On the data-driven COS method

Abstract

a b s t r a c tIn this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is O(1 / √ n ) , in line with Monte Carlo methods for pricing financial derivatives. The ddCOS method is then particularly interesting for density recovery and also for the efficient computation of the option's sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods.

Nonparametric Density Estimation by B-Spline Duality

“…is an unbiased estimate of the projection coefficient. The Hermite function approach of Schwartz (1967) is a prominent example with E = R. The basis is indexed by N, with g k (x) : Schwartz (1967), Watson (1969), and Leitao et al (2018) study Harmonic series.…”

“…The literature on density estimation has steadfastly evolved in response to the growing applications of such techniques. While kernel density estimators prevail as the principal estimation approach, alternatives such as orthogonal sequence estimators have also received appreciable attention, including Schwartz (1967), Watson (1969), Hall (1981), Wahba (1981), and Hall (1987), and more recently Leitao, Oosterlee, Ortiz-Gracia, and Bohte (2018). While orthogonal sequence estimators generally rely on a global basis expansion of the (unknown) density, local density estimators using uniform B-splines and wavelets have also been considered in Redner (1999), Donoho, Johnstone, Kerkyacharian, and Picard (1996), Peter and Rangarajan (2008), Penev and Dechevsky (1997), and Huang (1999).…”

SWIFT valuation of discretely monitored arithmetic Asian options

“…with ψ and φ as in Equation (35). This iterative formulation is obtained by simply applying the definition of moment generating function, the tower law of probabilities and some algebraic manipulations.…”

“…The resulting values are shown in Table 8, where a regular arithmetic Asian call is priced and we have employed the same parameter configuration as in the previous experiments corresponding to each dynamics. The reference values are computed by the data-driven COS method [35] and Rolling Adjoints method [36], for Lévy and square-root dynamics, respectively. These Monte Carlo-based techniques provide stable and accurate sensitivities.…”

Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion

“…The one-dimensional COS (1D COS) method in [22] was extended to the two-dimensional COS method (2D COS) by Ruijter and Oosterlee [23] to price financial options in two-dimensional asset price processes. Leitao et al [24] proposed a data-driven COS method. Except for option pricing, this method has been adopted in insurance ruin theory.…”