Put-call parity violation with zero rates
Question
Interest rates are zero. A stock trades at . A European call and a European put on it, both struck at with the same expiry , cost and respectively. Zero-coupon bonds paying at 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
. Parity requires but the market has , so the call-minus-put is cheap. Buy one call, sell one put, short one share and buy four bonds: you collect today and the position is worth zero at expiry. The count is .
Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- No-Arbitrage Bounds and Put-Call Parity
- Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
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