Results on the CEV Process, Past and Present

2010 ◽  
Author(s):  
Alan Lindsay ◽  
Dominic Brecher
Keyword(s):  
Cev Process

scholarly journals Approximating Explicitly the Mean-Reverting CEV Process

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
N. Halidias ◽  
I. S. Stamatiou
Keyword(s):  
Stochastic Volatility ◽  
Diffusion Coefficients ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Financial Mathematics ◽  
Two Dimensional ◽  
Nonnegative Solutions ◽  
Volatility Model ◽  
Cev Process ◽  
The Mean

We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form(xt)q,where1/2<q<1. Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameterq. Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the two-dimensional stochastic volatility model with instantaneous variance process given by the above mean-reverting CEV process.

scholarly journals Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Hui-qiang Ma
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Stock Price ◽  
Efficient Frontier ◽  
Optimal Portfolio ◽  
Portfolio Strategy ◽  
Cev Process ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

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.

Empirical analysis and calibration of the CEV process for pricing equity default swaps

2010 ◽  
Vol 11 (12) ◽  
pp. 1815-1823 ◽  
Author(s):  
Belal E. Baaquie ◽  
Tang Pan ◽  
Jitendra D. Bhanap
Keyword(s):  
Empirical Analysis ◽  
Cev Process

scholarly journals VOLATILITY DERIVATIVES IN MARKET MODELS WITH JUMPS

2011 ◽  
Vol 14 (07) ◽  
pp. 1159-1193 ◽  
Author(s):  
HARRY LO ◽  
ALEKSANDAR MIJATOVIĆ
Keyword(s):  
Asset Price ◽  
Jump Diffusion ◽  
Realized Variance ◽  
Market Prices ◽  
Price Process ◽  
Variance Gamma Process ◽  
Independent Increments ◽  
Volatility Derivatives ◽  
Cev Process ◽  
Convergence Of The Scheme

It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with càdlàg paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset was trading in a prespecified corridor. We thus obtain an algorithm for pricing and hedging volatility derivatives and derivatives on the corridor-realized variance in such a market. The class of models under consideration is large, as it encompasses jump-diffusion and Lévy processes. We prove the weak convergence of the scheme and describe in detail the implementation of the algorithm in the characteristic cases where S is a CEV process (continuous trajectories), a variance gamma process (jumps with independent increments) or an infinite activity jump-diffusion (discontinuous trajectories with dependent increments).

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