ACCA Strategic Professional · Advanced Financial Management · Application of option pricing theory in investment decisions
Arden Ltd shares trade at $100. A one-year European call (exercise $100) is valued at $12 and a one-year European put (exercise $100) at $7. The one-year risk-free rate, annually compounded, is r. Ignoring dividends, what is r implied by put-call parity?
Put-call parity gives call minus put equals share price minus the present value of the exercise price. So 5 equals 100 minus 100/(1+r), meaning 100/(1+r) is 95 and 1+r is 1.0526. The implied risk-free rate is about 5.3%.
- A4.0%
- B5.3%Correct
- C6.0%
- D7.1%
Explanation
Parity: C - P = S - X/(1+r). So 12 - 7 = 5 = 100 - 100/(1+r), giving 100/(1+r) = 95 and 1+r = 1.05263, so r = 5.26%, about 5.3%. Using 5/100 directly as r gives 5.0%, and using 100-95 over 100 as a rate would miss discounting the base.
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