Wells Fargo Put-Call Parity and the Effect of a Dividend
Summary
The document considers whether prices for Wells Fargo stock and options with a shared expiration violate put-call parity. It compares the stock price plus put value with the strike price plus call value, neglecting interest rates, and asks how an apparent positive difference could be arbitraged. The options are American-style, which complicates a direct comparison with the standard European parity relationship.
The answer identifies a pending cash dividend as the crucial omitted factor. Because the stock went ex-dividend before option expiration, a position that acquired shares through call exercise would not receive the dividend. Accounting for the announced dividend reduces the apparent parity gap to a small negative amount, which the answer says is likely insufficient to cover trading spreads. The example shows why dividend dates and actual bid-offer costs matter when assessing apparent arbitrage; it does not provide a full trade construction or account for interest rates.
Key ideas
- Put-call parity comparisons depend on matching the relevant asset and option cash flows over the contract period.
- The upcoming dividend changes the value comparison because shares acquired through later call exercise miss the payment.
- The stated dividend adjustment removes the apparent positive parity gap in this example.
- Bid-offer costs can eliminate an apparent arbitrage even when quoted prices suggest a discrepancy.
- The example neglects interest rates and does not lay out a complete arbitrage portfolio.
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Full text
# Violation of the call-put parity # Violation of the call-put parity The last price of Wells Fargo (Ticker: WFC) on Thursday, 10/26/17, was $55.62. Options with expiration 11/17/17 had following last prices: Options with expiration 11/17/17 had following last prices: call-strike-put 1.11-55-0.78 0.85-55.5-1.04 0.63-56-1.33 The spreads of the options were fairly low in the 0.04–0.06 range. The indicated price for the options is the average of bid and ask, which gives a good approximation for a realistic price. We will neglect interest rates in this problem. (a) Compute $S_0+p-K-c$ for each of the three strike prices. My answer: $$0.29,0.31,0.32$$ (b) The computations in (a) show that the call-put parity seems to be violated. Explain the reason for this. My answer: Wells Fargo is an American option. American options allow early exercise, unless, they are held until expiration. As we can see in the problem the expiration of the stock is 10/26 whereas the option expiration is 11/17. Since the expiration dates are not the same, there is opportunity for arbitrage, since the values in (a) are greater than 0, i.e. $S_0+p>K+c$. My question: I understand that there is opportunity for arbitrage, but I don't understand how the arbitrage actually occurs. In this case, would a person 1. buy the $S_o+p$ or $K+c$ 2. which dates would they buy it and 3. when would they sell it. Also, what it means for $S_0+p$ to be greater than $K+c$ for the buyer's decision? ## Answer by dm63 (score 6, accepted) https://quant.stackexchange.com/a/36756 On 10/24/17, Wells Fargo announced that they would pay a dividend of 0.39 to holders of record on 11/3/17. Thus, if you buy the stock after this date (through the exercise of the call) you do not get the dividend. This means that the potential arbitrage, instead of being 0.30, is -0.09. This is now sufficiently close to zero that there is likely no arbitrage opportunity after paying bid- offer on the put, call and stock. http://m.nasdaq.com/symbol/wfc/dividend-history
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