The SINC way: a fast and accurate approach to Fourier pricing

References

• Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J.-F., Modelling microstructure noise with mutually exciting point processes. Quant. Finance, 2013, 13(1), 65–77.
   Web of Science ®Google Scholar
• Bacry, E., Jaisson, T. and Muzy, J.-F., Estimation of slowly decreasing Hawkes kernels: Application to high-frequency order book dynamics. Quant. Finance, 2016, 16(8), 1179–1201.
   Web of Science ®Google Scholar
• Bakshi, G.S. and Chen, Z., An alternative valuation model for contingent claims. J. Financ. Econ., 1997, 44(1), 123–165.
   Web of Science ®Google Scholar
• Bates, D.S., Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Rev. Financ. Stud., 1996, 9(1), 69–107.
   Web of Science ®Google Scholar
• Bayer, C., Friz, P. and Gatheral, J., Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904.
   Web of Science ®Google Scholar
• Bayer, C., Ben Hammouda, C. and Tempone, R., Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model. Quant. Finance, 2020, 20(9), 1457–1473.
   Web of Science ®Google Scholar
• Bennedsen, M., Lunde, A. and Pakkanen, M.S., Decoupling the short-and long-term behavior of stochastic volatility. ArXiv preprint arXiv:1610.00332, 2016.
   Google Scholar
• Bennedsen, M., Lunde, A. and Pakkanen, M.S., Hybrid scheme for Brownian semistationary processes. Finance Stoch., 2017, 21(4), 931–965.
   Web of Science ®Google Scholar
• Callegaro, G., Grasselli, M. and Pages, G., Fast hybrid schemes for fractional Riccati equations (rough is not so tough). Math. Oper. Res., 2021, 46(1), 221–254.
   Web of Science ®Google Scholar
• Carr, P. and Madan, D., Option valuation using the fast Fourier transform. J. Comput. Finance, 1999, 2(4), 61–73.
   Google Scholar
• Carr, P., Geman, H., Madan, D.B. and Yor, M., The fine structure of asset returns: An empirical investigation. J. Business, 2002, 75(2), 305–332.
   Web of Science ®Google Scholar
• Chen, R.-R. and Scott, L., Pricing interest rate options in a two-factor Cox–Ingersoll–Ross model of the term structure. Rev. Financ. Stud., 1992, 5(4), 613–636.
   Web of Science ®Google Scholar
• Cherubini, U., Della Lunga, G., Mulinacci, S. and Rossi, P., Fourier Transform Methods in Finance, 2009 (John Wiley & Sons Inc.).
   Google Scholar
• Chourdakis, K., Option pricing using the fractional FFT. J. Comput. Finance, 2005, 8(2), 1–18.
   Google Scholar
• Diethelm, K., Ford, N.J. and Freed, A.D., Detailed error analysis for a fractional Adams method. Numer. Algorithms, 2004, 36(1), 31–52.
   Web of Science ®Google Scholar
• Duffie, D., Pan, J. and Singleton, K., Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 2000, 68(6), 1343–1376.
   Web of Science ®Google Scholar
• El Euch, O. and Rosenbaum, M., Perfect hedging in rough Heston models. Ann. Appl. Probab., 2018, December, 28(6), 3813–3856.
   Web of Science ®Google Scholar
• El Euch, O. and Rosenbaum, M., The characteristic function of rough Heston models. Math. Finance, 2019, 29(1), 3–38.
   Web of Science ®Google Scholar
• El Euch, O., Gatheral, J. and Rosenbaum, M., Roughening Heston. Risk, 2019, May, 84–89.
   Google Scholar
• Fang, F. and Oosterlee, C.W., A novel pricing method for European options based on Fourier-cosine series expansions. SIAM. J. Sci. Comput., 2009, 31(2), 826–848.
   Web of Science ®Google Scholar
• Fukasawa, M., Asymptotic analysis for stochastic volatility: Martingale expansion. Finance Stoch., 2011, 15(4), 635–654.
   Web of Science ®Google Scholar
• Fukasawa, M., The normalizing transformation of the implied volatility smile. Math. Finance, 2012, 22(4), 753–762.
   Web of Science ®Google Scholar
• Gatheral, J. and Radoicic, R., Rational approximation of the rough Heston solution. Int. J. Theor. Appl. Finance, 2019, 22(3), 1950010.
   Web of Science ®Google Scholar
• Gatheral, J., Jaisson, T. and Rosenbaum, M., Volatility is rough. Quant. Finance, 2018, 18(6), 933–949.
   Web of Science ®Google Scholar
• Hardiman, S.J., Bercot, N. and Bouchaud, J.-P., Critical reflexivity in financial markets: A Hawkes process analysis. Euro. Phys. J. B, 2013, 86(10), 442.
   Web of Science ®Google Scholar
• Hawkes, A.G., Point spectra of some mutually exciting point processes. J. R. Stat. Soc. Ser. B (Methodological), 1971a, 33(3), 438–443.
   Google Scholar
• Hawkes, A.G., Spectra of some self-exciting and mutually exciting point processes. Biometrika, 1971b, 58(1), 83–90.
   Web of Science ®Google Scholar
• Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud., 1993, 6(2), 327–343.
   Web of Science ®Google Scholar
• Jaisson, T. and Rosenbaum, M., Limit theorems for nearly unstable Hawkes processes. Ann. Appl. Probab., 2015, 25(2), 600–631.
   Web of Science ®Google Scholar
• Jaisson, T. and Rosenbaum, M., Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes. Ann. Appl. Probab., 2016, 26(5), 2860–2882.
   Web of Science ®Google Scholar
• Lewis, A.L., Option Valuation Under Stochastic Volatility with Mathematica Code, 2000 (Finance Press: Newport Beach, CA).
   Google Scholar
• Lewis, A.L., A simple option formula for general jump-diffusion and other exponential Lévy processes. SSRN working paper, http://ssrn.com/abstract=282110, 2001.
   Google Scholar
• Livieri, G., Mouti, S., Pallavicini, A. and Rosenbaum, M., Rough volatility: Evidence from option prices. IISE Trans., 2018, 50(9), 767–776.
   Web of Science ®Google Scholar
• McCrickerd, R. and Pakkanen, M.S., Turbocharging Monte Carlo pricing for the rough Bergomi model. Quant. Finance, 2018, 18(11), 1877–1886.
   Web of Science ®Google Scholar
• Scott, L.O., Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. Math. Finance, 1997, 7(4), 413–426.
   Web of Science ®Google Scholar
• Shannon, C.E., Communication in the presence of noise. Proc. IRE, 1949, 37(1), 10–21.
   Google Scholar