The prices of European call and put options on a non-dividend-paying stock with 12 months to maturity, a strike price of $120, and an expiration date in 12 months are $25 and $5, respectively. The current stock price is $135. What is the implied risk-free rate?
Draw a diagram showing the variation of an investor’s profit and loss with the terminal stock price for a portfolio consisting of
One share and a short position in one call option
Two shares and a short position in one call option
One share and a short position in two call options
One share and a short position in four call options
In each case, assume that the call option has an exercise price equal to the current stock price
As per Put-call parity:
C + X/(1+r)^t = So +P
C= call price
X = strike price
P= put price
Plugging the values, in the equation, we get:
25 + 120/(1+r)^1 = 135+5
120/(1+r) = 115
Hence, implied rate would be 4.35%.
Answer:The variation of an investor’s profit/loss with the terminal stock price for each of the four strategies is shown in Diagram. In each case the dotted line shows the profits from the components of the investor’s position and the solid line shows the total net profit.
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