Quantization meets Fourier: a new technology for pricing options

Option Pricing with Orthogonal Polynomial Expansions

“…Notable progress has recently been made on the pricing of early-exercise and path-dependent options with stochastic volatility using recursive marginal quantization as studied in Pagès and Sagna (2015); McWalter et al (2017); Callegaro et al (2017a). In the context of affine and polynomial models, this approach has been shown to perform well when combined with Fourier transform techniques as in Callegaro et al (2017b), or polynomial expansion techniques as in Callegaro et al (2017), whose results could be further improved with the new expansions presented in our paper. The calculation of Greeks for stochastic volatility models is a difficulty task often adressed by Monte Carlo simulations, see for examples Broadie and Kaya (2004) for a discussion of different simulation based estimators in the Heston model, and Chan et al (2015) for more recent advances using algorithmic differentiation.…”

Smiles & smirks: Volatility and leverage by jumps

“…The characteristic function of each model can then be obtained by substitution in the expressions reported in Table 2; finally we convert characteristic functions into option prices via an efficient algorithm for Fourier inversion. We adopt the COS method of Fang and Oosterlee (2008); other available methods are the ones proposed by Eberlein et al (2010), and more recently by Kirkby (2015), Callegaro et al (2019) and Cui et al (2019) amongst others.…”

Unified Moment-Based Modelling of Integrated Stochastic Processes

“…Compute the moments of Ψ(t, t + ∆) conditional on σ(t) and Φ(t, t + ∆) using Algorithm 1 5: Sample from the conditional Ψ(t, t + ∆) from ( 16) given the moments 6: Sample S(t + ∆) given S(t), σ(t), Φ(t, t + ∆) and Ψ(t, t + ∆) 7: end for 16) given the moments 6: Simulate X(t + ∆) from (33) given X(t) 7: end for Notes. Parameter sets H1-2, B1, DPS1 and H3-6 are from and Glasserman and Kim (2011), DH1-2 from Gauthier and Possamaï (2010) and Zhang and Feng (2019), SABR1-3 and SABR4-6 from and Leitao et al (2017), OU-SV1-3 from , 3/2-1 and 4/2-1 from and Callegaro et al (2019), 3/2-2 and 4/2-2 from Gnoatto et al (2016), NIGCIR1 from Corsaro et al (2019, Table 2) and SECIRJD1 from Fulop and Li (2019, Table 8). , Glasserman and Kim, 2011 for different models and parameter sets: the case of European plain vanilla option Notes.…”