283
Views
0
CrossRef citations to date
0
Altmetric
Research Papers

Numerical smoothing with hierarchical adaptive sparse grids and quasi-Monte Carlo methods for efficient option pricing

, ORCID Icon & ORCID Icon

References

  • Alfonsi, A., High order discretization schemes for the CIR process: Application to affine term structure and Heston models. Math. Comput., 2010, 79(269), 209–237.
  • Andersen, L., Efficient simulation of the Heston stochastic volatility model, 2007. Available online at: SSRN 946405.
  • Andersen, L. and Brotherton-Ratcliffe, R., Extended libor market models with stochastic volatility, 2001. Available online at: SSRN 294853.
  • Barthelmann, V., Novak, E. and Ritter, K., High dimensional polynomial interpolation on sparse grids. Adv. Comput. Math., 2000, 12(4), 273–288.
  • Bayer, C., Siebenmorgen, M. and Tempone, R., Smoothing the payoff for efficient computation of basket option pricing. Quant. Finance, 2018, 18(3), 491–505.
  • 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, 2020a, 20(9), 1457–1473.
  • Bayer, C., Ben Hammouda, C. and Tempone, R., Multilevel Monte Carlo combined with numerical smoothing for robust and efficient option pricing and density estimation, 2020b. Preprint, arXiv:2003.05708.
  • Bayer, C., Ben Hammouda, C., Papapantoleon, A., Samet, M. and Tempone, R., Optimal damping with hierarchical adaptive quadrature for efficient Fourier pricing of multi-asset options in Lévy models, 2022. Preprint, arXiv:2203.08196.
  • Ben Hammouda, C., Hierarchical approximation methods for option pricing and stochastic reaction networks. PhD Thesis, 2020.
  • Broadie, M. and Kaya, Ö., Exact simulation of stochastic volatility and other affine jump diffusion processes. Oper. Res., 2006, 54(2), 217–231.
  • Bungartz, H.-J. and Griebel, M., Sparse grids. Acta Numer., 2004, 13, 147–269.
  • Chan, J.H. and Joshi, M., Fast Monte Carlo Greeks for financial products with discontinuous pay-offs. Math. Finance: Int. J. Math. Stat. Financ. Econ., 2013, 23(3), 459–495.
  • Chen, P., Sparse quadrature for high-dimensional integration with Gaussian measure. ESAIM: Math. Model. Numer. Anal., 2018, 52(2), 631–657.
  • De Luigi, C., Lelong, J. and Maire, S., Robust adaptive numerical integration of irregular functions with applications to basket and other multi-dimensional exotic options. Appl. Numer. Math., 2016, 100, 14–30.
  • Dick, J., Kuo, F.Y. and Sloan, I.H., High-dimensional integration: The quasi-Monte Carlo way. Acta Numer., 2013, 22, 133–288.
  • Ernst, O.G., Sprungk, B. and Tamellini, L., Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic pdes). SIAM J. Numer. Anal., 2018, 56(2), 877–905.
  • Fries, C.P. and Joshi, M.S., Conditional analytic Monte-Carlo pricing scheme of auto-callable products, 2008. Available online at: SSRN 1125725.
  • Gerstner, T. and Griebel, M., Numerical integration using sparse grids. Numer. Algorithms, 1998, 18(3), 209–232.
  • Giles, M.B. and Waterhouse, B.J., Multilevel quasi-Monte Carlo path simulation. Adv. Financ. Model. Radon Ser. Comput. Appl. Math., 2009, 8, 165–181.
  • Giles, M.B., Nagapetyan, T. and Ritter, K., Multilevel Monte Carlo approximation of distribution functions and densities. SIAM/ASA J Uncertain. Quantif., 2015, 3(1), 267–295.
  • Griebel, M., Kuo, F. and Sloan, I., The smoothing effect of integration in Rd and the ANOVA decomposition. Math. Comput., 2013, 82(281), 383–400.
  • Griebel, M., Kuo, F. and Sloan, I., Note on “the smoothing effect of integration in Rd and the ANOVA decomposition”. Math. Comput., 2017, 86(306), 1847–1854.
  • Griewank, A., Kuo, F.Y., Leövey, H. and Sloan, I.H., High dimensional integration of kinks and jumps-smoothing by preintegration. J. Comput. Appl. Math., 2018, 344, 259–274.
  • Haji-Ali, A.-L., Nobile, F., Tamellini, L. and Tempone, R., Multi-index stochastic collocation for random PDEs. Comput. Methods Appl. Mech. Eng., 2016, 306, 95–122.
  • 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.
  • Jeanblanc, M., Yor, M. and Chesney, M., Mathematical Methods for Financial Markets, 2009 (Springer Science & Business Media: London).
  • Kahl, C. and Jäckel, P., Fast strong approximation Monte Carlo schemes for stochastic volatility models. Quant. Finance, 2006, 6(6), 513–536.
  • Lord, R., Koekkoek, R. and Van Dijk, D., A comparison of biased simulation schemes for stochastic volatility models. Quant. Finance, 2010, 10(2), 177–194.
  • Mastroianni, G. and Monegato, G., Error estimates for Gauss-Laguerre and Gauss-Hermite quadrature formulas. In Approximation and Computation: A Festschrift in Honor of Walter Gautschi, pp. 421–434, 1994 (Springer: Boston, MA).
  • Niederreiter, H., Random Number Generation and Quasi-Monte Carlo Methods, Vol. 63, 1992 (SIAM: Philadelphia).
  • Nuyens, D., The construction of good lattice rules and polynomial lattice rules. In Uniform Distribution and Quasi-Monte Carlo Methods, pp. 223–256, 2014 (De Gruyter: Berlin).
  • Sloan, I.H., Lattice methods for multiple integration. J. Comput. Appl. Math., 1985, 12–13, 131–143.
  • Sloan, I.H. and Woźniakowski, H., When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complex., 1998, 14(1), 1–33.
  • Xiao, Y. and Wang, X., Conditional quasi-Monte Carlo methods and dimension reduction for option pricing and hedging with discontinuous functions. J. Comput. Appl. Math., 2018, 343, 289–308.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.