Pricing Asian options in a semimartingale model

Večeř, Jan; Xu, Mingxin

doi:10.1088/1469-7688/4/2/006

Cited by 33 publications

(15 citation statements)

References 17 publications

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“…When explicit formulas do not exist some accurate analytic approximations have been proposed, as in [8]. Paper [9] is the only one, to our knowledge, dealing with the valuation problem of Arithmetic Asian options in a general semimartingale setting, where a Partial Integro-Differential Equation is provided solving the problem in the special case of an underlying described by a process with independent increments. As far as lower and upper bounds on prices are concerned some results are available for Arithmetic Asian options both in the continuous [10] and the discrete monitoring case [11], where a convenient use of the comonotonicity property is exploited in order to provide such bounds.…”

Section: Introductionmentioning

confidence: 99%

“…As far as stochastic volatility models are concerned, paper [15] deals with the evaluation problem for Arithmetic Asian options by extending the reduction technique introduced in [9], while Cheung and Wong [16] obtain via a perturbation method some semi-analytical formulas for Geometric Asian options in stochastic volatility models exhibiting a meanreverting behavior.…”

Section: Introductionmentioning

confidence: 99%

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On the explicit evaluation of the Geometric Asian options in stochastic volatility models with jumps

Hubalek

Sgarra

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tIn the present paper we provide a semiexplicit valuation formula for Geometric Asian options, with fixed and floating strike under continuous monitoring, when the underlying stock price process exhibits both stochastic volatility and jumps. More precisely, we shall work in the Barndorff-Nielsen and Shephard (BNS) model framework. We shall provide some numerical illustrations of the results obtained.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the explicit evaluation of the Geometric Asian options in stochastic volatility models with jumps

Hubalek

Sgarra

2011

Journal of Computational and Applied Mathematics

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“…An also accurate double-transform at low volatility levels is suggested in Fusai [38], whereas Cai and Kou [14] generalize to a double-Laplace transform under the hyperexponential jump diffusion model, encompassing the Gaussian model and Kou's double exponential jump diffusion as special cases. Večeř and Xu [70] show that the option price satisfies a partial integro-differential equation (PIDE) in the case of exponential Lévy price dynamics, which is solved numerically in Bayraktar and Xing [9] for the special case of jump diffusion models. Finally, Ewald et al [36] propose a solution under the Heston model by means of a PDE and a Monte Carlo simulation method, whereas Yamazaki [71] a pricing formula based on the GramCharlier expansion.…”

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confidence: 99%

General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options

Fusai

Kyriakou

2016

Mathematics of OR

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This is the accepted version of the paper.This version of the publication may differ from the final published version. We propose an accurate method for pricing arithmetic Asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation. In particular, we derive analytical expressions for the lower bound in the Fourier domain. This is then recovered by a single univariate inversion and sharpened using an optimization technique. In addition, we derive an upper bound to the error from the lower bound price approximation. Our proposed method can be applied to computing the prices and price sensitivities of Asian options with fixed or floating strike price, discrete or continuous averaging, under a wide range of stochastic dynamic models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. Our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases. Permanent repository linkKey words : arithmetic Asian options; CEV diffusion; stochastic volatility models; Lévy processes; discrete average; continuous average MSC2000 subject classification : Primary: 91B70, 91B25, 60J25; Secondary: 60H30, 91B24 OR/MS subject classification : Primary: asset pricing, diffusion, Markov processes, stochastic model applications 1. Introduction. We develop accurate analytical pricing formulae for discretely and continuously monitored arithmetic Asian options under general stochastic asset models, including exponential Lévy models, stochastic volatility models, and the constant elasticity of variance diffusion. The payoff of the arithmetic Asian option depends on the arithmetic average price of the underlying asset monitored over a pre-specified period. For more than two decades, much effort has been put into the research on efficient methodologies for computing the price of this option or, in general, expected values of functionals of the average value, under different model assumptions for the underlying. Developing such methods is of considerable practical importance as arithmetic averages see wide application in many fields of finance. Amongst others, we mention uses in computing net present value in project valuation (see [72]), optimal capacity planning under average demand uncertainty for a single firm (see [32]) and stock-swap merger proposals (see [60]). Weighted arithmetic averages also appear in technical analysis and in algorithmic trading; for example, we recall the moving average trading rule and its use from an asset allocation perspective (see [75]). Moving average automatic trading strategies set buying and selling orders depending on the position of the average price for a given period with respect to the current market price (see [50]). Finally, weighted arithmetic average indexes are used as trading benchmarks in pension plans (see [11]).Arithmetic Asian options are very popular among derivatives traders and risk managers. Their...

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“…We show that v is the fixed point of the functional operator. Finally, we show that v satisfies the certain regularity properties, which ensures that it is the classical solution of the partial integro-differential equation in Večeř and Xu (2004). This proof technique is similar to that of Bayraktar (2009), in which the regularity of the American put option prices is analyzed.…”

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confidence: 71%

Pricing Asian Options for Jump Diffusion

Bayraktar

Xing

2010

Mathematical Finance

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We construct a sequence of functions that uniformly converge (on compact sets) to the price of an Asian option, which is written on a stock whose dynamics follow a jump diffusion. The convergence is exponentially fast. We show that each element in this sequence is the unique classical solution of a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accuracy versus speed characteristics can be controlled. We analyze the performance of our numerical algorithm on several examples. KEY WORDS: pricing Asian options, jump diffusions, an iterative numerical scheme, classical solutions of integro partial differential equations.

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Pricing Asian options in a semimartingale model

Cited by 33 publications

References 17 publications

On the explicit evaluation of the Geometric Asian options in stochastic volatility models with jumps

On the explicit evaluation of the Geometric Asian options in stochastic volatility models with jumps

General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options

Pricing Asian Options for Jump Diffusion

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