Investment Basics: XLII. Options pricing using the Black-Scholes Model

2000 ◽  
Vol 29 (52) ◽  
pp. 45-50
Author(s):  
GTF Brooke ◽  
ET Fraser
Keyword(s):  
Options Pricing ◽  
Black Scholes Model ◽  
Black Scholes

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.

UNCERTAINTY IN PRICING TRADABLE OPTIONS

2003 ◽  
Vol 06 (02) ◽  
pp. 103-117 ◽  
Author(s):  
JORGE R. SOBEHART ◽  
SEAN C. KEENAN
Keyword(s):  
Interest Rates ◽  
Market Equilibrium ◽  
Expected Value ◽  
Options Pricing ◽  
Options Market ◽  
Pricing Model ◽  
Random Delays ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Random Fluctuations

In this paper we introduce an options pricing model consistent with the level of uncertainty observed in the options market. By assuming that the price at which an option can be traded is intrinsically uncertain, either because of the inability to hedge continuously or because of errors in the estimation of the security's volatility and interest rates, random delays in the execution of orders or information deficiencies, we show that the Black-Scholes model produces a biased estimate of the expected value of tradable options. Information deficiencies lead to a call-put relationship that reduces to the standard call-put expression on average but shows random fluctuations consistent with the concept of market equilibrium. The same information deficiencies can contribute to the volatility skew that affects the Black-Scholes model.

Beyond Black–Scholes: A Neural Networks-Based Approach to Options Pricing

2003 ◽  
Vol 06 (05) ◽  
pp. 469-489 ◽  
Author(s):  
Christopher A. Zapart
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Bootstrap Method ◽  
Feature Space ◽  
Options Pricing ◽  
Black Scholes Model ◽  
Volatility Model ◽  
Starting Point ◽  
Black Scholes ◽  
Artificial Neural

The paper presents two alternative schemes for pricing European and American call options, both based on artificial neural networks. The first method uses binomial trees linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the non-linear feature space. Neural networks are used to infer future volatility levels from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. In the second approach neural networks are trained with genetic algorithms in order to reverse-engineer the Black–Scholes formulae. The standard Black–Scholes model provides a starting point for an evolutionary training process, which yields improved options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black–Scholes model and the proposed options pricing schemes. The proposed models produce as good as and often better options prices than the conventional Black–Scholes formulae.

Analysis of Options Pricing Methods: the Black-Scholes Model and the Monte-Carlo Method

2020 ◽  
Vol 9 (3) ◽  
pp. 39-42
Author(s):  
Leysen Yunusova
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Investment Decisions ◽  
Estimation Methods ◽  
Options Pricing ◽  
Financial Instruments ◽  
Strategic Investment ◽  
Black Scholes Model ◽  
The Monte Carlo Method ◽  
Black Scholes

Currently, the market of financial instruments is quite developed. Traditional financial instruments prevail on the Russian market, while derivatives of these financial instruments (options, futures, forwards, bills, etc.) are faintly developed. The reason for this situation is that few participants in the financial market can correctly evaluate financial products. Scientific researchers and large companies use different methods of estimating the value of financial instruments in making strategic investment decisions, since incorrect calculations can be irreparable. Therefore, it is important to apply the appropriate pricing methodology to various derivative financial instruments. The topic of derivative financial instruments in terms of scientific and theoretical aspects has been worked out in sufficient volume, but as for the pricing of these instruments, there are some gaps. There is still no method for pricing derivatives that would allow you to accurately assess the value of financial instruments for subsequent effective investment decisions. In this article considers the methodology of pricing of derivative financial instruments using the Black-Scholes model and the Monte Carlo method. The presented estimation methods allow us to calculate the range of price values that allows us to provide the most accurate expected results.

scholarly journals A mean bound financial model and options pricing

2017 ◽  
Vol 04 (04) ◽  
pp. 1750047 ◽  
Author(s):  
Yu Li
Keyword(s):  
Implied Volatility ◽  
Heavy Tails ◽  
Asset Returns ◽  
Mathematical Explanation ◽  
Options Pricing ◽  
Fat Tails ◽  
Volatility Smile ◽  
Financial Model ◽  
Black Scholes Model ◽  
Black Scholes

Most of financial models, including the famous Black–Scholes–Merton options pricing model, rely upon the assumption that asset returns follow a normal distribution. However, this assumption is not justified by empirical data. To be more concrete, the empirical observations exhibit fat tails or heavy tails and implied volatilities against the strike prices demonstrate U-shaped curve resembling a smile, which is the famous volatility smile. In this paper we present a mean bound financial model and show that asset returns per time unit are Pareto distributed and assets are log Gamma distributed under this model. Based on this we study the sensitivity of the options prices to a change in underlying parameters, which are commonly called the Greeks, and derive options pricing formulas. Finally, we reveal the relation between correct volatility and implied volatility in Black–Scholes model and provide a mathematical explanation of volatility smile.

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