Question

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

Answer #1

As per Put-call parity:

C + X/(1+r)^t = So +P

C= call price

X = strike price

T= 1

So=Spot price

P= put price

Plugging the values, in the equation, we get:

25 + 120/(1+r)^1 = 135+5

120/(1+r) = 115

1+r=120/115

R= 4.35%

Hence, implied rate would be 4.35%.

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