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CFA Level I · CFA Level I Exam · Option Replication Using Put-Call Parity

A trader observes that a put is priced above the level implied by put-call parity. Holding the call, stock and bond prices constant, which strategy would most likely capture the arbitrage profit?

Sell the overpriced put and buy a synthetic put made of a long call, a short stock position and lending the present value of the strike. The payoffs offset at expiry, locking in the price difference today as risk-free profit.

  1. ABuy the put, sell the call, short the stock, and lend the present value of the strike
  2. BSell the put, buy the call, short the stock, and lend the present value of the strikeCorrect
  3. CSell the put, buy the stock, and borrow the present value of the strike

Explanation

Parity: p = c + PV(X) - S. An overpriced put is sold. Buy a synthetic put by buying the call, shorting the stock and lending PV(X). Option C leaves the position long stock and short the put, which adds risk rather than hedging it. Option A buys the overpriced put.

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