Hi, Hopefully someone can help me. Sept 2016 Q7(ii) Let S0 = 50 and let the price rise by 10% or fall by 5% each month for the next 3 months. Assume risk-free rate is 5% pa. q = (exp(0.05*3/12) – 0.95)/(1.1-0.95) = 0.3612 April 2017 Q5(i) Consider a European put option on this stock, with maturity in three months (i.e. at time t = 3) and strike price $90. q = (exp(0.0025) – 0.85)/(1.18-0.85) = 0.4621 How do we know when to put a fraction of time into the exp term when trying to calculate q? Thanks
The fraction of time is required when the length of the binomial time-step is different to the unit in which the interest rate is expressed. If the interest rate is given per annum and the time-steps are of length one year, then no time fraction is required. If the time steps of the model are monthly, the dt = 1/12 is required.