# Chapter 5Delta Δ

Delta (the Greek letter for the capital letter) is the change of the option value compared to the change of the underlying value. It is the first derivative of the value of an option: . The formula for calculating it is as follows: , where is the standard normal cumulative distribution function where stands for a specific formula.

With a long call option, one could expect an increase in value when the market increases. This change in the value of the option versus a one dollar change in the Future is called the delta. The delta of a call option has a positive value. Obviously a put option would lose value when the market rises, so put options have a negative delta: with a decreasing Future they increase in value.

Delta is a very important measure of a portfolio, it indicates how long or short one is. In this chapter the characteristics of the delta will be explained, how it changes and how it is distributed according to the Future level, volatility and time to maturity. ...

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