How do I construct a synthetic put from a call?

Question

AcadiFi · Accepted Answer

Rearranging put-call parity C + PV(K) = P + S gives: P = C - S + PV(K). A synthetic long put = long call + short stock + long zero-coupon bond paying K at expiry.

Example: Tessera Biotech stock at $85, European call K=$90, T=3 months, r=4%, call price $2.10. Synthetic put = $2.10 (buy call) - $85 (short stock, cash in) + $89.105 (buy T-bill with face $90) = $6.205. If market put trades at $6.50, sell the market put and buy the synthetic to arbitrage $0.295 per share.

Payoff verification at expiry: if S_T=$75, call expires worthless (0), short stock loses $75 to cover (but bond matures to $90), net = 0 + (90 - 75) = $15, which matches put payoff max(90-75, 0)=$15. If S_T=$100, call pays $10, bond pays $90, short stock costs $100 to cover, net = 10 + 90 - 100 = 0, matching put payoff max(90-100,0)=0.

Key uses: synthetic puts are essential when exchange-traded puts are illiquid or expensive, or for creating protective-put strategies via calls when shorting is already in place. The cost comparison between market put and synthetic put reveals funding costs and borrowing-fee embedded in the parity relationship.

How do I construct a synthetic put from a call?

Master Part I with our FRM Course

Related Questions

Practice Questions