Question

5.8. The prices of European call and put options on a non-dividend-paying stock with 15 months to maturity, a strike price of $118, and an expiration date in 15 months are $21 and $5, respectively. The current stock price is $125. What is the implied risk-free rate?

Answer 1

As per Put Call Parity Formula,

C + (X)e^-rt = P + S₀

C = Price of Call Option

X = Strike Price of Option

P = Price of Put Option

S₀ = Spot Price of underlying

So,

21 + (118)e^-(r*1.25) = 5 + 125

e^-(r*1.25) = 0.9237

Using Log,

-(1.25r)log(e) = log(0.9237)

r = 6.35%

So,

Risk Free Rate = 6.35%