Related papers: iCOS: Option-Implied COS Method
We provide a unified framework to obtain numerically certain quantities, such as the distribution function, absolute moments and prices of financial options, from the characteristic function of some (unknown) probability density function…
The goal of this paper is to investigate the method outlined by one of us (PR) in Cherubini et al. (2009) to compute option prices. We name it the SINC approach. While the COS method by Fang and Osterlee (2009) leverages the Fourier-cosine…
The COS method is a very efficient way to compute European option prices under L\'evy models or affine stochastic volatility models, based on a Fourier Cosine expansion of the density, involving the characteristic function. This note shows…
The COS method proposed in Fang and Oosterlee (2008), although highly efficient, may lack robustness for a number of cases. In this paper, we present a Stable pricing of call options based on Fourier cosine series expansion. The Stability…
The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number…
The Fourier cosine expansion (COS) method is used for pricing European options numerically very fast. To apply the COS method, a truncation range for the density of the log-returns need to be provided. Using Markov's inequality, we derive a…
A popular approach to nonparametric option pricing is the Minimum Cross Entropy (MCE) method based on minimization of the relative Kullback-Leibler entropy of the price density distribution and a given reference density, with observable…
We present an alternative formula to price European options through cosine series expansions, under models with a known characteristic function such as the Heston stochastic volatility model. It is more robust across strikes and as fast as…
In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of…
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices…
We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as…
Inverse Optimal Control (IOC) seeks to recover an unknown cost from expert demonstrations, and it provides a systematic way of modeling experts' decision mechanisms while considering the prior information of the cost functions.…
We provide a rigorous convergence proof demonstrating that the well-known semi-analytical Fourier cosine (COS) formula for the inverse Fourier transform of continuous probability distributions can be extended to discrete probability…
No--arbitrage property provides a simple method for pricing financial derivatives. However, arbitrage opportunities exist among different markets in various fields, even for a very short time. By knowing that an arbitrage property exists,…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection…
Fourier pricing methods such as the Carr-Madan formula or the COS method are classic tools for pricing European options for advanced models such as the Heston model. These methods require tuning parameters such as a damping factor, a…
In this paper, we derive the price of a European call option of an asset following a normal process assuming stochastic volatility. The volatility is assumed to follow the Cox Ingersoll Ross (CIR) process. We then use the fast Fourier…
We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…