# 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?

## 1 Answer

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

• Thank you for the explanation. So would Wells Fargo do this to encourage holders to purchase the stock directly instead of purchasing a call because Wells Fargo wants holders to possess the stock directly rather than through the call? If that makes sense. – thisisme Nov 5 '17 at 21:05
• No, Wells Fargo dividend decisions are likely made based on how much they want to return to shareholders whilst maintaining an appropriate capital structure, and have nothing to do with any preference for stocks versus calls. In any case this was just a regular quarterly dividend. The options market knows how to adjust for it. – dm63 Nov 6 '17 at 12:23