# Chapter 10Theta

Theta (θ or for the capital letter Θ) is the change of the value of an option in relation to the change in time, also called time-decay.

It is the derivative of the value in relation to time, mathematically: . Throughout the book the Greek letter Θ will be used for denoting the theta, sometimes time decay will be used. The formula for calculating it is as follows: (interest rate and dividend yield at 0%), where is the probability density function. Theta has a log normal distribution.

The theta, as shown in Chart 10.1, is expressed in dollars (or rather cents) per day. The theta value indicates the amount with which the value of an option will decrease overnight. An option will get cheaper every day towards maturity. At expiration date the option (when not in the money) has lost all of its value, each time decreasing in value at a daily time decay rate.

When the interest rate and the dividend yield are both at 0%, theta for calls will be the same as theta for puts. Theta ...

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