# Market Maker option's pricing with reference spot

When a option's market maker receives a quote from a broker, usually the underlying spot prices is locked with a reference.

Let's suppose the following example:

Broker: "Buy 10k call 2800 of ABC Index for August. Ref: 2670"

How the market maker is suppose to quote this option?

I believe that this is to simplify the client/broker to see what is the best quote he has, then trade the cheapest one; but the price from the market maker is really the price that will be traded or something would be adjusted?

• Options are often bought "delta-neutral", which means the buyer buys the call and also sells some of the underlying (or futures contract on the index, in this case) so that it's roughly delta-hedged, the price for this spot trade is specified in the quote's spot reference. Let me know if you want me to expand as a full answer. Jul 31 '20 at 0:46

It is just whatever the option is worth assuming the underlying is currently trading at the reference rate and assuming the option carries the amount of deltas the brokers says it has. Usually there is some negotiating on what the fair delta is - since different people use different models/assumptions and have different deltas. If the delta is different from what you have, you just manually adjust for it by (current price - reference price) * number of residual deltas. This adjustment is added to the "fair value" of the option you are looking to quote.

So you price up the option (changing the underlying price to the reference rate), adjust that price by any residual deltas, and you quote around that price.

The reason they quote it tied up is they don't want to have to constantly ask you to re-price the option every time the underlying moves. It also makes a market maker's life easy because they don't have to immediately go into the market and hedge the delta on their own. It could also make the other side's life easy if they are looking to trade vol itself, and not the underlying.

May I ask what market you are looking at?

• Thanks for the answer. I am looking to equities options (and equity indexes). With “residual delta” do you mean the delta calculated form the reference price? Why market maker wouldn’t immediately delta-hedges? After market maker quotes the broker, and the client close the deal some time latter, the delta would be different. The market maker would delta-hedge with the delta from the quote with the reference price, or from the delta from the moment the client closes the deal? Aug 1 '20 at 21:52
• Lets supposed the following example: I receive a quote for a ABC call 15.08, ref \$15.0 My model says that with the spot fixed at \$15.0 I should sell it for \$0.49 and it has 50% delta. If the price goes to \$14.90, my fair value would be: \$0.49 + (\$14.90 - \$15.0) * 50% = \$0.44 (which is in line with my model and it has 47% delta). When market maker delta-hedges this positions, it would hedges 50% or 47%? Could you also explain the logical about this math of (current price - reference price) * residual deltas, please? Many thanks! Aug 1 '20 at 21:53
• I got the math behind it, calculating the PnL that the trading desk would have immediately with the hedge leg, that would be equals to the PnL from the option's leg, where the final option price is implied. Thanks!! Aug 1 '20 at 22:42
• Ah interesting I didn't know equity options had brokers - always thought they are electronic. If I understand you correctly, the MM would still delta hedge any residual deltas if it is different from their model when the do the trade. But the price of the structure would be change depending on difference in delta so the MM has to adjust their quotes accordingly. Aug 3 '20 at 4:04
• Yeah, I am from Brazil and basically all institutional investors need to quote equity options with a broker that quotes a market maker, due a lack of liquidity "on the screen", low quantity orders at the book and very wide spreads for not blue chips options. Equity Index options and FX options (USDBRL) has no "screen", only quotes via a broker/MM. Despite that, derivatives market are much bigger than "cash market", but it's harder to individual investor that don't have much money to be a private banking client or has a good amount at the broker to have access to a good variability of options. Aug 3 '20 at 20:23