Hedging of Asian options under exponential Lévy models: computation and performance

Ballotta, Laura; Gerrard, Russell; Kyriakou, Ioannis

doi:10.1080/1351847x.2015.1066694

Cited by 9 publications

(3 citation statements)

References 35 publications

(37 reference statements)

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“…It takes around 0.2 seconds to generate one numerical result of delta via our method. For a detailed study for computing greeks of Asian options under exponential Lévy models, we refer to the paper by Ballotta et al (2014).…”

Section: Computing the Greeksmentioning

confidence: 99%

A General Framework for Pricing Asian Options Under Markov Processes

Cai

Song

Kou

2015

Operations Research

101

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A general framework is proposed for pricing both continuously and discretely monitored Asian options under onedimensional Markov processes. For each type (continuously monitored or discretely monitored), we derive the double transform of the Asian option price in terms of the unique bounded solution to a related functional equation. In the special case of continuous-time Markov chain (CTMC), the functional equation reduces to a linear system that can be solved analytically via matrix inversion. Thus the Asian option prices under a one-dimensional Markov process can be obtained by first constructing a CTMC to approximate the targeted Markov process model, and then computing the Asian option prices under the approximate CTMC by numerically inverting the double transforms. Numerical experiments indicate that our pricing method is accurate and fast under popular Markov process models, including the CIR model, the CEV model, Merton's jump diffusion model, the double-exponential jump diffusion model, the variance gamma model, and the CGMY model.

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Section: Computing the Greeksmentioning

confidence: 99%

A General Framework for Pricing Asian Options Under Markov Processes

Cai

Song

Kou

2015

Operations Research

101

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“…We conclude this section by citing some related works based on the Fourier transform in computational finance. As an alternative to MC and QMC, the Fourier transform is employed to the pricing and hedging of options (Ballotta et al, 2017;Fang and Oosterlee, 2008;Fusai et al, 2016). In our numerical experiments, we focus on comparing the proposed method with some existing QMC methods to evaluate the quality of our strategy in the QMC literature.…”

Section: Introductionmentioning

confidence: 99%

An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering

Wang

2020

Comput Econ

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Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the performance of the QMC method. This paper develops an integrated method that overcomes the challenges of the high dimensionality and discontinuities concurrently. For this purpose, a smoothing method is proposed to remove the discontinuities for some typical functions arising from financial engineering. To make the smoothing method applicable for more general functions, a new path generation method is designed for simulating the paths of the underlying assets such that the resulting function has the required form. The new path generation method has an additional power to reduce the effective dimension of the target function. Our proposed method caters for a large variety of model specifications, including the Black-Scholes, exponential normal inverse Gaussian Lévy, and Heston models. Numerical experiments dealing with these models show that in the QMC setting the proposed smoothing method in combination with the new path generation method can lead to a dramatic variance reduction for pricing exotic options with discontinuous payoffs and for calculating options' Greeks. The investigation on the effective dimension and the related characteristics explains the significant enhancement of the combined procedure.

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“…Finally, another advantage of our method is that the option price sensitivities (also known as the Greeks) can be obtained assuming that we can differentiate equations (16)- (17) under the integral sign (a usual assumption in option pricing via Fourier transform) with respect to parameters of interest, e.g., the initial variance υ 0 , etc. (see Ballotta et al 2016 for the case of general Lévy log-increments of the underlying asset price).…”

Section: Proof We Prove By Induction On K That E((e Ynmentioning

confidence: 99%

Jumps and stochastic volatility in crude oil prices and advances in average option pricing

Kyriakou

Pouliasis

Papapostolou

2016

Quantitative Finance

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Hedging of Asian options under exponential Lévy models: computation and performance

Abstract: This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent

Cited by 9 publications

References 35 publications

A General Framework for Pricing Asian Options Under Markov Processes

A General Framework for Pricing Asian Options Under Markov Processes

An Integrated Quasi-Monte Carlo Method for Handling High Dimensional Problems with Discontinuities in Financial Engineering

Jumps and stochastic volatility in crude oil prices and advances in average option pricing

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