In: Statistics and Probability
Q1. Uniform Distribution
You believe stock price will follow uniform distribution with mean of 100 and MAD 20. You are pricing a CALL option with strike at 110.
a. what is the mean and range of the distribution?
b. what is the probability that the call will be ITM at expiration (ie stock price ends above strike at 110)?
c. what is the conditional mean of stock price when CALL is ITM (aka stock price is above strike 110)?
d. what is the conditional CALL option average payment when the CALL is ITM?
e. what is the fair value of the CALL today, ie the unconditional average payment today?