Use the following European call option’s information. K=$60, S0 = $65, T= 9 mont

Question

Use the following European call option’s information.
K=$60, S0 = $65, T= 9 months, r = 8%, ?=12%
a) Find the probability of an up movement (P) based on the risk-neutral valuation.
b) Find the European call option’s price using the risk-neutral valuation.
c) Suppose that you use the real-world valuation rather than the risk-neutral valuation. 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

let So 65 becomes 75 or 55

upside = 75/65 = 1.154

downside = 55/65 = 0.846

Risk free rate for 9months is 8% i.e. 1.08

probability can be find using R - d / u - d = 1.08 - 0.846 / 1.154 - 0.846  

= 0.76 = 76%

i.e. becoming 75 probability is 76%

becoming 55 probability is 24%

callupper value  @ 75 = 75-60 = 15

calllower value @ 55 = 0

Value of call option = 15 * 76% + 0*24% / 1.08   

= 10.55

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