lin and X.J. He, A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model, Chaos Solitons Fractals 144 (2021), pp. 110644.
   Web of Science ®Google Scholar
• C.F. Lo and C.H. Hui, Valuing double barrier options with time-dependent parameters by Fourier series expansion, IAENG Int. J. Appl. Math. Comput. Sci. 36 (2007), pp. 1–5.
   Google Scholar
• The MathWorks Inc., MATLAB, Natick, MA, 1994, Software available at http://www.mathworks.com/.
   Google Scholar
• R.C Merton, Theory of rational option pricing, Int. J. Appl. Math. Comput. Sci. 4 (1973), pp. 141–183.
   Google Scholar
• R. Naz and I. Naeem, Exact solutions of a Black–Scholes model with time-dependent parameters by utilizing potential symmetries, Discret. Contin. Dyn. Syst.-Ser. S. 13 (2020), pp. 2841–2851.
   Web of Science ®Google Scholar
• M.R. Rodrigo and R.S. Mamon, An alternative approach to solving the Black–Scholes equation with time-varying parameters, Appl. Math. Lett. 19 (2006), pp. 398–402.
   Web of Science ®Google Scholar
• M.R. Rodrigo and R.S. Mamon, An application of mellin transform techniques to a Black–Scholes equation problem, Anal. Appl. 5 (2007), pp. 51–66.
   Web of Science ®Google Scholar
• D. Tavella and C. Randall, Pricing Financial Instruments: the Finite Difference Method, Vol. 13, Jone Wiely and Sons, New York, 2000.
   Google Scholar
• L. Thomas, Elliptic Problems in Linear Differential Equations Over a Network: Watson Scientific Computing Laboratory, Columbia University, New York, 1949.
   Google Scholar
• H. Windfcliff, P.A. Forsuth and K.R. Vetzal, Analysis of the stability of the linear boundary condition for the Black–Scholes equation, J. Comput. Financ. 8 (2004), pp. 65–92.
   Google Scholar
• S.H.I. Yunxia and Z.H.A.O. Xiping, A novel method for prediction of option pricing for a market model, Econ. Comput. Econ. Cybern. Stud. 47 (2013), pp. 1–14.
   Web of Science ®Google Scholar