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.

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.

Application of CAPM in the Indian Stock Market A Comprehensive Reassessment

2005 ◽  
Vol 1 (2) ◽  
pp. 1-12 ◽  
Author(s):  
Raj S. Dhankar ◽  
Rohini Singh
Keyword(s):  
Stock Market ◽  
Capital Market ◽  
Stock Exchange ◽  
Capital Asset Pricing ◽  
Pricing Model ◽  
Capital Asset ◽  
Asset Pricing Model ◽  
Conflicting Evidence ◽  
Empirical Tests ◽  
Indian Stock Market

There is conflicting evidence on the applicability of Capital Asset Pricing Model in the Indian stock market. Data for 158 stocks listed on the Bombay Stock Exchange was analyzed using a number of tests from 1991–2002, the period which roughly coincides with the period after liberalization and initiation of capital market reforms. Taken in aggregate the various empirical tests show that CAPM is not valid for the Indian stock market for the period studied.

scholarly journals Nonparametric Estimation of Fractional Option Pricing Model

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Qing Li ◽  
Songlin Liu ◽  
Misi Zhou
Keyword(s):  
Option Pricing ◽  
Stock Exchange ◽  
Option Price ◽  
Integral Function ◽  
The State ◽  
Pricing Model ◽  
State Price ◽  
Black Scholes ◽  
Option Pricing Model ◽  
State Price Density

The establishment of the fractional Black–Scholes option pricing model is under a major condition with the normal distribution for the state price density (SPD) function. However, the fractional Brownian motion is deemed to not be martingale with a long memory effect of the underlying asset, so that the estimation of the state price density (SPD) function is far from simple. This paper proposes a convenient approach to get the fractional option pricing model by changing variables. Further, the option price is transformed as the integral function of the cumulative density function (CDF), so it is not necessary to estimate the distribution function individually by complex approaches. Finally, it encourages to estimate the fractional option pricing model by the way of nonparametric regression and makes empirical analysis with the traded 50 ETF option data in Shanghai Stock Exchange (SSE).

A new method to solve fuzzy stochastic finance problem

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jayanta Kumar Dash ◽  
Sumitra Panda ◽  
Golak Bihari Panda
Keyword(s):  
Option Pricing ◽  
Market Price ◽  
Pricing Model ◽  
Strike Price ◽  
Content Type ◽  
Fuzzy Environment ◽  
Black Scholes ◽  
Option Pricing Model ◽  
A New Technique ◽  
Log Normal

PurposeThe authors discuss the value of portfolio and Black–Scholes (B–S)-option pricing model in fuzzy environment.Design/methodology/approachThe B–S option pricing model (OPM) is an important role of an OPM in finance. Here, every decision is taken under uncertainty. Due to randomness or vagueness, these uncertainties may be random or fuzzy or both. As the drift µ, the degree of volatility s, interest rate r, strike price k and other parameters of the value of the portfolio V(t), market price S_0 (t) and call option C(t) are not known exactly, so they are treated as positive fuzzy number. Partial expectation of fuzzy log normal distribution is derived. Also the value of portfolio at any time t and the B–S OPM in fuzzy environment are derived. A numerical example of B–S OPM is illustrated.FindingsFirst, the authors are studying some various paper and some stochastic books.Originality/valueThis is a new technique.

scholarly journals Multidimensional Liquidity: Evidences from Indian Stock Market

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Sharad Nath Bhattacharya ◽  
Pramit Sengupta ◽  
Mousumi Bhattacharya ◽  
Basav Roychoudhury
Keyword(s):  
Machine Learning ◽  
Stock Market ◽  
Stock Markets ◽  
Trading Volume ◽  
Stock Exchange ◽  
Market Liquidity ◽  
Percentage Error ◽  
Efficiency Coefficient ◽  
Learning Tools ◽  
Indian Stock Market

Various dimensions of liquidity including breadth, depth, resiliency, tightness, immediacy are examined using BSE 500 and NIFTY 500 indices from Indian Equity market. Liquidity dynamics of the stock markets were examined using trading volume, trading probability, spread, Market Efficiency coefficient, and turnover rate as they gauge different dimensions of market liquidity. We provide evidences on the order of importance of these liquidity measures in Indian stock market using machine learning tools like Artificial Neural Network (ANN) and Random Forest (RF). Findings reveal that liquidity variables collectively explains the movements of stock markets. Both these machine learning tools performs satisfactorily in terms of mean absolute percentage error. We also evidenced lower level of liquidity in Bombay Stock Exchange (BSE) than National Stock Exchange (NSE) and findings supports the liquidity enhancement program recently initiated by BSE.

Analysis on Indian Stock Market Prediction Using Deep Learning Models

2021 ◽  
pp. 80-90
Author(s):  
Kalaivani Karuppiah ◽  
Umamaheswari N. ◽  
Venkatesh R.
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Deep Learning ◽  
Stock Market ◽  
Multilayer Perceptron ◽  
Stock Exchange ◽  
Market Price ◽  
Learning Models ◽  
Stock Market Prediction ◽  
Indian Stock Market

The neural network is one of the best data mining techniques that have been used by researchers in different areas for the past 10 years. Analysis on Indian stock market prediction using deep learning models plays a very important role in today's economy. In this chapter, various deep learning architectures such as multilayer perceptron, recurrent neural networks, long short -term memory, and convolutional neural network help to predict the stock market prediction. There are two different stock market price companies, namely National Stock Exchange and New York Stock Exchange, are used for analyzing the day-wise closing price used for comparing different techniques such as neural network, multilayer perceptron, and so on. Both the NSE and NYSE share their common details, and they are compared with various existing models. When compared with the previous existing models, neural networks obtain higher accuracy, and their experimental result is shown in betterment compared with existing techniques.

Self-attribution, Overconfidence and Dynamic Market Volatility in Indian Stock Market

2018 ◽  
Vol 21 (4) ◽  
pp. 970-989
Author(s):  
Venkata Narasimha Chary Mushinada ◽  
Venkata Subrahmanya Sarma Veluri
Keyword(s):  
Stock Market ◽  
Trading Volume ◽  
Stock Exchange ◽  
Empirical Evaluation ◽  
Market Volatility ◽  
Crisis Period ◽  
Asymmetric Volatility ◽  
Attribution Bias ◽  
Indian Stock Market ◽  
Overconfidence Bias

The article provides an empirical evaluation of self-attribution, overconfidence bias and dynamic market volatility at Bombay Stock Exchange (BSE) across various market capitalizations. First, the investors’ reaction to market gain when they make right and wrong forecasts is studied to understand whether self-attribution bias causes investors’ overconfidence. It is found that when investors make right forecasts of future returns, they become overconfident and trade more in subsequent time periods. Next, the relation between excessive trading volume of overconfident investors and excessive prices volatility is studied. The trading volume is decomposed into a first variable related to overconfidence and a second variable unrelated to investors’ overconfidence. During pre-crisis period, the analysis of small stocks shows that conditional volatility is positively related to trading volume caused by overconfidence. During post-crisis period, the analysis shows that the under-confident investors became very pessimistic in small stocks and tend to overweight the future volatility. Whereas, the analysis of large stocks indicates that the overconfidence component of trading volume is positively correlated with the market volatility. Collectively, the empirical results provide strong statistical support to the presence of self-attribution and overconfidence bias explaining a large part of excessive and asymmetric volatility in Indian stock market.

Impact of Stock Splits and Rights Issue Announcements on Market Price: Evidence from India

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Babitha Rohit ◽  
Prakash Pinto ◽  
Shakila B.
Keyword(s):  
Stock Market ◽  
Stock Returns ◽  
Stock Exchange ◽  
Market Price ◽  
Abnormal Returns ◽  
Market Model ◽  
Stock Splits ◽  
Indian Stock Market ◽  
Rights Issue ◽  
The Impact

The current paper studies the impact of two events i.e stock splits and rights issue announcement on the stock returns of companies listed on the Bombay Stock Exchange. The study consists of a sample of 90 announcements for stock splits and 29 announcements for rights issue during the period 2011-2014. Market model is used to calculate the abnormal returns of securities. Positive Average Abnormal Returns were observed for the two events on the day their announcements, however they are not statistically significant. The study concludes that the Indian stock market is efficient in its semi-strong form.

An Empirical Test of the Black-Scholes Option Pricing Model and the Implied Variance: A Confidence Interval Approach

1987 ◽  
Vol 2 (4) ◽  
pp. 355-369 ◽  
Author(s):  
Haim Levy ◽  
Young Hoon Byun
Keyword(s):  
Confidence Interval ◽  
Option Pricing ◽  
Implied Volatility ◽  
Empirical Test ◽  
Market Price ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
S Model ◽  
Over Time

The empirical studies on the Black-Scholes (B-S) option pricing model have reported that the model tends to exhibit systematic biases with respect to the exercise price, time to expiration, and the stock's volatility. This paper attempts to test the B-S model with a new approach: derive the confidence interval of the model call option value based on the confidence interval of the. estimated variance. The test reports that even when the variance's confidence interval is considered, a systematic deviation between the theoretical “range” of the option price values and the observed market price still exist. If the stock variance is constant over time, the interpretation of the results is that the B-S model is wrong. However, if stock variance changes over time, the interpretation of the results is that the implied volatility in options market prices had a tendency to be significantly higher than the estimate that could have been obtained from historical data.

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