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A Simple Approach for Pricing Equity Options

Buy custom A Simple Approach for Pricing Equity Options essay

Buy custom A Simple Approach for Pricing Equity Options essay

Options refer to contracts that give the owner a right to buy or sell an underlying instrument or asset at a specific strike price on or before a specified date. An option that gives the owner a right of buying at specified prices is considered to be a call, whereas an option that gives the owner a right of selling something at a specified price is known as a put. The following variables affect the pricing of options. They include a strike price that refers to the price contracted for exchange of the option in the exercise that the person wishes to buy the contract; hence it plays an important role in determining the price of an option. If a stock splits it changes the strike price which in turn affects the exercise price. This makes the price of the option to fluctuate. Remaining time to expiry of an option contract affects the price of the option. The price of an option is directly related to the time to expiry of the option contract. A decrease in time to expiration erodes the value of the option. Interest rates have an impact on the prices of the option because an increase in the rate of interest leads to the higher call option price which yields to a decrease in put option price and vice versa.

Expected dividends have substantial impact on the price of an option where an increase in dividends from the underlying stock reduces the call prices thus put prices increase. A decrease in expected dividends increases the call prices which in turn decreases the put prices. Price of the underlying stock has also a considerate effect on the option pricing because it affects the price of premium for a given strike price. If the market price is closer to the strike price then the rate of change is high and when strike prices are away from the market price then the lower the rate of change in the option premium (Bailey & Stulz 1989). Finally, the underlying security volatility highly determines the changes in the price of options. Volatility is a measure of uncertainty or the variability in prices of the underlying security option. When a market becomes volatile, the option premium from the contracts goes up. Buying options before volatility expansion lead to a higher probability of success. Therefore, higher volatility reflects larger expected fluctuations in the underlying price levels (Bailey & Stulz 1989).

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 The Black-Scholes model is a mathematical model which gives the price of European options that can only be exercised at the end of their lives (Bhattacharya 1980), while a Binomial model is used to value American options that can be exercised any time in a given interval (Chi-Cheng 1983).  Binomial model is computationally slower than Black-Scholes model but is more accurate, especially for options on securities that are longer dated with divided payments. Binomial pricing models are less practical for options that have complicated features and those with numerous sources of uncertainty due to a number of difficulties. Black-Scholes pricing model differs from the real world prices due to the simplifying assumptions within the model. A limitation from this model is that in practicality security prices cannot undergo a log – normal process that is strictly stationary and the risk-free interest rate is not constant.  

The underlying assumptions concerning stock prices emphasize on the binomial and Black-Scholes models. They show that stock prices have stochastic processes which follow a geometric Brownian motion. This shows that European options that are valued by binomial model will converge on Black-Scholes formula after some time as the binomial calculation steps increase. This clearly shows that binomial pricing model will have to undergo the multiple steps so that it is similar to Black-Scholes model. Binomial model generally gives discrete approximations to the Black-Scholes model which follows a continuous process.

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