Here we develop an option pricing method for European options based on the Fourier-
cosine series and call it the COS method. The key insight is in the close relation of the …

The COS method for pricing European and Bermudan options with one underlying asset
was developed in [F. Fang and CW Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826 …

The development of affine processes in modelling has shadowed the expansion of financial
mathematics ever since the pioneering works of Black and Scholes [20] and Merton [106] in …

This paper presents an algorithm for a complete and efficient calibration of the Heston
stochastic volatility model. We express the calibration as a nonlinear least-squares problem …

We rigorize the work of Lewis (2007) and Durrleman (2005) on the small-time asymptotic
behavior of the implied volatility under the Heston stochastic volatility model (Theorem 2.1) …

At the time of writing this article, Fourier inversion is the computational method of choice for a
fast and accurate calculation of plain vanilla option prices in models with an analytically …

Fourier transform techniques are playing an increasingly important role in Mathematical
Finance. For arbitrary stochastic price processes for which the characteristic functions are …

In this article, we propose an efficient approach for inverting computationally expensive
cumulative distribution functions. A collocation method, called the Stochastic Collocation …

This paper presents a flexible valuation approach for variable annuity (VA) contracts
embedded with guaranteed minimum maturity benefit (GMMB) riders written on an …

We recommend the addition of a deterministic displacement to multi-factor affine models to
calibrate and hedge SPX and VIX derivatives jointly. The proposed model, labeled …