Consider a 6-month European call option on a stock now selling for 100, with a strike price of 97. You are given that σ = 0.25 and the force of interest for a 1-year period is 0.10. You would like to replicate this option by a trading strategy involving holdings in the stock and risk-free zero-coupon bonds of face amount 97, maturing in 6 months. You plan to use the Black-Scholes-Merton formula.
(a) What is the initial portfolio at time 0?
(b) At the end of 2 months, the stock price has risen to 105. What is your portfolio now?
(c) At the end of 4 months, the stock price has fallen to 95. What is your portfolio now?