scholarly journals Pricing arithmetic asian options under the cev process

2010 ◽  
Vol 15 (29) ◽  
pp. 7-13
Author(s):  
Bin Peng ◽  
◽  
Fei Peng ◽  
Keyword(s):  
Stock Price ◽  
Numerical Results ◽  
Asian Options ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Binomial Tree ◽  
Cev Process ◽  
Parameter Values ◽  
Tree Method

This paper discusses the pricing of arithmetic Asian options when the underlying stock follows the constant elasticity of variance (CEV) process. We build a binomial tree method to estimate the CEV process and use it to price arithmetic Asian options. We find that the binomial tree method for the lognormal case can effectively solve the computational problems arising from the inherent complexities of arithmetic Asian options when the stock price follows CEV process. We present numerical results to demonstrate the validity and the convergence of the approach for the different parameter values set in CEV process.

scholarly journals SHORT MATURITY ASIAN OPTIONS FOR THE CEV MODEL

2018 ◽  
Vol 33 (2) ◽  
pp. 258-290 ◽  
Author(s):  
Dan Pirjol ◽  
Lingjiong Zhu
Keyword(s):  
Analytical Approximation ◽  
Time Averaging ◽  
Asian Options ◽  
Option Prices ◽  
Asymptotic Results ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Practical Applications ◽  
Rigorous Study

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the constant elasticity of variance (CEV) model. The leading order short maturity limit of the Asian option prices under the CEV model is obtained in closed form. We propose an analytical approximation for the Asian options prices which reproduces the exact short maturity asymptotics, and demonstrate good numerical agreement of the asymptotic results with Monte Carlo simulations and benchmark test cases for option parameters relevant for practical applications.

scholarly journals Dynamic Mean-Variance Model with Borrowing Constraint under the Constant Elasticity of Variance Process

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Stock Price ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Dynamic Programming Principle ◽  
Legendre Transform ◽  
Order Partial Differential Equation ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Time Dynamic ◽  
Mean Variance

This paper studies a continuous-time dynamic mean-variance portfolio selection problem with the constraint of a higher borrowing rate, in which stock price is governed by a constant elasticity of variance (CEV) process. Firstly, we apply Lagrange duality theorem to change an original mean-variance problem into an equivalent optimization one. Secondly, we use dynamic programming principle to get the Hamilton-Jacobi-Bellman (HJB) equation for the value function, which is a more sophisticated nonlinear second-order partial differential equation. Furthermore, we use Legendre transform and dual theory to transform the HJB equation into its dual one. Finally, the closed-form solutions to the optimal investment strategy and efficient frontier are derived by applying variable change technique.

scholarly journals PENERAPAN METODE BINOMIAL TREE DALAM MENGESTIMASI HARGA KONTRAK OPSI TIPE AMERIKA

2016 ◽  
Vol 5 (4) ◽  
pp. 156
Author(s):  
I GUSTI AYU MITA ERMIA SARI ◽  
KOMANG DHARMAWAN ◽  
TJOKORDA BAGUS OKA
Keyword(s):  
Stock Price ◽  
Price Movement ◽  
Binomial Tree ◽  
Option Contracts ◽  
Black Scholes ◽  
Risk Neutral ◽  
Price Option ◽  
Tree Method

Binomial tree is a method that can be used to determine price option contracts. In this method, the stock price movement is presented in the form of a  tree with each branch representing the probability of the stock price to move up or move down. The purpose of this paper was to determine the price of the options contracts with the American type on Binomial Tree method and compare the three methods that is variance matching, proportional , and risk neutral of determining the value of price option contracts used in Binomial Tree method with Black-Schole method. The result of this research was the value of the options contract using the variance matching more similar with the value of the Black-Scholes contract.

Estimation in the Constant Elasticity of Variance Model

2001 ◽  
Vol 7 (2) ◽  
pp. 275-292 ◽  
Author(s):  
K.C. Yuen ◽  
H. Yang ◽  
K.L. Chu
Keyword(s):  
Diffusion Process ◽  
Stock Price ◽  
Estimation Procedure ◽  
Stock Option ◽  
Parameter Estimates ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Black Scholes ◽  
Two Parameters

ABSTRACTThe constant elasticity of variance (CEV) diffusion process can be used to model heteroscedasticity in returns of common stocks. In this diffusion process, the volatility is a function of the stock price and involves two parameters. Similar to the Black-Scholes analysis, the equilibrium price of a call option can be obtained for the CEV model. The purpose of this paper is to propose a new estimation procedure for the CEV model. A merit of our method is that no constraints are imposed on the elasticity parameter of the model. In addition, frequent adjustments of the parameter estimates are not required. Simulation studies indicate that the proposed method is suitable for practical use. As an illustration, real examples on the Hong Kong stock option market are carried out. Various aspects of the method are also discussed.

On the Performance of the Comonotonicity Approach for Pricing Asian Options in Some Benchmark Models from Equities and Commodities

2017 ◽  
Vol 20 (01) ◽  
pp. 1750005
Author(s):  
Jilong Chen ◽  
Christian Ewald
Keyword(s):  
Upper Bounds ◽  
Stochastic Volatility Model ◽  
Asian Options ◽  
Convenience Yield ◽  
Yield Model ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Hedging Strategies ◽  
Volatility Model

In this paper, we investigate the applicability of the comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Lévy models as in Albrecher et al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz’ 1997 stochastic convenience yield model. We show how the technical difficulties of inverting the distribution function of the sum of the comonotonic random vector can be overcome and that the method delivers rather tight upper bounds for the prices of Asian Options in these models, at least for strikes which are not too large. As a by-product the method delivers super-hedging strategies which can be easily implemented.

scholarly journals Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong ◽  
Hui Zhao ◽  
Chu-bing Zhang
Keyword(s):  
Stock Price ◽  
Optimal Investment ◽  
Dynamic Programming Principle ◽  
Power Utility ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Consumption Decisions ◽  
Optimal Investment And Consumption ◽  
Consumption Strategies

We consider an investment and consumption problem under the constant elasticity of variance (CEV) model, which is an extension of the original Merton’s problem. In the proposed model, stock price dynamics is assumed to follow a CEV model and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithm utility for our analysis and apply variable change technique to obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.

Perpetual American put options in a level-dependent volatility model

2003 ◽  
Vol 40 (03) ◽  
pp. 783-789 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Stock Price ◽  
Variance Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Put Options ◽  
American Put Options ◽  
Volatility Model ◽  
American Put

We find the explicit value of perpetual American put options in the constant elasticity of variance model using the concept of smooth fit. We show that the price is increasing in the volatility and convex in the underlying stock price. Moreover, as the model converges to the standard Black and Scholes model, the value of the put is shown to approach the ‘correct’ limit.

Perpetual American put options in a level-dependent volatility model

2003 ◽  
Vol 40 (3) ◽  
pp. 783-789 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Stock Price ◽  
Variance Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Put Options ◽  
American Put Options ◽  
Volatility Model ◽  
American Put

We find the explicit value of perpetual American put options in the constant elasticity of variance model using the concept of smooth fit. We show that the price is increasing in the volatility and convex in the underlying stock price. Moreover, as the model converges to the standard Black and Scholes model, the value of the put is shown to approach the ‘correct’ limit.

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