Price and settlement gain calculation in options on an index

The Cboe S&P 500 Index Options - SPX are peculiar in that there is no underlying stock or ETF - they trade the index. I want to make sure that I understand the pricing.

Large Notional Size -- around $200,000 per Contract with the SPX index at 2000 (10 times that of SPDR options). Say the S&P 500 is at$2,668.$Would then a contract have a notional (?) value of$\$266,800$?

Now say that I want to buy a single call option with a strike of $2,710$ expiring May 9, 2018 - it's for illustration only, but the contract does exist: SPXW180509C02710000.

The last trading price is very recent, and at $0.65.$ Assuming that there is no price further price movement, and leaving aside ask/bid differences.

How would I go about calculating the price of $1$ contract?

And assume that the index climbs to $2,800$ (to make things easy) by the expiration date. Evidently I would exercise my option to buy at the strike price of $2,710.$

But what would be the final calculus of the gain minus the purchase price?

Not sure about what follows, but now that the question is "answered" with a hyperlink, I'm taking my chances... Negative feedback will act as an answer by proxy...

The notional value is explained here and here, and compared to other securities trading the index:

Notional value tells us how much total value a security theoretically controls.

Standard equity option contracts control $100$ shares of an underlying. The notional value of these option contracts is $100$ times the current market price of the underlying.

$$\text{Contract Size } \times \text{ Underlying Price} = \text{ Notional Value}$$

If we purchase an at the money (ATM) call trading for $\$2.00$in$XYZ$while$XYZ$is at$\$30.00,$ the notional value of the option will be $\$3,000.00$: $$100 \text{ shares the option controls} \times \30.00 \text{ price of the underlying}.$$ Alternatively, the market price of an option contract is how much it currently trades for in the market. In the above example, the ATM call has a market price of$\$200.00$

$$100 \text{ shares the option controls }\times \2.00 \text{ price of the option contract}.$$

In the case in the question:

The notional value of the option is $\$2,710 \times 100= \$271,000.$

The market price is $100 \times \$0.65=\$65.$

In the fictional situation of the S&P 500 reaching $2,800$ before expiration, the payoff would be

\begin{align} &100\,(\,\text{S&P @ selling time } - \text{ strike price }) - \text{option price}\\[2ex] &=100\,(\,\2,800-\2,710)-\65\\[2ex]&=\8,935 \end{align}.

• "The multiplier for CBOE listed S&P500 options is 100". That is all you have to remember, all the calculations you did follow from this. – Alex C May 7 '18 at 23:11
• Thank you, @AlexC. I take it that the calculations are correct. If you find any inclination to give me a formal answer, perhaps explaining a bit what we are trading here, and this "notional value", I'll be happy to accept your answer. – Toni May 7 '18 at 23:13

http://www.neweratrader.com/Resources/the-sap-e-min.html This should help explain the tick value and minimum incremental tick size

• It's basically what I got directly from the Cboe, and the reason why I posted a question to avoid misunderstandings. It is considered bad form to answer with just a link. What is the added value? We all have Google. – Toni May 7 '18 at 20:58
• Sorry I thought it was self explanatory – catsally1 May 7 '18 at 22:28
• Maybe you should reflect on the fact that you are getting downvotes in all your answers. And teach yourself a much more self-explanatory and trivial thing - you don't just paste the URL; you embed it. This answer is worthless, and you should erase it. I think you are out of your depth in this site. – Toni May 7 '18 at 22:31
• Have you ever traded? Unless I'm mistaken your profit would be 2800-2710 or \$22,500 minus the cost of your option. Is that simple enough? – catsally1 May 7 '18 at 23:02