Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps

Chung, Shing Fung; Wong, Hoi Ying

doi:10.1016/j.jbankfin.2014.04.011

Cited by 22 publications

(15 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that all risk premium related to the jump are artificially absorbed by the change in the intensity of the jump from λ under the physical measure to λ Q under the risk-neutral measure, see [17]. Moreover, we assume in (4) that J(S, δ, Y ) = Y , where Y is a random variable which follows a normal distribution N (0, σ Y ), see [24], [4] and [23] among others. Therefore,…”

Section: Empirical Applicationmentioning

confidence: 99%

A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models

Gómez-Valle

Habibilashkary

Martínez-Rodríguez

2017

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

In order to price commodity derivatives, it is necessary to estimate the market prices of risk as well as the functions of the stochastic processes of the factors in the model. However, the estimation of the market prices of risk is an open question in the jump-diffusion derivative literature when a closed-form solution is not known. In this paper, we propose a novel approach for estimating the functions of the risk-neutral processes directly from market data. Moreover, this new approach avoids the estimation of the physical drift as well as the market prices of risk in order to price commodity futures. More precisely, we obtain some results that relate the risk-neutral drifts, volatilities and parameters of the jump amplitude distributions with market data. Finally, we examine the accuracy of the proposed method with NYMEX (New York Mercantile Exchange) data and we show the benefits of using jump processes for modelling the commodity price dynamics in commodity futures models. JEL classification: G13, G17.

show abstract

Section: Empirical Applicationmentioning

confidence: 99%

A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models

Gómez-Valle

Habibilashkary

Martínez-Rodríguez

2017

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…Fusai, Marena, and Roncoroni (2008) show the importance of mean reversion for commodity derivatives and derive an analytic solution to discrete Arithmetic Asian options. Chung and Wong (2014) further generalize it to include jumps.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing with Threshold Mean Reversion

Chi

Dong

Wong

2016

Journal of Futures Markets

Self Cite

View full text Add to dashboard Cite

Mean reversion and regime switching are well‐known features of commodity prices. Recent empirical research additionally documents the time variation of the mean reversion rate and volatility. This paper considers the option pricing framework for an underlying commodity price with mean reversion rate and volatility change according to a self‐exciting regime switching model. We offer empirical evidence for the proposed model and derive analytic pricing formulas for the European and barrier options. Numerical examples demonstrate the application and the ability of the proposed model in capturing volatility smile and regime‐switching in the mean reversion rate, simultaneously. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:107–131, 2017

show abstract

“…Future research can focus on alternative specifications of the drift term in the return process, such as the mean reversion process considered by [21]. The proposed Bayesian pricing framework can be generalized to other SV models such as the DSARV model by [7], and to incorporate information for the Volatility Index (VIX) data as suggested by [22].…”

Section: Discussionmentioning

confidence: 99%

Bayesian Option Pricing Framework with Stochastic Volatility for FX Data

Wang

Choy

Wong

2016

Risks

View full text Add to dashboard Cite

Abstract:The application of stochastic volatility (SV) models in the option pricing literature usually assumes that the market has sufficient option data to calibrate the model's risk-neutral parameters. When option data are insufficient or unavailable, market practitioners must estimate the model from the historical returns of the underlying asset and then transform the resulting model into its risk-neutral equivalent. However, the likelihood function of an SV model can only be expressed in a high-dimensional integration, which makes the estimation a highly challenging task. The Bayesian approach has been the classical way to estimate SV models under the data-generating (physical) probability measure, but the transformation from the estimated physical dynamic into its risk-neutral counterpart has not been addressed. Inspired by the generalized autoregressive conditional heteroskedasticity (GARCH) option pricing approach by Duan in 1995, we propose an SV model that enables us to simultaneously and conveniently perform Bayesian inference and transformation into risk-neutral dynamics. Our model relaxes the normality assumption on innovations of both return and volatility processes, and our empirical study shows that the estimated option prices generate realistic implied volatility smile shapes. In addition, the volatility premium is almost flat across strike prices, so adding a few option data to the historical time series of the underlying asset can greatly improve the estimation of option prices.

show abstract

Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps

Cited by 22 publications

References 16 publications

A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models

A new technique to estimate the risk-neutral processes in jump–diffusion commodity futures models

Option Pricing with Threshold Mean Reversion

Bayesian Option Pricing Framework with Stochastic Volatility for FX Data

Contact Info

Product

Resources

About