Thursday, 19 April 2012

Six inputs are required for the Black-Scholes model:

Model Inputs

From the formula and code above you will notice that six inputs are required for the Black-Scholes model:
  1. Underlying Price (price of the stock)
  2. Exercise Price (strike price)
  3. Time to Expiration (in years)
  4. Risk Free Interest Rate (rate of return)
  5. Dividend Yield
  6. Volatility
Out of these inputs, the first five are known and can be found easily. Volatility is the only input that is not known and must be estimated.

Black-Scholes Volatility

Volatility is the most important factor in pricing options. It refers to how predictable or unpredictable a stock is. The more an asset price swings around from day to day, the more volatile the asset is said to be. From a statistical point of view volatility is based on an underlying stock having a standard normal cumulative distribution.
To estimate volatility, traders either:
  1. Calculate historical volatility by downloading the price series for the underlying asset and finding the standard deviation for the time series. See my Historical Volatility Calculator.
  2. Use a forecasting method such as GARCH.

Implied Volatility

By using the Black-Scholes equation in reverse, traders can calculate what's known as implied volatility. That is, by entering in the market price of the option and all other known parameters, the implied volatility tells a trader what level of volatility to expect from the asset given the current share price and current option price.

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