Question

A day trader buys an option on a stock that will return ​$100 profit if the stock goes up today and lose ​$500 if it goes down. If the trader thinks there is a 70​% chance that the stock will go​ up, find the standard deviation of the day​ trader's option value.

Answer 1

$274.95

Explanation:

The mean return for the option is:

`\mu=100*0.70-500*(1-0.70)\\\mu=-\$80`

The variance and standard deviation are given by:

`V=x_1^2p_1+x_2^2p_2-\mu^2\\SD=\sqrt V`

Where "x" represents the possible returns ($100 and -$500), and "p" represents their respective likelihoods (70% and 30%). The standard deviation is:

`V=100^2*0.7+(-500)^2*0.30-(-80)^2\\V=75,600\\SD=\sqrt 75,600\\SD=\$274.95`

The standard deviation of the day trader's option value is $274.95.