Derive the expression for its mean life in terms of the decay constant
Answers
Time decay is the rate of change in an option (or other security) as time to expiration nears. Because options are wasting assets, their value declines over time. If an option approaches its expiry date and is not in the money, then its time value declines because the probability of that option being profitable, or in the money, is reduced. For options traders, the risk factor (known as the "Greeks") that measures the change in an options price - or a book of options value - over time is called the theta.
Time decay in options is most influential on at-the-money options and those closest to expiration. Longer-term options, such as LEAPS, do not lose much value on a daily basis. On the other hand, an option expiring in a day will soon lose all its intrinsic value.