3 step binomial tree - difference in t values for formula

Discussion in 'CM2' started by Trainee_Act, Sep 24, 2021.

  1. Trainee_Act

    Trainee_Act Keen member

    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
     
  2. Steve Hales

    Steve Hales ActEd Tutor Staff Member

    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.
     

Share This Page