Option Pricing Essay Example | Topics and Well Written Essays - 3250 words

Option Pricing - Essay Example Options are used by holders for leverage or for protection. The leverage function helps the holder to control the shares bought for a portion what they would have cost. On the other hand, protection measures are adopted when the holder wants to guard against price fluctuations. He enters into a contract with the rights to acquire the stock for a fixed period and specific price. The contracts, in either case, should be highly observed and monitored for efficient outcomes. The methods used in pricing options have been applied for years and can only be effective if the worth of the option is achieved. This is determined by the probability that on the expiration, the option price will be on a substantial amount of money. Any holder of an option expects a gain on his underlying asset to attain the worth of holding for the time given. The Black Scholes and the Binomial method are the elaborated on below in determining the true worth of an option. The Black Scholes Model: This model dates b ack in the twentieth century in its application. It was developed by Fisher Black and Myles Scholes in 1973 hence the name Black Scholes (Marion, 2003, 16). It is still in use today. This model uses the theoretical call price whereby the dividends amounting during the life of the option is not included in the computation.   Theoretically, the price of an option (OP) has been determined by the formulae given below: In this case: (Simon & Benjamin, 2000, 255; Brajendra, 2011, 372) The variables in the above formulae are expressed as shown below: S is the stock price X is the strike price t is the time remaining until the expiration, denoted as percent of a year r is the compounded risk-free interest rate predominant in the current market v is the annual volatility of stock price.   ln is the natural logarithm N(x) is the standard normal cumulative distribution function e is the exponential function Below are the necessary requirements for validating this model: Dividends are not p aid during the stock period. Variance and interest rate does not change in the course of the option contract. There is no discontinuity in the stock price i.e. a shift from one price to another like the case of tenders. This model applies volatility and normal distribution to determine the movement of options. The Excel add-in format can be used to calculate the normal distribution. Volatility, on the other hand, can be implied or historical. The implied volatility of an option allows market traders to observe the current prices of options to determine how volatile they are. This is done by calculating the standard deviation i.e. v2, and in this case, all other variables have to be known. Nevertheless, historical analysis is not left out. The traders have to observe the performance of the option over past years to assess volatility.