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Put-call parity violation with zero rates

Question

Interest rates are zero. A stock trades at 1010. A European call and a European put on it, both struck at 44 with the same expiry TT, cost 44 and 33 respectively. Zero-coupon bonds paying 11 at TT are also available, and you may go long or short anything.

Build the arbitrage, then report (number of shares) + (number of calls) + (number of puts) + (number of bonds), using negative numbers for short positions.

Short answer

33. Parity requires C−P=S−K=6C-P = S-K = 6 but the market has C−P=1C-P = 1, so the call-minus-put is cheap. Buy one call, sell one put, short one share and buy four bonds: you collect 55 today and the position is worth zero at expiry. The count is −1+1−1+4=3-1+1-1+4 = 3.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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