A General Framework for Pricing Asian Options Under Markov Processes

Cai, Ning; Song, Yingda; Kou, Steven

doi:10.1287/opre.2015.1385

Cited by 97 publications

(65 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of the ASV models considered in this study, obtaining the characteristic functions based on the continuous average by applying the same limiting argument as in the Lévy model case on the discrete average-based characteristic functions (16) and (19) is not trivial. Alternatively, it is necessary to derive first the characteristic function of the triple (V, X, Y ) (see [47] for the case of ASV models).…”

Section: Continuous Averagementioning

confidence: 99%

“…Consider the functions φ andφ given respectively by the expressions (14) and (18) for X driven by a Lévy model; (16) and (19) for X driven by an ASV model. Then, we have that…”

Section: Theorem 3 (Fixed and Floating Strike Continuous Asian Optiomentioning

confidence: 99%

“…The special case of γ = 1 corresponds to the well known square root process of Cox and Ross [25], whereas when γ = 2 we obtain the lognormal model. The CEV diffusion with γ = 1 has been applied to the pricing of arithmetic Asian options in Dassios and Nagaradjasarma [29], Fusai et al [39] and, more recently, in its general form in Cai et al [15], Sesana et al [64] and Cai et al [16].…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Fusai

Kyriakou

2016

Mathematics of OR

View full text Add to dashboard Cite

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...

show abstract

Section: Continuous Averagementioning

confidence: 99%

“…Consider the functions φ andφ given respectively by the expressions (14) and (18) for X driven by a Lévy model; (16) and (19) for X driven by an ASV model. Then, we have that…”

Section: Theorem 3 (Fixed and Floating Strike Continuous Asian Optiomentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

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

Fusai

Kyriakou

2016

Mathematics of OR

View full text Add to dashboard Cite

show abstract

“…For instance, Angus (1999) works under the Black-Scholes model to investigate the prices of geometric Asian options. Cai, Song, and Kou (2015) propose a general framework for pricing both continuously and discretely monitored Asian options under one-dimensional Markov processes and derive the double transform of the Asian option price in terms of the unique bounded solution to a related functional equation. Bayraktar and Xing (2011) find a sequence of functions that uniformly converge to the price of an arithmetic Asian option, when the dynamics of the underlying asset follows a jump-diffusion process.…”

Section: Introductionmentioning

confidence: 99%

Analytical valuation of Asian options with counterparty risk under stochastic volatility models

Wang

2019

Journal of Futures Markets

View full text Add to dashboard Cite

In this paper, we consider Asian options with counterparty risk under stochastic volatility models. We propose a simple way to construct stochastic volatility models through the market factor channel. In the proposed framework, we obtain an explicit pricing formula of Asian options with counterparty risk and illustrate the effects of systematic risk on Asian option prices. Specially, the U-shaped and inverted U-shaped curves appear when we keep the total risk of the underlying asset and the issuer's assets unchanged, respectively.

show abstract

“…A number of empirical studies demonstrate that no single model can offer superior performance for all possible types of derivative contracts. Therefore different model selection frameworks have been proposed (Cai et al, 2015;Shcherbakov and Larsson, 2016;Orbay et al, 2016) but in this paper we shall stick to a model selection that is based on the characteristics of the underlying asset and is not driven by an optimization procedure. The selection frameworks described above can still be applied to weather derivatives in combination with our approach, where valuation method is chosen by the researcher and then model dimensions and assumptions are selected through a predefined procedure.…”

Section: Introductionmentioning

confidence: 99%

Modelling Environment Changes for Pricing Weather Derivatives

Kabaivanov

Markovska

2017

Scientific Annals of Economics and Business

View full text Add to dashboard Cite

This paper focuses on modelling environment changes in a way that allows to price weather derivatives in a flexible and efficient way. Applications and importance of climate and weather contracts extends beyond financial markets and hedging as they can be used as complementary tools for risk assessment. In addition, option-based approach toward resource management can offer very special insights on rareevents and allow to reuse derivative pricing methods to improve natural resources management. To demonstrate this general concept, we use Monte Carlo and stochastic modelling of temperatures to evaluate weather options. Research results are accompanied by R and Python code.

show abstract

A General Framework for Pricing Asian Options Under Markov Processes

Cited by 97 publications

References 25 publications

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

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

Analytical valuation of Asian options with counterparty risk under stochastic volatility models

Modelling Environment Changes for Pricing Weather Derivatives

Contact Info

Product

Resources

About