SPX Option Notional Value, Premium, and Expiration Payoff
Summary
The document explains the distinction between an option’s notional exposure and the price paid for the contract. Using the SPX example, the response applies a contract multiplier of 100 to the index level to calculate notional value, and applies the same multiplier to the quoted option premium to calculate the purchase cost. It then calculates an in-the-money call’s expiration payoff from the difference between the index level and strike, multiplied by the contract size, and subtracts the premium to obtain gain net of that cost.
The example treats the quoted last price as the purchase price and assumes no further price movement before expiration, while setting aside bid and ask differences. It is an illustrative calculation, not a discussion of changing option value before expiration, transaction costs, or other trading considerations. The document also includes a pointer about tick value and minimum tick size without explaining those mechanics.
Key ideas
- Notional exposure is calculated as the contract multiplier times the index level.
- The option purchase cost is the quoted premium multiplied by the contract size.
- For the example call, expiration payoff is the index level above the strike multiplied by the contract size.
- The example subtracts the purchase premium from the expiration payoff to calculate gain net of that cost.
- The calculation assumes a fixed quoted purchase price and excludes bid and ask differences.
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Full text
# Price and settlement gain calculation in options on an index
# 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.
On the link above the following sentence can be read:
> 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?
## Answer by Antoni Parellada (score 1)
https://quant.stackexchange.com/a/39679
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
$$\begin{align} &100\,(\,\text{S&P @ selling time } - \text{ strike price }) - \text{option price}\\[2ex] &=100\,(\,\$2,800-\$2,710)-\$65\\[2ex]&=\$8,935 \end{align}.$$
## Answer by catsally1 (score -1)
https://quant.stackexchange.com/a/39676
http://www.neweratrader.com/Resources/the-sap-e-min.html This should help explain the tick value and minimum incremental tick sizeShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.