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3 step binomial tree - difference in t values for formula

T

Trainee_Act

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
 
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.
 
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