Market Making as Short Volatility: Spread Income and Inventory Risk
Summary
The document proposes a simplified analogy between single-level market making in a linear product and selling a straddle. A market maker may earn the bid–ask spread when incoming market orders are limited and balanced, but price movement beyond a quote can leave the maker holding inventory whose value changes with the underlying. The stated PnL sketch contrasts spread revenue with a loss tied to that price movement and filled quantity.
The author frames this as a question rather than a validated model. They recognize that it omits multiple periods and competing market makers, and ask how multi-depth quoting changes inventory exposure as prices move. They also wonder whether market-maker PnL can be approximated with a Taylor expansion and related to implied volatility, spread width, and quote size. No empirical results or complete pricing framework are supplied, so the analogy is a starting point for analysis, not a general equivalence between market making and short straddles.
Key ideas
- A market maker can earn spread revenue when order flow fills quotes in a sufficiently balanced way.
- Filled quotes can leave the market maker with inventory exposed to subsequent price changes.
- The proposed single-period payoff resembles short volatility exposure under simplifying assumptions.
- Multiple quoting levels, competing market makers, and repeated trading complicate the analogy.
- Quote width and size may need to reflect volatility and the distribution of trade sizes.
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Full text
# Market making in linear products, analogous to a short straddle under simplifying assumptions?
# Market making in linear products, analogous to a short straddle under simplifying assumptions?
To preface, I am not a market-maker or trader, but I have an ok understanding of options and classic vanilla option theory.
For a market maker providing quotes at a single level (i.e 99 bid - 101 offer), they are able to monetise their spread whilst market orders coming into the market are less than the posted amounts, an amount $q_{b,a}$, and there is sufficiently balanced flow. If the price moves beyond the bid/offer, then the MM has a delta of $q_{b,a}$, leaving a risk profile of $q_{b,a} \,\ \cdot |{\Delta S}|$.
In this simplistic model, the PnL is: $$ PnL = S_t \cdot spread \cdot q \,\ - [q \cdot abs(S_{t+1} - S_t) \,\ | S_{t+1} < bid_t \ or \ S_{t+1} > offer_t] $$
To me this seems similar to selling a straddle. Does anybody have any improvements to offer or papers to suggest? Again I reiterate I am very unfamiliar with intricacies of market making, and am aware that this model does not factor out into the multi-period, or under the presence of multiple market makers with competing bid/offers. I am curious as I am unable to find papers which visualise the relationship between the underlying movement at some time-slice, t, and PnL. Is this because it does not exist?
I should imagine that at the point where a market maker is quoting at multiple depths simultaneously, that there is an effect analogous to gamma where the MM picks up delta as the market moves away from their quotes. From an options perspective (or even just non-linear payoffs) this seems to point to a notion of implied volatility, fair spread width, and fair quoting amounts under some distribution of trade sizes, and underlying volatility. Is there some way to Taylor expand market maker PnL?
Thanks!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.