Assume the log-normal model. The spot price is $100. The expected rate of return is 10%. The volatility is 20%. The risk-free rate is 3%. A power derivative pays you the square of the underlying asset price in 4 months.

A. Calculate its and today

B. Suppose the asset price jump up by $0.05 today. Use your computation of the to estimate the new price. Without computing the new price exactly, argue whether this is an underestimate or and overestimate, based on your computation for . (Possibly Useless Hint: consider the parabola y = ax^2 ; for what values of the constant a is the tangent-line approximation of the parabola at the origin an overestimate and for what values is it an underestimate?)