Please show work. Using the following European call options information: K = $60
ID: 2742388 • Letter: P
Question
Please show work.
Using the following European call options information:
K = $60, S0 = $70, T = 7.5 months, r = 6%, = 12%
a) Find the probability of an up movement (P) based on the risk – neutral valuation.
b) Find the European call option price using the risk – neutral valuation.
c) Suppose that you use the real – world interest rate for this call option contains some risk premium and it is estimated at 20% now. Assuming that the call option’s price obtained from part (b) does not change, the others being held constant, find the probability of an up movement in the real – world valuation.
Explanation / Answer
a.)
Su and sd have to be assumed and decline and up should be at the same rate and S0 should be taken as mid-point.
b.)
c.)
exponent of rate and time 1.038212 Stock rate* exponent of time and rate(sert) 72.67484 Stock up (su) 75 Stock down (sd) 65 (Sert-S0)/(Su-Sd)= probablity of up movement 0.267484