The Price Behind the Screen

Shorting constraints, synthetic forwards, and listening to the right spot

“Do not judge by appearances, but judge with right judgment.”
— John 7:24

When people first start pricing options, they assume the hardest part is choosing the right mathematical model. Textbooks reinforce this idea, spending hundreds of pages on pricing formulas and numerical derivations. For the pure theory, John Hull’s Options, Futures, and Other Derivatives covers everything you need. But in actual trading, getting the formula right means nothing if you feed it the wrong input—and the price you see on your screen is often the wrong input.

We trade options on a range of underlyings. Take 510500, an ETF listed on the Shanghai exchange, as an example. On your terminal you see a live traded price. It feels obvious to take that number and plug it into your model as the spot price. But from the first day I started trading, my supervisor told me never to use that number directly. He said it needed adjustment. I did not understand why at the time; I just followed the rule. It was only later, when I started looking at implied volatility surfaces, that I saw what he meant. If you back out implied volatilities using the ETF’s traded price, the smile for the calls and the smile for the puts do not sit on top of each other. They split into two distinct curves, and the gap is impossible to ignore.

That split should not happen if the model and the spot price are both correct. Put-call parity is an identity that holds without any model assumptions: a call minus a put at the same strike equals a forward position in the underlying. If you price both sides with the same spot and the same volatility, the relationship has to hold. But when I backed out implied volatilities using the ETF’s screen price, the two curves separated. The puts were implying a systematically higher volatility than the calls at the same strike. It looked like a data glitch, but it was there every single day.

The explanation comes down to market friction. The price on the screen—the ETF’s last trade—was not the price the options market was actually using. You can construct a synthetic forward from the options themselves by buying a call and selling a put at the same strike and expiry. If you compare the price implied by that synthetic position to the ETF’s traded price, allowing for financing and dividends, you frequently find a gap: the ETF trades higher than its synthetic counterpart.

The reason for this persistent gap is that only one side of the arbitrage can be executed freely. If the synthetic forward ever gets too expensive relative to the ETF, anyone can buy the ETF and sell the synthetic to lock in a profit. That trade is straightforward. But when the ETF is the expensive side, closing the gap requires you to short the ETF and buy the synthetic. In this market, shorting the ETF requires borrowing shares, which is often restricted, costly, or outright unavailable. Because the trade that would push the ETF’s price back down cannot be executed freely, the ETF can stay persistently rich relative to its synthetic forward.

Once you switch to using the synthetic forward price—the spot implied by put-call parity from the options themselves—the two volatility curves collapse onto each other. The smile becomes a single coherent surface again, and the internal consistency checks all pass. The options market was never confused; it was pricing itself correctly the whole time. When the synthetic sits below the traded ETF price, naively using the ETF price forces the call curve to sit below the put curve. Fix the spot, and the two curves meet.

The practical judgment is simple: the ETF quote on your screen tells you what it costs to buy or sell the ETF right now. It does not tell you the price the options market is using to value optionality. The formula is just a tool for making the market’s statement precise, but getting the right answer starts with listening to the right price.