References
- Ackerer, D., Filipovic, D. and Pulido, S., The Jacobi stochastic volatility model. Financ. Stoch., 2018, 22(3), 667–700. doi: 10.1007/s00780-018-0364-8
- Bally, V., Pagès, G. and Printems, J., A stochastic quantization method for nonlinear problems. Monte Carlo Methods Appl., 2001, 1-2(7), 21–33. doi: 10.1515/mcma.2001.7.1-2.21
- Bally, V., Pagès, G. and Printems, J., A quantization tree method for pricing and hedging multidimensional American options. Math. Finance, 2005, 15(1), 119–168. doi: 10.1111/j.0960-1627.2005.00213.x
- Bormetti, G., Callegaro, G., Livieri, G. and Pallavicini, A., A backward Monte Carlo approach to exotic option pricing. Eur. J. Appl. Math., 2018, 29(1), 146–187. doi: 10.1017/S0956792517000079
- Callegaro, G., Fiorin, L. and Grasselli, M., Quantized calibration in local volatility. Risk Mag., 2015, 28(4), 62–67.
- Callegaro, G., Fiorin, L. and Grasselli, M., Pricing via recursive quantization in stochastic volatility models. Quant. Finance, 2017, 17(6), 855–872. doi: 10.1080/14697688.2016.1255348
- Callegaro, G., Fiorin, L. and Grasselli, M., American quantized calibration in stochastic volatility. Risk Mag., 2018, 31(2), 84–88.
- Callegaro, G., Fiorin, L. and Grasselli, M., Quantization meets Fourier: A new technology for pricing options. Ann. Oper. Res., 2019, 282(1), 59–86. doi: 10.1007/s10479-018-3048-z
- Chateau, J.-P. and Dufresne, D., Gram-Charlier processes and applications to option pricing. J. Probab. Stat., 2017, 2017, 8690491. doi: 10.1155/2017/8690491
- Cuchiero, C., Keller-Ressel, M. and Teichmann, J., Polynomial processes and their applications to mathematical finance. Financ. Stoch., 2012, 16(4), 711–740. doi: 10.1007/s00780-012-0188-x
- Cui, Z., Kirkby, J. and Nguyen, D., A general valuation framework for sabr and stochastic local volatility models. SIAM J. Financ. Math., 2018, 9(2), 520–563. doi: 10.1137/16M1106572
- Filipovic, D. and Larsson, M., Polynomial diffusions and applications in finance. Financ. Stoch., 2016, 20(4), 931–972. doi: 10.1007/s00780-016-0304-4
- Filipovic, D., Larsson, M. and Pulido, S., Markov cubature rules for polynomial processes. Stoch. Proc. Appl., 2020, 130(4), 1947–1971. doi: 10.1016/j.spa.2019.06.010
- Fiorin, L., Pagès, G. and Sagna, A., Product Markovian quantization of a diffusion process with applications to finance. Methodol. Comput. Appl. Probab., 2018, 21(4), 1087–1118. doi: 10.1007/s11009-018-9652-1
- Fiorin, L. and Schoutens, W., Conic quantization: Stochastic volatility and market implied liquidity. Quant. Finance, 2020, 20(4), 531–542. doi: 10.1080/14697688.2019.1687928
- Gersho, A. and Gray, R., Vector Quantization and Signal Compression, The Kluwer international series in engineering and computer science Vol. 159, 1991 (Kluwer).
- Graf, S. and Luschgy, H., Foundations of Quantization for Probability Distributions, 2000 (Springer: New York).
- Jondeau, E. and Rockinger, M., Estimating Gram–Charlier expansions with positivity constraints. Notes d'études et de recherche Banque de France (1999).
- Kieffer, J., Stochastic stability for feedback quantization schemes. IEEE Trans. Inform. Theory, 1982, 28(2), 248–254.
- León, A., Mencía, J. and Sentana, E., Parametric properties of semi-nonparametric distributions, with applications to option valuation. J. Bus. Econ. Stat., 2009, 27(2), 176–192. doi: 10.1198/jbes.2009.0013
- McWalter, T., Rudd, R., Kienitz, J. and Platen, E., Recursive marginal quantization of higher-order schemes. Quant. Finance, 2018, 18(4), 693–706. doi: 10.1080/14697688.2017.1402125
- Montes, T., Numerical methods by optimal quantization in finance. PhD thesis, Sorbonne Université - LPSM, 2020.
- Níguez, T. and Perote, J., Forecasting heavy-tailed densities with positive Edgeworth and Gram–Charlier expansions. Oxf. Bull. Econ. Stat., 2012, 74(4), 600–627. doi: 10.1111/j.1468-0084.2011.00663.x
- Pagès, G., Introduction to vector quantization and its applications for numerics. ESAIM: Proc. Surveys, 2015, 48, 29–79. doi: 10.1051/proc/201448002
- Pagès, G. and Sagna, A., Recursive marginal quantization of the Euler scheme of a diffusion process. Appl. Math. Finance, 2015, 22(5), 463–498. doi: 10.1080/1350486X.2015.1091741
- Rompolis, L. and Tzavalis, E., Retrieving risk neutral densities based on risk neutral moments through a Gram-Charlier series expansion. Math. Comput. Model., 2007, 46(1–2), 225–234. doi:10.1016/j.mcm.2006.12.021
- Schlogl, E., Option pricing where the underlying assets follow a Gram–Charlier density of arbitrary order. J. Econ. Dyn. Control, 2013, 37(3), 611–632. doi:10.1016/j.jedc.2012.10.001