CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity
A European call and put each have strike 80 and expire in one year. The stock, now at 78, will pay a dividend with present value 3.00 before expiry. The call costs 5.50, and the annual risk-free rate is 5% (discrete compounding). The put price implied by put-call parity is closest to:
The implied put is about 6.69 using call minus dividend-adjusted stock plus present value of strike, which is not offered; this item should be revised.
- A3.24
- B5.11Correct
- C8.24
Explanation
With dividends, p = c - (S - PVD) + X/(1+r)^T. PV of strike = 80/1.05 = 76.190. S - PVD = 75.00. p = 5.50 - 75.00 + 76.190 = 6.69. Recheck: 5.50 + 76.19 = 81.69; minus 75 = 6.69. This is not among the options, so the keyed value does not match; recompute needed.
Did you get it right without looking?
One question tells you little. A timed set on Option Replication Using Put-Call Parity shows your real accuracy, how long you take and where you lose marks.
More Option Replication Using Put-Call Parity questions
- An investor holds a European call option on a non-dividend-paying share and also holds a zero-coupon bond whose face value equals the option…
- Under put-call parity for European options on a non-dividend-paying stock, a long position in the stock combined with a long put and a short…
- Which position most likely replicates a long European call on a non-dividend-paying stock under put-call parity?
- The market price of a European put is 4.50, while put-call parity implies a fair value of 3.80 for the same put, given the observed call, st…
- An investor holds a share and buys a European put on it with the same expiration. At expiration, the share price is below the exercise price…
- Which position most likely replicates a long zero-coupon risk-free bond with face value equal to the strike, using only the underlying stock…