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?
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%
5.8. The prices of European call and put options on a non-dividend-paying stock with 15 months to...
The prices of European call and put options on a dividend-paying stock with 6 months to maturity and a strike price of $125 are $20 and $5, respectively. If the current stock price is $140, what is the implied annual continuously compounded risk-free rate? Assume the present value of dividend to be paid out over the next 6 months is $3.
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What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?
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