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This note shows that the cosine expansion based on the Vieta formula is equivalent to a discretization of the Parseval identity. We then evaluate the use of simple direct algorithms to compute the Shannon coefficients for the payoff. Finally, we explore the efficiency of a Filon quadrature instead of the Vieta formula for the coefficients related to the probability density function.
This paper proposes the sample path generation method for the stochastic volatility version of CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to
In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs, instead of s
In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called G
The Fourier cosine expansion (COS) method is used for pricing European options numerically very fast. To apply the COS method, a truncation interval for the density of the log-returns need to be provided. Using Markovs inequality, we derive a new for
We present new numerical schemes for pricing perpetual Bermudan and American options as well as $alpha$-quantile options. This includes a new direct calculation of the optimal exercise barrier for early-exercise options. Our approach is based on the