Problem $2.$

An asset price is currently $$80.$ Its expected return and volatility are $8\%$ and $25\%,$ respectively.

A$.$ What is the probability distribution $($i$.$e$.,$ mean and variance$)$ for the annual continuously compounded rate of return earned on this asset?

B$.$ Suppose a European call option exists on this asset with an exercise price of $$80.$ The time to expiration on this option is two years. The riskless rate of interest is $3\%.$ What is the value of this option and what is the risk neutral probability that this option will expire in the money?

C$.$ What is the "true" probability that this option will expire in the money?

D$.$ Why is there a difference between the two probabilities calculated in parts B and C above?