Purchase or Sell an Underlying

¶ … purchase or sell an underlying asset at a given time for a given price. There are two common option structures, the European and American. A European option can only be exercised at expiry, while an American option can be exercised at any point until expiry. This difference has led to two different models for pricing options, but they both rely on the same variables to determine the value of the option. The price of an option is generally divided into two portions -- the intrinsic value of the option today plus the time value of the option, expressed as the likelihood of the option's price changing prior to expiry or exercise.

There are a number of different variables that impact the pricing of options. These variables can be understood by analyzing the models that are used to price options. The two most widely-accepted models are the Black-Scholes Model and the Binomial Model. The Black-Scholes model takes into account the following variables -- the underlying price of the asset, the strike price of the option, the time until expiration, the implied volatility and the risk-free interest rates (Folger, 2013). These factors are important for the following reasons.

The price of the underlying asset is important because the price of the option is based to some extent on the value of this asset and the volatility of that value. The volatility, expressed as beta, reflects the degree to which the price of the asset fluctuates. The value of the option is dependent on the degree of fluctuation, and the dollar amount of the fluctuation, thus the importance of both volatility and the price of the underlying asset.

The strike price of the option is also important to its pricing. The Black-Scholes formula assumes that the likelihood of the option to be in the money is a critical factor in its value. Thus, the degree to which the strike price is likely to be crossed is a function of the current price, the volatility and the strike price itself. In addition to these factors, the likelihood of the option being in the money -- and by how much -- is also determined by time. Thus, the time to expiry is an important factor in the value of the option as well. The model assumes a normal distribution, so the greater the time to expiry, the greater the expected fluctuation in the stock's price. Thus, if the option is in the money, the greater the risk that it will expire out of the money; if the option is out of the money, the greater the likelihood that it will expire in the money. The risk-free rate is also important, because the value of the option is essentially a premium over the risk-free rate.

The binomial model begins by creating a pricing tree. The probability of each incidence is recorded, and the price of each incidence is also calculated. The final result will be the weighted-average of all of the possible outcomes for the option. The binomial model features the risk free rate, the strike price and the probability of the strike price occurring as important variables. The spot price of the underlying asset at a particular period is also important, as is the volatility of the underlying asset and the time to expiry.