Introduction To Black Scholes Option Pricing Model

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The Black Scholes option model is a simple mathematical formula that is used valuing European Options. A European option is an option to purchase an asset (such as a stock) on only a single given date, by contrast American options allow the holder the right to purchase at any time up until the option expiry date.

The Black Scholes model is not suitable for for valuing other types of options such as American options, lookback options or barrier options since it cannot incorporate the more complex exercise features of these options or their path dependencies like the knock in/out of barrier options. The main advantages of using Black Scholes is its speed and valuation accuracy.

Black Scholes has five primary inputs - Spot Price, Strike Price, Time to Maturity, Interest Rate and Volatility.

Spot Price - the price in the open market of the underlying asset as at the valuation date such as the closing price of a stock on a stock exchange.

Strike Price - the price at which the holder of the option has the right to purchase or sell the underlying asset. This is typically a very straightforward input since this is specified in the option documentation.

Time to Maturity - the time (in years) till the option expiry. After this date the option is no longer valid.

Interest Rate - the risk-free interest rate for the term up until the option expiry.

Volatility - this is probably the single most important input to the Black Scholes option pricing model. There are server methods for estimating volatility. Historic volatility uses historic prices for asset price movements to estimate the volatility whereas implied volatility uses the volatility implied by traded option prices to estimate the volatility.

Yield (optional) - this is the average yield generated by the asset for the period up until the expiry of the option. This can either be a dividend (such as a stock or stock index) or alternatively the income generated by a commodity (eg lease fees paid on rented gold).
It is usually difficult to forecast the asset yield for the option's life so the historic yield of the asset is normally used instead.

Black Scholes does however have several limitations in addition to the limited types of options they can value. It can only accommodate a single interest rate and a single volatility input and as such derivatives specialists often use other option valuation models such as lattice models or Monte-Carlo simulations.

About the Author:
Michael Sargent is a frequent author on derivatives and the Black Scholes model.



Article Originally Published On: http://www.articlesnatch.com


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