CFA Level I · CFA Level I Exam · Option Replication Using 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, stock and risk-free bond prices. To exploit the mispricing, an arbitrageur would most likely:
The put is overpriced relative to parity, so the arbitrageur should sell it and buy the cheaper synthetic put made of a long call, a short stock position and a long risk-free bond. The payoffs offset at expiration, locking in the 0.70 difference.
- Asell the put and buy a synthetic put built from the call, short stock and bondCorrect
- Bbuy the put and sell a synthetic put built from the call, short stock and bond
- Cbuy the put and the call, and sell the stock short
Explanation
The put is overpriced at 4.50 versus 3.80. Sell the overpriced put and buy the synthetic put (long call, short stock, long risk-free bond), which costs 3.80 and has the same payoff. This locks in 0.70 with no net payoff risk.
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