A Constant Elasticity of Variance (CEV) Family of Stock Price Distributions in Option Pricing, Review, and Integration

2010 ◽  
pp. 1615-1625 ◽  
Author(s):  
Ren-Raw Chen ◽  
Cheng-Few Lee
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance

CONSTANT ELASTICITY OF VARIANCE OPTION PRICING MODEL WITH TIME-DEPENDENT PARAMETERS

2000 ◽  
Vol 03 (04) ◽  
pp. 661-674 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Option Pricing ◽  
Algebraic Approach ◽  
Time Dependent ◽  
Model Parameters ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Pricing Options ◽  
Term Structures ◽  
Option Values

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

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.

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.

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