Is this parity arb real after costs?

Question

Stock at 100, zero rates, no dividends. Using mid prices, the 100-strike call is \8.10 and the 100-strike put is \8.00, so C - P = 0.10 against a fair value of 0. It looks like a \0.10 arbitrage. But every instrument trades with a bid-ask spread, and the half-spread you cross is \0.05 on the call, \0.05 on the put, and \0.05 on the stock. Is there actually an arbitrage you can capture?

Accepted Answer

Parity (zero rates, no dividends) says C - P = S - K = 0. The mids show C - P = 0.10, a synthetic forward that looks \0.10 rich, so the textbook trade is a conversion: sell the call, buy the put, buy the stock. The catch is that you cannot trade at mids. To put on the conversion you must: - Sell the call, so you hit the bid, giving up \0.05 versus mid. - Buy the put, so you lift the offer, paying \0.05 over mid. - Buy the stock, so you lift the offer, paying \0.05 over mid. Total slippage against mid: 0.05 + 0.05 + 0.05 = \0.15. Your apparent edge was only \0.10, so executing at real tradeabl…

Is this parity arb real after costs?

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