scholarly journals COMPARISON OF THREE OPTION PRICING MODELS FOR INDIAN OPTIONS MARKET

2021 ◽  
Vol 5 (4) ◽  
pp. 54-64
Author(s):  
Arun Chauhan ◽  
Ravi Gor
Keyword(s):  
Stock Market ◽  
Option Pricing ◽  
Stock Options ◽  
Market Price ◽  
Economic Science ◽  
Option Prices ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Indian Stock Market

Black-Scholes option pricing model is used to decide theoretical price of different Options contracts in many stock markets in the world. In can find many generalizations of BS model by modifying some assumptions of classical BS model. In this paper we compared two such modified Black-Scholes models with classical Black-Scholes model only for Indian option contracts. We have selected stock options form 5 different sectors of Indian stock market. Then we have found call and put option prices for 22 stocks listed on National Stock Exchange by all three option pricing models. Finally, we have compared option prices for all three models and decided the best model for Indian Options. Motivation/Background: In 1973, two economists, Fischer Black, Myron and Robert Merton derived a closed form formula for finding value of financial options. For this discovery, they got a Nobel prize in Economic science in 1997. Afterwards, many researchers have found some limitations of Black-Scholes model. To overcome these limitations, there are many generalizations of Black-Scholes model available in literature. Also, there are very limited study available for comparison of generalized Black-Scholes models in context of Indian stock market. For these reasons we have done this study of comparison of two generalized BS models with classical BS model for Indian Stock market. Method: First, we have selected top 5 sectors of Indian stock market. Then from these sectors, we have picked total 22 stocks for which we want to compare three option pricing models. Then we have collected essential data like, current stock price, strike price, expiration time, rate of interest, etc. for computing the theoretical price of options by using three different option pricing formulas. After finding price of options by using all three models, finally we compared these theoretical option price with market price of respected stock options and decided that which theoretical price has less RMSE error among all three model prices. Result: After going through the method described above, we found that the generalized Black-Scholes model with modified distribution has minimum RMSE errors than other two models, one is classical Black-Scholes model and other is Generalized Black-Scholes model with modified interest rate.

scholarly journals A Study of Black–Scholes Model’s Applicability in Indian Capital Markets

Paradigm ◽  
2020 ◽  
Vol 24 (1) ◽  
pp. 73-92
Author(s):  
Anubha Srivastava ◽  
Manjula Shastri
Keyword(s):  
Stock Market ◽  
Option Pricing ◽  
Trading Volume ◽  
Stock Exchange ◽  
Market Price ◽  
Significant Degree ◽  
Pricing Model ◽  
Fair Price ◽  
Black Scholes ◽  
Indian Stock Market

Derivative trading, started in mid-2000, has become an integral and significant part of Indian stock market. The tremendous increase in trading volume in Indian stock market has reflected into high volatility in the option prices. The pricing of options is very complex aspect of applied finance and has been subject of extensive research. Black–Scholes option model is a scientific pricing model which is applied for determining the fair price for option contracts. This article examines if Black–Scholes option pricing model (BSOPM) is a good indicator of option pricing in Indian context. The literature review highlights that various studies have been conducted on BSOPM in various stock exchange across the world with mixed outcome on its relevance and applicability. This article is an empirical study to test the relevance of BSOPM for which 10 most popular industry’s stock listed on National Stock Exchange have been taken. Then the BSOPM has been applied using volatility and risk-free rate. Furthermore, t-test has been used to test the hypothesis and determine the significant relationship between BS model values and actual model values. This study concludes that BSOPM involves significant degree of mispricing. Hence, this model alone cannot be adopted as an indicator for option pricing. The variation from market price is synchronised with respect to moneyness and time to maturity of the option.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

scholarly journals The Performance of Skewness and Kurtosis Adjusted Option Pricing Model in Emerging Markets

2016 ◽  
Vol 5 (3) ◽  
pp. 70-84
Author(s):  
Özge Sezgin Alp
Keyword(s):  
Emerging Markets ◽  
Option Pricing ◽  
Option Prices ◽  
Pricing Model ◽  
European Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Skewness And Kurtosis ◽  
Pricing Formula

In this study, the option pricing performance of the adjusted Black-Scholes model proposed by Corrado and Su (1996) and corrected by Brown and Robinson (2002), is investigated and compared with original Black Scholes pricing model for the Turkish derivatives market. The data consist of the European options written on BIST 30 index extends from January 02, 2015 to April 24, 2015 for given exercise prices with maturity April 30, 2015. In this period, the strike prices are ranging from 86 to 124. To compare the models, the implied parameters are derived by minimizing the sum of squared deviations between the observed and theoretical option prices. The implied distribution of BIST 30 index does not significantly deviate from normal distribution. In addition, pricing performance of Black Scholes model performs better in most of the time. Black Scholes pricing Formula, Carrado-Su pricing Formula, Implied Parameters

Comparison of European Option Pricing Models at Multiple Periods

2021 ◽  
pp. 149-166
Author(s):  
Amir Ahmad Dar ◽  
N. Anuradha ◽  
Ziadi Nihel
Keyword(s):  
Option Pricing ◽  
Graphical Representation ◽  
European Option ◽  
Pricing Models ◽  
European Option Pricing ◽  
Black Scholes Model ◽  
Time Period ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Anderson Darling

The point of this chapter is to think about the correlation of two well-known European option pricing models – Black Scholes Model and Binomial Option Pricing Model. The above two models not statistically significant at one period. In this examination, it is shown how the above two European models are statistically significant when the time period increases. The independent paired t-test is utilized with the end goal to demonstrate that they are statistically significant to vary from one another at higher time period and the Anderson Darling test being used for the normality test. The Minitab and Excel programming has been utilized for graphical representation and the hypothesis testing.

Notes on Options, Hedging, Prudential Reserves and Fair Values

2005 ◽  
Vol 11 (2) ◽  
pp. 199-293 ◽  
Author(s):  
A. D. Wilkie ◽  
M. P. Owen ◽  
H. R. Waters
Keyword(s):  
Option Pricing ◽  
Real World ◽  
Investment Strategy ◽  
Option Prices ◽  
Pricing Models ◽  
World Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Options Hedging ◽  
The Many

ABSTRACTIn this paper we present many investigations into the results of simulating the process of hedging a vanilla option at discrete times. We consider mainly a ‘maxi’ option (paying Max(A, B)), though calls, puts and ‘minis’ are also considered. We show the sensitivity of the variability of the hedging error to the actual investment strategy adopted, and to the many ways in which the simulated real world can diverge from the assumed option pricing model. We show how prudential reserves can be calculated, using conditional tail expectations, and how net premiums or fair values (which we present as the same) can be calculated, allowing for the necessary prudential reserves. We use two bond models, the very simple Black-Scholes one and a less unrealistic one. We also use the Wilkie model as an even more realistic real-world model, allowing for many complications in it to make it more realistic. We make observations on the important difference between real-world models and option pricing models, and emphasise the latter as the way of getting hedging quantities, and not just option prices.

scholarly journals A modification term for Black-Scholes model based on discrepancy calibrated with real market data

2021 ◽  
Vol 1 (4) ◽  
pp. 313-326
Author(s):  
Xiaozheng Lin ◽  
◽  
Meiqing Wang ◽  
Choi-Hong Lai ◽  
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Option Prices ◽  
Market Prices ◽  
Market Data ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Real Market ◽  
S Model

<abstract><p>The Black-Scholes option pricing model (B-S model) generally requires the assumption that the volatility of the underlying asset be a piecewise constant. However, empirical analysis shows that there are discrepancies between the option prices obtained from the B-S model and the market prices. Most current modifications to the B-S model rely on modelling the implied volatility or interest rate. In contrast to the existing modifications to the Black-Scholes model, this paper proposes the concept of including a modification term to the B-S model itself. Using the actual discrepancies of the results of the Black-Scholes model and the market prices, the modification term related to the implied volatility is derived. Experimental results show that the modified model produces a better option pricing results when compare to market data.</p></abstract>

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