Question

A day trader buys an option on a stock that will return ​$200 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

Expected value = p*Profit + (1-p)*Loss

= 200*.7+(-500)*.3

= 140-150

= -$10

Now,the E(x^2) = .7*(200^2) + (.3)*(-500^2)

= .7*(40000)+.3*250000

=28000+75000

= 103000

Standard deviation. = Sqrt(E(x^2)-E(x)^2))

= Sqrt(103000-100)

= Sqrt(102900)

=$ 320.780