scholarly journals A review of the binomial and trinomial models for option pricing and their convergence to the Black-Scholes model determined option prices

Econometrics ◽  
2020 ◽  
Vol 24 (2) ◽  
pp. 53-85
Author(s):  
Dushko Josheski ◽  
Mico Apostolov
Keyword(s):  
Option Pricing ◽  
Option Prices ◽  
Black Scholes Model ◽  
Black Scholes

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

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 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>

scholarly journals PREFERENCES, LÉVY JUMPS AND OPTION PRICING

2007 ◽  
Vol 03 (01) ◽  
pp. 0750001 ◽  
Author(s):  
CHENGHU MA
Keyword(s):  
Option Pricing ◽  
Contingent Claims ◽  
Economic Variable ◽  
European Options ◽  
Jump Risk ◽  
Representative Agent ◽  
Potential Explanation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Lévy Jumps

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black–Scholes, Naik–Lee, Cox–Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black–Scholes model is explored.

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.

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