Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing

1993 ◽  
Vol 103 (417) ◽  
pp. 395 ◽  
Author(s):  
Stewart Hodges ◽  
Andrew Carverhill
Keyword(s):  
Stock Market ◽  
Option Pricing ◽  
Mean Reversion ◽  
Economic Equilibria ◽  
Black Scholes

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.

scholarly journals Quanto Pricing beyond Black–Scholes

2021 ◽  
Vol 14 (3) ◽  
pp. 136
Author(s):  
Holger Fink ◽  
Stefan Mittnik
Keyword(s):  
Option Pricing ◽  
Goodness Of Fit ◽  
Calibration Procedure ◽  
Barrier Options ◽  
Pricing Models ◽  
Modeling Framework ◽  
Double Barrier ◽  
Parameter Stability ◽  
Comprehensive Data ◽  
Black Scholes

Since their introduction, quanto options have steadily gained popularity. Matching Black–Scholes-type pricing models and, more recently, a fat-tailed, normal tempered stable variant have been established. The objective here is to empirically assess the adequacy of quanto-option pricing models. The validation of quanto-pricing models has been a challenge so far, due to the lack of comprehensive data records of exchange-traded quanto transactions. To overcome this, we make use of exchange-traded structured products. After deriving prices for composite options in the existing modeling framework, we propose a new calibration procedure, carry out extensive analyses of parameter stability and assess the goodness of fit for plain vanilla and exotic double-barrier options.

Value-at-Risk and Expected Shortfall approaches for option premiums and the probability of default estimation based on ARMA models

2021 ◽  
Vol 57 (3) ◽  
pp. 126
Author(s):  
Nikolai Berzon
Keyword(s):  
Time Series ◽  
Option Pricing ◽  
Discrete Time ◽  
Value At Risk ◽  
Probability Of Default ◽  
Pricing Models ◽  
Arma Process ◽  
Underlying Asset ◽  
Black Scholes

The need to address the issue of risk management has given rise to a number of models for estimation the probability of default, as well as a special tool that allows to sell credit risk – a credit default swap (CDS). From the moment it appeared in 1994 until the crisis of 2008, that the CDS market was actively growing, and then sharply contracted. Currently, there is practically no CDS market in emerging economies (including Russia). This article is to improve the existing CDS valuation models by using discrete-time models that allow for more accurate assessment and forecasting of the selected asset dynamics, as well as new option pricing models that take into account the degree of risk acceptance by the option seller. This article is devoted to parametric discrete-time option pricing models that provide more accurate results than the traditional Black-Scholes continuous-time model. Improvement in the quality of assessment is achieved due to three factors: a more detailed consideration of the properties of the time series of the underlying asset (in particular, autocorrelation and heavy tails), the choice of the optimal number of parameters and the use of Value-at-Risk approach. As a result of the study, expressions were obtained for the premiums of European put and call options for a given level of risk under the assumption that the return on the underlying asset follows a stationary ARMA process with normal or Student's errors, as well as an expression for the credit spread under similar assumptions. The simplicity of the ARMA process underlying the model is a compromise between the complexity of model calibration and the quality of describing the dynamics of assets in the stock market. This approach allows to take into account both discreteness in asset pricing and take into account the current structure and the presence of interconnections for the time series of the asset under consideration (as opposed to the Black–Scholes model), which potentially allows better portfolio management in the stock market.

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

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