The Constant Elasticity of Variance Models: New Evidence from S&P 500 Index Options

2004 ◽  
Vol 07 (02) ◽  
pp. 173-190 ◽  
Author(s):  
C. F. Lee ◽  
Ta-Peng Wu ◽  
Ren-Raw Chen
Keyword(s):  
European Contract ◽  
Chi Square ◽  
Index Options ◽  
Market Prices ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Model ◽  
New Evidence

The seminal work by Cox (1975, 1996), MacBeth and Merville (1979, 1980) and Emanuel and Macbeth (1982) show that, both theoretically and empirically, the constant elasticity of variance option model (CEV) is superior to the Black–Scholes model in explaining market prices. In this paper, we extend the MacBeth and Merville (1979, 1980) research by using a European contract (S&P 500 index options). We find supportive evidence to the MacBeth and Merville results although our sample is not subject to American premium biases. Furthermore, we reduce the approximation errors by using the non-central chi-square probability functions proposed by Shroder (1989).

PRICING BARRIER OPTIONS WITH SQUARE ROOT PROCESS

2001 ◽  
Vol 04 (05) ◽  
pp. 805-818 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Hypergeometric Functions ◽  
Barrier Options ◽  
Square Root ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Confluent Hypergeometric Functions ◽  
Black Scholes Model ◽  
Expansion Technique ◽  
Black Scholes

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are the confluent hypergeometric functions. The numerical results obtained from the formulae are compared with the corresponding model prices under the Black–Scholes model. We find that the differences in the model prices between the square root CEV model and the Black–Scholes model can be significant as the time to maturity and volatility increases.

scholarly journals Efficacy of Nifty Index Options through BSM Model

2019 ◽  
Vol 8 (3S2) ◽  
pp. 947-949
Keyword(s):  
Options Pricing ◽  
Price Determination ◽  
Strike Price ◽  
Index Options ◽  
Put Options ◽  
Black Scholes Model ◽  
Exercise Price ◽  
Black Scholes ◽  
Long Time ◽  
Optimum Price

Options are one of the products in financial derivatives, which gives the rights to buy and sell the product to an option holder in pre-fixed price which known as the strike price or exercise price at certain periods. Options contract was existed in various countries for long time, but it became very popular among the investors when the Fisher Black, Myron Scholes and Robert Merton were introduced the Black-Scholes Model in the year of 1973. This model was formerly developed by these three economists who were also receiving the Nobel prize for finding this innovative model. This model is mainly used to deal with the theoretical pricing challenge in options price determination. In India the trading in Index Options commenced on 4th June 2001 and Options on individual securities commenced on 2nd July 2001. There are many types in options contracts like stock options; Index options, weather options, real options and etc. This study has mainly been focusing on Nifty 50 index options which are effectively trade at NSE. This paper goes to describe about the importance of options pricing and how the BSM model has effectively used to find the optimum price of the theoretical value of call and put options.

A simple closed-form approximation for constant elasticity of variance spread options

2020 ◽  
Vol 07 (04) ◽  
pp. 2050047
Author(s):  
C. F. Lo ◽  
X. F. Zheng
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Option Price ◽  
Analytical Approximation ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Spread Options ◽  
Operator Splitting Method ◽  
Black Scholes ◽  
Closed Form Approximation

By applying the Lie–Trotter operator splitting method and the idea of the WKB method, we have developed a simple, accurate and efficient analytical approximation for pricing the constant elasticity of variance (CEV) spread options. The derived option price formula bears a striking resemblance to Kirk’s formula of the Black–Scholes spread options. Illustrative numerical examples show that the proposed approximation is not only extremely fast and robust, but it is also remarkably accurate for typical volatilities and maturities of up to two years.

Calibrating the model parameters in pricing using the trust region method

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Zuo-liang Xu ◽  
Qing-hua Ma ◽  
Li-ping Wang
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
Model Parameters ◽  
Market Prices ◽  
Parameter Recovery ◽  
Trust Region Algorithm ◽  
Region Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Recovery Problem

AbstractIn this paper, we aim to calibration pricing models from market prices. We investigate the problem of calibrating the parameters using the trust region method from given price data. We start with the Hull–White model and formulate the problem by obtaining the first kind integral equation, and then consider the parameter recovery problem of the Black–Scholes model. We apply trust region algorithm for numerical retrieval problems. Numerical simulations are given to illustrate the feasibility of our proposed method.

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.

CALL WARRANTS IN CHINA'S SECURITIES MARKET: PRICING BIASES AND INVESTORS' CONFUSION

2011 ◽  
Vol 07 (02) ◽  
pp. 333-345 ◽  
Author(s):  
WEI FAN ◽  
XINYI YUAN
Keyword(s):  
Lower Bounds ◽  
Securities Market ◽  
Market Pricing ◽  
Market Prices ◽  
No Arbitrage ◽  
Black Scholes Model ◽  
Price Performance ◽  
Black Scholes ◽  
Trading Mechanism ◽  
Using Data

This paper examines the price performance of call warrants in China's securities market. A recent sample of daily call warrant prices observed during the period from August 2005 to March 2007 is used. To the best of our knowledge this is the only recent study to using data from China and as such it greatly enhances our understanding of this particular market. On average, we find that the observed market prices are irrationally higher than the Black-Scholes model prices by 80.38% (using 180-day historical volatility) and 140.50% (using EGARCH volatility). However, we find another anomalous phenomenon that some of the call warrants prices are not only lower than the model prices, but have also recently been anomalously under their lower bounds. This finding seems to violate the "no arbitrage" principle. Among the convincing reasons, our findings indicate that trading mechanism constraints in China's securities market prevent rational investors from driving the prices of these call warrants to a reasonable level. Arbitrage chances are found to exist in some specific cases when the call warrant prices are below their lower bounds.

scholarly journals PENENTUAN NILAI KONTRAK OPSI SAHAM TIPE EROPA MENGGUNAKAN MODEL CONSTANT ELASTICITY OF VARIANCE

2020 ◽  
Vol 9 (1) ◽  
pp. 37
Author(s):  
LUSIA EMITRIANA MAGOL ◽  
KOMANG DHARMAWAN ◽  
DESAK PUTU EKA NILAKUSMAWATI
Keyword(s):  
Stock Options ◽  
Option Price ◽  
Stock Option ◽  
Option Value ◽  
Due Date ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Black Scholes ◽  
Real Value ◽  
Stock Investments

Investment is a very sensitive matter especially relating to securities commonly known as shares. Shares are not merely as securities or certificates of ownership but as a business area in achieving profits. One alternative factor for investment is option. Stock options are one of the trading tools used to secure stock investments owned by investors. The real value of stock options can be known when the due date. The stock option value formula can be used to find out the value before the due date. The most widely known stock option value is to use the Black-Scholes equation which is obtained from a constant volatility value. Then it was developed because it saw the conditions in the market based on the volatility of the value (not constant). The purpose of this study is to determine the value of stock options in the market based on volatile values ??that change using the Constant Elasticity of Variance model with the limit of European stock purchase options. If the resulting stock option value is greater than the option price in the market, investors are advised to buy the stock option.

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