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Black Scholes Theory Assignment Help

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What is Black Scholes Theory?

The Black Scholes or BSM (Black Scholes Merton) theory is a mathematical model that is used to estimate financial instruments over time. This theory assumes that instruments such as stocks have a lognormal distribution of prices. The Black Scholes model also assumes that the price of heavily traded assets follows a geometric Brownian motion. The motion has a constant drift and volatility. The Black Scholes Model, when applied in stock, incorporates the time value of money, the strike price, variation of the stock, and the time of the stock's expiry. This was the first model to be used for option pricing. It can calculate the theoretical value of options using aspects such as:
  • The current stock prices
  • Expected dividends
  • Time of expiration
  • The strike price of the option
  • Expected interest rates
  • Expected volatility

The Black Scholes Model's formula was developed by Fischer Black, Myron Scholes, and Robert Merton. These economists introduced it in their paper, "The Pricing of Options and Corporate Liabilities." The article was published in the Journal of Political Economy in 1973. The BSM theory won a Nobel Prize in Economics in 1997 for finding a new method of determining the value of derivatives.

Assumptions made by the Black Scholes Theory

  • The volatility and risk-free rate of the option are constant and known
  • The returns are normally distributed
  • Market movements are efficient and cannot be predicted
  • No transaction costs are incurred in buying the option
Earlier, the Black Scholes model never considered the effects of dividends paid during the life of the option. However, it has frequently been adapted to account for dividends. The model does this by determining the ex-dividends date value of the underlying stock.

The Black Scholes Formula

The Black Scholes model involves complicated and intimidating mathematical concepts. Fortunately for students, they can sign up for our Black Scholes theory assignment help when they are stuck with their assignments. Additionally, when modeling strategies, they can use a variety of online calculators. The internet also boasts of a wide range of robust analysis tools like spreadsheets and indicators that can calculate and produce the pricing values of options. The Black Scholes Formula is calculated by: (Stock Price) x Cumulative Standard Normal Probability Distribution function - Net present value of the strike price x the Cumulative Standard Normal Distribution

In summary

The Black Scholes Model is an essential concept in modern-day financial theory. It is widely used today and regarded as one of the best ways of determining fair prices of options. Asset prices cannot be negative. They are bounded by zero. As a result, the BSM model assumes that prices follow a lognormal distribution. This concept is also known as a Gaussian distribution. In most cases, asset prices are observed to have some degree of fat tails (kurtosis) and right skewness. This means, the market often experiences high-risk downward moves than a normal distribution predicts it.

Limitations of the Black Scholes model

  • The Black Scholes model doesn't take into account that US options can be exercised before the expiration date. It only prices European options.
  • The assumption that dividends and risk-free rates may not be a reality
  • Volatility often fluctuates with the level of demand and supply
  • Most of the assumptions deviate from the real world
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