Principles of valuing options – Delta

A concept that is important to people that are considering the purchase of stock options (I will strictly deal with “call” options for the purposes of this discussion) is the concept of delta.

Delta is the change in price of the option over the change in price of the underlying. For those that are calculus-minded, it is the instantaneous change, given that all other variables are constant (parameters such as strike price, time to expiry, implied volatility, etc.)

As an example, if you owned an option contract (100 shares) to buy stock XYZ at $50/share, and if XYZ was trading at $50, with an implied volatility of 50%, expiring on the 3rd week of Friday January 2011, would have a delta of 0.537, according to the Black-Scholes Model. This effectively means that the current price you have exposure to the equivalent of 53.7 common shares at the current price and time. This increases as the stock price increases – a $55 share price translates into a delta of 0.729, and a $45 share price results in a delta of 0.318.

Intuitively, this makes sense – as your option goes deeper “into the money”, you start to have more real equity in the underlying stock.