Scholes Option Pricing Model

The Scholes Option Pricing model has two parts: SN(d1) and Ke(-rt)N(d2). The first part of the option pricing model is based on buying stock outright and the expected benefit derived from this action. The way to determine this is to multiply [S], which is the stock price, by the call premium's change with respect to the underlying stock price change or [N(d1)].

Scholes Option Pricing Model Part Two

The second part of the Scholes Option Pricing Model, Ke(-rt)N(d2), is based on the value on the date of expiration. Calculating the difference between both parts of the equation results in the option's fair market value.

Scholes Option Pricing Model Assumption 1

The first assumption of the Scholes Option Pricing Model is that during the life of the option no dividends are paid. The vast majority of shareholders are paid dividends by their companies. To many, this appears to be one of the model's limitations. The way this limitation is handled is by take the stock price's future dividend and subtracting the discounted value. This adjustment works well and keeps the model consistent and accurate.

Scholes Option Pricing Model Assumption 2

The second assumption of the Scholes Option Pricing Model is that only on the expiration date can the option be exercised. This is based on European exercise terms, which is important to keep in mind because American exercise terms are quite different by allowing the option to be exercised at any point during the option's life. This makes the Scholes Option Pricing Model less flexible.

Scholes Option Pricing Model Assumption 3

The third assumption of the Scholes Option Pricing Model is that individual stocks and/or the market cannot be predicted consistently. The stocks and market are based on a continuous process that has no end, which means consistent predictions of the options or market is impossible.

Scholes Option Pricing Model Assumption 4

In most cases, in order to buy and sell options a commission is paid. The commission may be small or large based on whether it's a trader or investor, nevertheless the model can be distorted by these commission payments and as a result are not included.

Scholes Option Pricing Model Assumption 5

The fifth assumption of the Scholes Option Pricing Model is that interest rates are known. In order to always have known and constant interest rates this model uses the risk free rate from the US Government's discount rate with 30 days left.