scholarly journals Optimal pairs trading with time-varying volatility

2016 ◽  
Vol 03 (03) ◽  
pp. 1650023 ◽  
Author(s):  
Thomas Nanfeng Li ◽  
Agnès Tourin
Keyword(s):  
Generalized Method Of Moments ◽  
Fixed Time ◽  
Time Varying ◽  
Pairs Trading ◽  
Power Utility ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Control Techniques ◽  
Daily Frequency ◽  
Trading Model

In this paper, we propose a pairs trading model that incorporates a time-varying volatility of the constant elasticity of variance type. Our approach is based on stochastic control techniques; given a fixed time horizon and a portfolio of two cointegrated assets, we define the trading strategies as the portfolio weights maximizing the expected power utility from terminal wealth. We compute the optimal pairs strategies by using a finite difference method. Finally, we illustrate our results by conducting tests on historical market data at daily frequency. The parameters are estimated by the generalized method of moments.

On the Theoretical Valuation of V-KOSPI 200 Futures

2017 ◽  
Vol 25 (3) ◽  
pp. 405-424
Author(s):  
Young Ho Eom ◽  
Woon Wook Jang
Keyword(s):  
Process Model ◽  
Generalized Method Of Moments ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Volatility Index ◽  
Moments Method ◽  
Risk Neutral ◽  
The Mean ◽  
The Empirical Analysis

Although the V-KOSPI 200 Futures markets opened in November 2014, trading has not been active until recently. One of the reasons for the illiquidity is due to the lack of a market consensus on the stochastic process model for the underlying volatility index (V-KOSPI 200). Given this fact, there is no theoretical pricing model that can be used for the determination of the benchmark price for the V-KOSPI 200 Futures. In this paper, we use the generalized method of moments method to search for a model that fits well with the time series of V-KOSPI 200 under the historical measure. In addition, we compare the performance of each model for the pricing of the V-KOSPI 200 Futures under the risk neutral measure. In the empirical analysis, we find that the CEV (constant elasticity of variance) parameter with the value about 1.5 is needed to price both the underlying V-KOSPI 200 process (under the physical measure) and the V-KOSPI 200 Futures (under the risk neutral measure). We also find that the mean reversion property is necessary to explain the dynamics of V-KOSPI 200.

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.

scholarly journals Leverage Effect and Stochastic Volatility in the Agricultural Commodity Market under the CEV Model

2017 ◽  
Vol 65 (5) ◽  
pp. 1671-1678
Author(s):  
Michal Čermák
Keyword(s):  
Stochastic Volatility ◽  
Generalized Method Of Moments ◽  
Commodity Prices ◽  
Commodity Price ◽  
Leverage Effect ◽  
Commodity Market ◽  
Agricultural Commodity ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance

The problem of price fluctuation is crucial to the concept of financial engineering nowadays. The aim of this paper is twofold; first to investigate the leverage effect of the main agricultural commodities – wheat and corn, i. e. the relationship between monetary returns and the volatility of commodity prices and, secondly to capture their stochastic volatility by forming an appropriate model. The data are considered as ‘post‑crisis’ data. That means the period after the biggest shock to the world economy. Thus, the Constant Elasticity of Variance (CEV) model is used calibrated to the Generalized Method of Moments (GMM). The paper is briefly based on the research of Geman and Shih (2009), who propose an extension in capturing the leverege effect in the commodity market. Their results show a positive relationship between commodity price returns and the volatility in both the corn and wheat derivative market. According to these results, corn futures prices are characterized significantly under the CEV model. On the other side in the wheat futures market exists a driftless condition by using stochastic volatility models.

scholarly journals Determining Equivalent Administrative Charges for Defined Contribution Pension Plans under CEV Model

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Hongjing Chen ◽  
Zheng Yin ◽  
Tianhao Xie
Keyword(s):  
Pension Plan ◽  
Pension Plans ◽  
Defined Contribution ◽  
Power Utility ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
The Maximum Principle ◽  
Equivalent Equation ◽  
Defined Contribution Pension Plan

In defined contribution pension plan, the determination of the equivalent administrative charges on balance and on flow is investigated if the risk asset follows a constant elasticity of variance (CEV) model. The maximum principle and the stochastic control theory are applied to derive the explicit solutions of the equivalent equation about the charges. Using the power utility function, our conclusion shows that the equivalent charge on balance is related to the charge on flow, risk-free interest rate, and the length of accumulation phase. Moreover, numerical analysis is presented to show our results.

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