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An equity is currently priced at €75
An equity is currently priced at €75. The equity will either increase or decrease by 15% over the next year. Assume a risk-free interest rate of 12%, and an exercise price of €70. What is the put price with the same exercise price?
Expert Solution
HIgh Price = 75 * (1+0.15) = 86.25
Low Price = 75 * (1-0.15) = 63.75
r = 0.12
t = 1
U = High Price / Current Price = 85.25 / 75 = 1.15
D = Low Price / Current Price = 63.75 / 75 = 0.85
Probability of U = e^r*t - D / U -D
= e^(0.12*1) - 0.85 / 1.15 - 0.85
= 0.9250
Payoff at U = Max (Strike Price-High Price ,0)
= Max (70 - 86.25, 0)
= 0
Payoff at D = Max (Strike Price-Lower ,0)
= Max (70 - 63.75
= 6.25
Price of the Put Option = e^(-r*t) * (probability of U * Payoff at U + (1- probability of U) * Payoff at D)
= e^(-0.12*1) * (0.9250 * 0 + (1-0.9250)* 6.25)
=0.53 Euro
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