Purchase or Sell an Underlying Essay

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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.

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This model therefore uses the same variables, but a different of calculation. In practice, the binomial model is used for American options while Black Scholes is used for European options, reflecting the strengths and weaknesses of each model. These are, however, unrelated to the variables that comprise the price. The price of options remains a function of the value of the underlying asset, the strike price of the option, the volatility of the underlying asset and the time to expiry, with the risk-free rate as a baseline rate. Understanding the different variables and how they interact is key to understanding these two models, and the nature of options pricing. Neither model, it is noted, takes into account illiquidity in options, thereby only focusing on the intrinsic value and time value of the option, rather than the actual market value.

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