• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.123-135
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• 2016

This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.181-195
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• 2020

This paper suggests the price of vulnerable European option under a constant elasticity of variance model by using asymptotic analysis technique and obtains the approximated solution of the option price. Finally, we illustrate an accuracy of the vulnerable option price so that the approximate solution is well-defined.

• East Asian mathematical journal
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• v.31 no.1
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• pp.91-101
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• 2015

An explicit expression of the optimal investment strategy corresponding to the HARA utility function under the constant elasticity of variance (CEV) model has been given by Jung and Kim [6]. In this paper we give an explicit expression of the optimal solution for the extended logarithmic utility function. And we prove an a.s. convergence of the HARA solutions to the extended logarithmic one.

• East Asian mathematical journal
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• v.37 no.5
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• pp.553-566
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• 2021

In the over-the-counter market, option's buyers could have a problem for default risk caused by option's writers. In addition, many participants try to maximize their benefits obviously in investing the financial derivatives. Taking all these circumstances into consideration, we deal with the vulnerable power options under a constant elasticity variance (CEV) model. We derive an analytic pricing formula for the vulnerable power option by using the asymptotic analysis, and then we verify that the analytic formula can be obtained accurately by comparing our solution with Monte-Carlo price. Finally, we examine the effect of CEV on the option price based on the derived solution.

• Management Science and Financial Engineering
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• v.20 no.1
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• pp.27-32
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• 2014

This paper introduces three different simulation algorithms of the shifted Poisson distribution. The first algorithm is the inverse transform method, the second is the rejection sampling, and the third is gamma-Poisson hierarchy sampling. Three algorithms have different regions of parameters at which they are efficient. We numerically compare those algorithms with different sets of parameters. As an application, we give a simulation method of the constant elasticity of variance model.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• Journal of Korean Institute of Industrial Engineers
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• v.38 no.4
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• pp.244-248
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• 2012

We present a simple numerical method for pricing American put options under a constant elasticity of variance (CEV) model. Our analysis is done in a general framework where only the risk-neutral transition density of the underlying asset price is given. We obtain an integral equation of early exercise premium. By exploiting a modification of the integral equation, we propose a novel and simple numerical iterative valuation method for American put options.