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%.

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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