Option pricing in a subdiffusive constant elasticity of variance (CEV) model

2019 ◽  
Vol 06 (02) ◽  
pp. 1950018
Author(s):  
Kevin Z. Tong ◽  
Allen Liu
Keyword(s):  
Financial Markets ◽  
Analytical Formula ◽  
Planck Equation ◽  
Option Prices ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
New Process ◽  
Stable Variable ◽  
Classical Constant

In this paper, we extend the classical constant elasticity of variance (CEV) model to a subdiffusive CEV model, where the underlying CEV process is time changed by an inverse [Formula: see text]-stable subordinator. The new model can capture the subdiffusive characteristics of financial markets. We find the corresponding fractional Fokker–Planck equation governing the PDF of the new process. We also derive the analytical formula for option prices in terms of eigenfunction expansion. This method avoids the evaluation of PDF of an inverse [Formula: see text]-stable variable and also eliminates the need for numerical integration to calculate the option prices. We numerically investigate the sensitivities of the option prices to the key parameters of the newly developed model.

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.

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 Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation

2020 ◽  
Vol 2020 ◽  
pp. 1-19 ◽  
Author(s):  
Danping Li ◽  
Ruiqing Chen ◽  
Cunfang Li
Keyword(s):  
Differential Game ◽  
Exponential Utility ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Investment Strategies ◽  
Small Company ◽  
Cev Model ◽  
Constant Elasticity ◽  
Optimal Reinsurance ◽  
Constant Elasticity Of Variance

This paper focuses on a stochastic differential game played between two insurance companies, a big one and a small one. In our model, the basic claim process is assumed to follow a Brownian motion with drift. Both of two insurance companies purchase the reinsurance, respectively. The big company has sufficient asset to invest in the risky asset which is described by the constant elasticity of variance (CEV) model and acquire new business like acting as a reinsurance company of other insurance companies, while the small company can invest in the risk-free asset and purchase reinsurance. The game studied here is zero-sum where there is a single exponential utility. The big company is trying to maximize the expected exponential utility of the terminal wealth to keep its advantage on surplus while simultaneously the small company is trying to minimize the same quantity to reduce its disadvantage. In this paper, we describe the Nash equilibrium of the game and prove a verification theorem for the exponential utility. By solving the corresponding Fleming-Bellman-Isaacs equations, we derive the optimal reinsurance and investment strategies. Furthermore, numerical examples are presented to show our results.

scholarly journals Hedging with Liquidity Risk under CEV Diffusion

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 62
Author(s):  
Sang-Hyeon Park ◽  
Kiseop Lee
Keyword(s):  
Discrete Time ◽  
Nonlinear Partial Differential Equation ◽  
Liquidity Risk ◽  
Discrete Version ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Multi Scale ◽  
Replication Scheme ◽  
Scale Perturbation

We study a discrete time hedging and pricing problem in a market with the liquidity risk. We consider a discrete version of the constant elasticity of variance (CEV) model by applying Leland’s discrete time replication scheme. The pricing equation becomes a nonlinear partial differential equation, and we solve it by a multi scale perturbation method. A numerical example is provided.

Invariant approach to optimal investment-consumption problem: the constant elasticity of variance (CEV) model

2016 ◽  
Vol 40 (5) ◽  
pp. 1382-1395 ◽  
Author(s):  
Ahmet Bakkaloglu ◽  
Taha Aziz ◽  
Aeeman Fatima ◽  
F.M. Mahomed ◽  
Chaudry Masood Khalique
Keyword(s):  
Optimal Investment ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Invariant Approach

THE LARGE-MATURITY SMILE FOR THE SABR AND CEV-HESTON MODELS

2013 ◽  
Vol 16 (08) ◽  
pp. 1350047 ◽  
Author(s):  
MARTIN FORDE ◽  
ANDREY POGUDIN
Keyword(s):  
Implied Volatility ◽  
Large Time ◽  
Heston Model ◽  
Large Time Asymptotics ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Time Estimates ◽  
Time Asymptotics ◽  
Sabr Model

Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β < 1, ρ = 0. We also compute large-time asymptotics for the constant elasticity of variance (CEV) model in the large-time, fixed-strike regime and a new large-time, large-strike regime, and for the uncorrelated CEV-Heston model. Finally, we translate these results into a large-time estimates for implied volatility using the recent work of Gao and Lee (2011) and Tehranchi (2009).

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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