Problem
Value a call option with strike price $105, expiring in 2 years, where the underlying at time 0 has a sport price of 100. This asset has probability 0.65 to increase 30% relatively in value each year and probability 0.35 to increase only just 5% in relative value. At the same time, the interest rate at time 0 is 1%, this has probability 0.70 to increase 4% in absolute value year on year, or stay the same. Calculate the value of this call option.