Fourier Cosine Expansions and Put–Call Relations for Bermudan Options

Zhang, Bowen; Oosterlee, Cornelis W.

doi:10.1007/978-3-642-25746-9_10

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…For this reason we price Put options only using our approach and we employ the well-known Put-Call parity to price Calls via Puts. This is a rather standard argument (see, for instance, [17]).…”

Section: Bermudan Option Valuationmentioning

confidence: 96%

Pricing Bermudan options under local Lévy models with default

Borovykh

Pascucci

Oosterlee

2017

Journal of Mathematical Analysis and Applications

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We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy measure. We present a pricing method for Bermudan options based on an analytical approximation of the characteristic function combined with the COS method. Due to a special form of the obtained characteristic function the price can be computed using a Fast Fourier Transform-based algorithm resulting in a fast and accurate calculation. The Greeks can be computed at almost no additional computational cost. Error bounds for the approximation of the characteristic function as well as for the total option price are given.

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Section: Bermudan Option Valuationmentioning

confidence: 96%

Pricing Bermudan options under local Lévy models with default

Borovykh

Pascucci

Oosterlee

2017

Journal of Mathematical Analysis and Applications

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“…where L is a user-defined parameter to achieve a certain integration accuracy, and parameters ξ i represent the corresponding cumulants of the underlying stochastic process, refer to the paper [33] for more details.…”

Section: A1 Pricing Bermudan Optionsmentioning

confidence: 99%

On Calibration Neural Networks for extracting implied information from American options

Liu¹,

Leitao²,

Borovykh³

et al. 2020

Preprint

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Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem many thousands of times. We will employ a data-driven machine learning approach to estimate the Black-Scholes implied volatility and the dividend yield for American options in a fast and robust way. To determine the implied volatility, the inverse function is approximated by an artificial neural network on the computational domain of interest, which decouples the offline (training) and online (prediction) phases and thus eliminates the need for an iterative process. For the implied dividend yield, we formulate the inverse problem as a calibration problem and determine simultaneously the implied volatility and dividend yield. For this, a generic and robust calibration framework, the Calibration Neural Network (CaNN), is introduced to estimate multiple parameters. It is shown that machine learning can be used as an efficient numerical technique to extract implied information from American options.

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“…Shu et al [9] and Kovalov et al [10] use a partial differential equations approach. Zhang and Oosterlee [11] use a Fourier method based on Fourier cosine-series expansions. We follow an approach similar to the one by Mrad et al [12] and Bally and Pag es [13] based on a Monte Carlo method.…”

Section: Introductionmentioning

confidence: 99%

Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting

Daveloose

Khedher

Vanmaele

2019

Stochastic Analysis and Applications

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In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a L evy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.

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Fourier Cosine Expansions and Put–Call Relations for Bermudan Options

Cited by 8 publications

References 26 publications

Pricing Bermudan options under local Lévy models with default

Pricing Bermudan options under local Lévy models with default

On Calibration Neural Networks for extracting implied information from American options

Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting

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