Pricing Models Essay

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Black-Scholes and Binomial Models

There are different variables that usually impact the pricing options. This paper will be based on the attributes of the two widely accepted models that are used for pricing options; Black-Scholes and the Binomial Models. These two models are based on the same theoretical assumptions and foundations like risk neutral valuation and geometric price Brownian motion theory of stock price behavior.

Option pricing theory has become among the most powerful tools in commerce and finance. The famous Black-Scholes equation is an effective model that is used for option pricing. It was named after those who pioneered it; Black, Scholes and Merton who brought it up in 1973 and won a Nobel Prize economics in 19097 for discovering it. When we look at it mathematically we can say that it is a final value problem for a second order parabolic equation. In this case an option is a contract which gives the owner the right and not duty to purchase (call option) or sell (put option) an asset which in most cases is stock or parcel of shares of a company for a price that is pre-specified termed as "E" which is the strike price by a particular date "T" when payoffs will be received (Macbeth, & Merville, 1979).

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The basic problem in this case is to specify a fair price to be charged for permitting these rights. European options can only be exercised when the expiration date T. has reached, however for the American option exercise is normally permitted at any time until the expiry date reaches. When we look at the American call option, the value of a call option is V and is dependent on the current market price of the underlying assets, S and the time that remains time, t until the option expires therefore V=V (S, t) (Ehrhardt, & Mickens, 2007).

The Black-Scholes model is used to calculate a theoretical call price that ignores the dividends that are paid during the life of the option using the five key determinants of an option's price which are the stock price, strike price, the volatility, time to expiration and the short-term interest rates. The advantage….....

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