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The black Scholes model, also known as Black Scholes Merton is a mathematical model that is widely used in the financial market comprising certain derivative investment instruments. The Black–Scholes formula would give the European-style pricing options. The formulas that are derived with the help of this theory legitimize the activities carried out on the Chicago Board Options Exchange and other market options available across the globe. This theory comprises of various topics, including probability measures, call options, exotic options, etc. Though, this theory is interesting but has become a complicated part of statistics to understand especially for the students who are still in the learning phase. Our team of talented experts would cater to the assignment needs of students in this area of statistics. This theory is named after Black Scholes which was developed in the year 1973. This is a mathematical model that derives the investment instruments. This helps to calculate the European price theoretically besides overlooking the dividends that are paid for the option for a lifetime.
This mathematical formula is used to define the exact option that is available for the European style in the financial market. The main advantage offered by this theory is that it allows you to calculate many pricing options in the shortest period of time. This model is used to determine the fair or the theoretical price for just a call or select options based on six variables. These include – volatility, risk-free rate, time, strike price, a stock price that is underlying, and the option type. There is a lot of speculation in the stock market derivatives and the proper pricing option would keep the opportunity that is given for arbitrage at bay. There are two different models that are used in option pricing. There include – Binomial model and the other is a black Scholes model. This model is widely used to find out the price of the European call option. To be precise, this option can only be used on the expiration date. The price of the most often traded assets would embrace geometric Brownian motion that would drift and be volatile constantly.
When this model is applicable to the stock market, this model would apply various factors like change in the price of the stock constantly, value for money that comes with time, the option of the strike price, and time for the option to expiry. The formula for the black Scholes theory is obtained by multiplying the price of the stock by the cumulative standard normal probability distribution function. This is the most ideal theory that is used to determine fair prices of options. This theory would follow a lognormal distribution since the price of the asset cannot dip to a negative value. This is called a Gaussian distribution. This model has won Noble Prize in economics and this is a differential equation that is helpful to solve option prices.
The Black Scholes model would simply be the market for both the financial assets and derivatives that are defined in the mathematical rules. This model would act as a foundation for different analysis that is carried out in the market. The formula of this model would give the theoretical objective price that let the investors know the actual price of the asset. The best part of this model is that it works totally on the objective over human judgment. Another benefit that is offered is to carry out complicated human calculations with ease. This is a very small formula in terms of mathematics, so you do not need to use complicated computer programs for doing the computations.
The main use of this model is to determine options pricing. A party will buy an asset like stocks and the other party would pay the price that is agreed on the future date. The market price of the asset can be higher than the price on the agreed date. This helps the buyers to use this option, buy the asset and sell it immediately for profits. This is very beneficial for a buyer where the buyer has to close the deal irrespective of the market price that is on the completion date.
Based on the options contract system, the buyer has the right to sell this option to another party prior to the completion date. This will turn options into their asset on which they have rights with the change in the market price due to an increase in demand and supply. The Black Scholes model will use mathematics to take various factors that would take a toll on the demand and supply. This is a pricing formula that would consider 5 variable factors. These include – the current value of the asset on which the option is based, the price at which the option holder possesses all rights to buy the asset, a duration that is left until the contract expiration date, volatility of the asset price that will forecast the market price until the expiry date and the rate on which risk-free investments are offered like government bonds.
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