Broker Option Quotes: Reference Prices, Delta, and Spot Adjustments
Summary
The document describes a broker or over-the-counter convention in which an option quote combines a price, a reference spot price, and delta. Because a trade may occur after the quote is issued, delta estimates the first-order price adjustment for a change in the underlying between quote time and trade time: the quoted option price is adjusted by delta times the spot move. This lets counterparties interpret a quote even if the market has moved before execution.
The explanation contrasts this convention with quoting solely in implied volatility. An implied-volatility quote also depends on inputs such as rates, the forward, and the time-to-expiry convention for a European option; American options add further complications. Delta adjustment is an approximation, so a quote may be withdrawn if too much time passes, volatility changes, or the spot move makes the estimate unreliable. The discussion is conceptual and does not give a worked numerical example or address higher-order adjustments.
Key ideas
- Broker and OTC option quotes may state a price together with a reference spot and delta.
- Delta estimates the option price change caused by a small move in the underlying between quote and trade.
- An implied-volatility quote depends on additional conventions and pricing inputs, including rates, forwards, and expiry timing.
- A delta-based spot adjustment is only a first-order approximation and may become unreliable after larger changes.
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Full text
# Quoting options with reference price and delta
# Quoting options with reference price and delta
I always thought equity options where quoted with implied volatility, the price being given by the Black-Scholes price of the option with volatility equal to the implied volatlity.
But apparently there is another way to quote option : with reference implied vol (or reference price) and delta for an underlying at a price near the spot price. I also heard about "target price" in this context.
I cannot find any reference about this, so more more information or an explanation would be great
## Answer by LocalVolatility (score 1, accepted)
https://quant.stackexchange.com/a/36854
In the equity space and between different institutions, options are usually not quoted in implied volatilities. For this to work, you'd additionally have to also quote at least a risk-free rate, forward and a measure of time-to-expiry (e.g. a day count convention) for European options. For American options, it get's even less feasible.
In the broker/OTC market, options are usually quoted as a price, spot reference and delta combination. The delta and spot reference determine how the price is adjusted to account for spot moves between quote and trade time to the first order. This is necessary as a trade usually does not happen immediately immediately but only after the broker collected a sufficient number of quotes and the initiating counterpart made a decision. Let $T_\text{quote}$ and $T_\text{trade}$ be the times of the quote and trade, respectively. The traded price is then given by
$$ P \left( T_\text{trade} \right) = P \left( T_\text{quote} \right) + \Delta \left( T_\text{quote} \right) \left[ S \left( T_\text{trade} \right) - S \left( T_\text{quote} \right) \right]. $$
Of course, you (as the one providing the quote) can always retract it while it hasn't been traded yet. E.g. when the too much time passed, the implied volatility changed or the spot price moved too much for the delta approximation to be valid.
On the screen, there is not need for this as you can update your quotes at all times.Shown 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.