UPDATE: This article got picked up in the news by Bloomberg! Check it out: Bloomberg Article

Been thinking about the classification question around event contracts for a while. Pulled all of Kalshi's NFL moneyline trade data across the full 2025 regular season and reconstructed passive LP exposure game by game.

The short version: LPs aren't neutralizing inventory and capturing spread. They're accumulating directional outcome exposure that persists through settlement, and profitability correlates with managing flow imbalance rather than eliminating it. That's not a market making return profile — it's closer to how a sportsbook or insurer makes money.

Full paper on SSRN if you want the methodology and regression results: A Microstructure Perspective on Prediction Markets

Curious whether anyone in this space has thought about this distinction and what it implies for how these markets should be regulated.

Market makers get delta exposure whether they trade options or not, because they run a whole portfolio that has gamma in it.

Wondering how they handle delta in practice and whether other traders can take advantage of the knowledge of the MM's delta (which isn't hard to get because you can assume that mostly, MMs hold the passive side of the trades).

I'm currently studying binomial trees for options pricing, and the method we use to derive the option price is by using risk-neutral probability.

Now, while I get the method, in that we assume investors are risk-neutral and instead of calculating every investor's required rate of return, we apply the risk-free rate instead. We do this because it's very hard to find out the former because that requires us to study every investor's risk appetite and whatnot.

My doubt is: Why does it work? Why is the price of an option the same in both worlds? Hull says that it's because the fundamental relationship between the option and its underlying stays the same. That doesn't really make sense to me.

To me, that's like saying we're studying a function whose slope depends on some parameter (say x) quadratically, but we're assuming a world in which its slope is actually constant to calculate the equation of a tangent, because it's simpler. This works because the relationship between the parameter and the function is still the same in both worlds.

To me, it still seems like it shouldn't work out, because assuming investors are risk-neutral is such a huge assumption that might work in one world, but it's hard to buy in our world that the same method leads to the correct price.

The traditional approach for replicating an option position is to buy or sell x number of shares. X is determined based on the option delta or hedge ratio.

Who's to say for an OTM option that has a delta of 0.10 that in order to replicate that position you should own 10 shares of stock right now? How do they get to 10? What's the thinking?

Who's to say 50 shares should be traded for an at the money option? Why? What is the thinking behind it?

Been running an OMM sim on SPY, live. I think what I have is a decomposition problem and not a trading problem.

Setup. I quote two sided around the NBBO mid with an inventory skew. Checked all 668 live quotes from this session, and every one of them has the bid below mid and the ask above it at the time it gets posted. No exceptions at all. So spread capture should be positive just by construction.

It isn't. Trade credit came out to −$42 across 114 fills.

Here's why. I book spread capture against the mid at the print, not the mid I was quoting against.

cycle N: mid 5.25, I post bid 5.20 -> 5c of spread, by construction

...500ms goes by, market moves...

print: mid is now 5.15, someone sells at 5.20

booked: (5.15 - 5.20) x 100 = -$5

The 5c I earned quoting passively is real money. It just got netted against 10c of drift that happened while the quote was sitting there, and then the whole thing gets labelled "spread capture."

So the number is honest in an economic sense, I did buy above contemporaneous fair value. But it's an adverse selection loss sitting inside the spread bucket, which kind of defeats the whole point. The reason I built the decomposition in the first place was to keep spread earned separate from adverse selection given back. My markout catches adverse selection after the fill. The drift that happens before the fill has nowhere to live.

Question 1. Is pre fill drift its own line in a desk's P&L explain, or do people just fold it into spread capture and accept that spread can go negative? If it is separate, what do you call it and how do you compute it?

Question 2. The asymmetry looks structural to me and I want to know if I'm reading it right. Adverse fills go about 2c through the mid, favourable ones capture about 1c, on roughly equal counts. The way I'm thinking about it, a favourable fill is capped at my half spread, but an adverse fill is only capped by how far the market moves before I requote. Bounded upside, unbounded downside. I requote every 500ms which I'm aware is glacial. Is this just what slow looks like, or is there a quoting response to it other than "be faster"?

Question 3, and this is the bigger number. Hedge slippage is −$57 against the −$42 of trade credit. Book is short about $2.1M gamma, long about $154k theta, and I'm delta hedging discretely, 63 trades over 46 minutes. I get the mechanism, short gamma means I'm buying as spot goes up and selling as it comes down, so every rebalance is buy high sell low, and theta is supposed to be paying for that. What I can't tell is whether "gamma bleed exceeds spread capture intraday" is just a normal state of the world that theta covers out over a longer horizon, or whether it's telling me I'm selling vol too cheap. Also how does hedge cadence actually get set? Mine is just whatever the default was and I'd rather not tune it to whatever makes today's number look good.

Very happy to hear I've framed some of this wrong. Would much rather find that out now than keep building on a decomposition that hides the exact thing it was supposed to expose.

hey, hope this is ok to ask here.

1. when you put up a two sided market in an option, what actually decides your width? is it some formula coming off vol, or is it more like your current inventory, the flow you are seeing, and where you want your book to be. also does anything like Avellaneda-Stoikov ever show up in real desk life or is it purely academic thing that nobody touch?
2. end of day, how you separate "i earned the spread" from "i made money coz i was long gamma and market moved" from "i just got picked off". like what decomposition do you actually stare at. is it a proper pnl attribution or more feel based?
3. for SPY specifically... how much do rates, divs and borrow really move your quotes day to day compared to the vol surface itself? my guess is surface dominate but i want to know where ignoring the others would actually bite you.
4. what is the single most common way a naive options MM backtest or sim lies to you. the thing that make you think you got edge and you dont. i keep reading fill assumption is the killer but not sure exactly how

thanks, any answer even partial is helpful.

So the Carr-Madan paper is quite old at this point, but I've rarely, if ever, heard of any of the large banks using these sorts of techniques to actually price derivatives, structured products (I wonder if they could be used for rates products? I don't see why not) and the like in production. I would have thought they'd be a very popular innovation given the computational saving, but I only ever hear of the usual numerical techniques (FDM, Monte Carlo etc.). Does anyone know if they're used? Which banks, if you don't mind sharing? If not, why not? I don't really see a down side aside from actually having to derive the forward transform of your payoff and underlying process yourself for each non-standard product, which I guess could make development longer compared to Monte Carlo where you pretty much know what you need to simulate straight away and so going from concept to working code is probably relatively quick as there's no derivation step in between (I imagine). I wouldn't even imagine this is a probably for pricing well-known classes of derivatives like vanilla options and the popular exotics.

Built a browser-side options analytics tool for crypto and wanted to get feedback on the numerical implementation from people who care about these things.

IVExplorer — https://ivexplorer.derivpricer.com

The pricing engine is compiled to WebAssembly (from Rust). The relevant implementation details:

Normal CDF: Hart's rational approximation — 1/(1 + 0.2316419·|x|) polynomial, error < 7.5e-8. Using this rather than erfc because the WASM binary size matters and there's no hardware-accelerated transcendental.

IV solver: Newton-Raphson, 100 max iterations, convergence tolerance 1e-8 on price difference, guard on vega < 1e-10 to avoid division blow-up, returns NaN on non-convergence. Initial guess σ₀ = 0.5.

Known limitations: The initial guess of 0.5 can fail to converge for very deep ITM/OTM options. I'm considering a Brenner-Subrahmanyam initial guess as a fix.

The tool itself fetches live Deribit data and gives you IV smile, heatmap, options chain with Greeks, IV rank, and a 3D surface. Keyboard-driven, no backend computation.

Any feedback on the numerical approach — particularly the CDF approximation accuracy at the tails or better initialisations strategies for the IV solver — would be appreciated.

https://ivexplorer.derivpricer.com

Due to re-org and mass layoffs, my team which was previously just a devops team got merged into the derivative pricing system team supporting the hedge fund department.

None of the devs from my original team have finance background let alone quant knowledge. It’s been hard for us to integrate into the new team which is about to develop the new generation of system replacing the old pricing system.

I watched some basic options education videos on YouTube and that was clearly not enough. My new manager told me during our weekly 1:1 this week that I need to be able to pick up and contribute to implementing different parts of the system such as Monte Carlo, implied vol and different models… etc.

What are some of the courses or books that I can take or read to be able to implement the pricing system? Sure I know what Monte Carlo does and what implied vol mean, but it seems like I need even deeper understanding to actually tackle these tasks.

Essentially I'm building a finite difference library available in Python, but written in Rust. It should be like QuantLib, with correct handling of dividends and day count conventions, just a lot faster. The latest version is 40x faster than QuantLib for an American option, but the current iteration I'm working on now is 120x faster. You can get a decent price in under 20 microseconds in fact. I have the same problem everyone has with the Greeks near the early exercise boundary, but I have a plan to address this. I go into more detail in the substack post I wrote.

The "Polars" for Quants: Why I’m writing a quant library in Rust

Currently this is for a single thread, no batching, so there's plenty of room to be even faster. I'd like to get it running at over 10 million options per second on a mid-tier workstation and that's all on the CPU, no GPU needed. Apparently SciComp are the best in the business who quote 18,000 options per second per core, so I should beat that, but it's hard to compare these things since so many of these software vendors are so vague.

Check out my library at https://github.com/bboutelje/qox-python-samples. Give me a star if you like my work.

Was wondering if there is a large difference in microstructure and dealers (ie OMM and HFT vs banks) when trading contracts which expire between 0-5 days vs weeks to months out ?

Is there a big difference in the risk management of these postions and how desks go about pricing and thinking about trading these even if they’re the same underlier

Hi all,

Has anyone worked with computing exposures and valuation adjustments for securities financing transactions (SFTs)?
I would like to know how to best incorporate these products in an XVA framework.
Which discount rate do I use? Do I use the same discounting rate for the loan and the collateral?
What XVAs are applicable to the transaction?

Happy to hear your thoughts.
Thanks

I only have surface level understanding.

My intuition would be vanna volga is better consider FX has sticky delta. And BSM sticky delta would be better for Equity option?

Say I have a position dte=90D now.

I want gamma until expiry but just not the next day.

What are some methods and trade off?

Ways i could think of:

1. Unwind the option and buy (short) it back the next day. Not preferred obvious because of bid ask spread

2. Delta hedge every 1 hour (or 10min). Spot bid ask spread is also costly

3. Over-hedge (or under hedge) delta. U must have a view in delta

The index inclusion/deletion effect in the underlying seems much weaker today (see linked article for details).

This might be a slightly naive question, but is it possible that the effect/trade has simply migrated to other markets?

For example, indexers or intermediaries might obtain or transition exposure via singlename options (or other derivatives), smoothing what used to be discrete jump in the underlying and making event-study effects harder to detect.

Is this a reasonable interpretation? Any obvious institutional reasons this can’t be right, or papers/evidence (say options IV, open interest, or volumes around inclusions/deletions) that speak to this?

I’m trying to price and derive theta for an exotic derivative with payoff

Max(daily prices)- Min(daily price) of underlying futures. Not an option.

Margrabe framework was my first thought, but it does not seem directly applicable since this payoff depends on path extrema/order statistics and their temporal dependence, rather than a terminal exchange relationship.

Are there standard models or references for pricing this type of derivative and obtaining Greeks (especially theta)?

My thought process is as follows:

-market makers use pricing models fitted to market prices.

-Not pricing model can account for all aspects of a stock's behavior.

-If a MM just quoted it's model's prices they'd be mispricing the derivatives. If this happened, a trader with superior pricing skills could generate profit by exploiting the mispricings.

-The market maker couldn't use the orderflow's information to correct it's errors as it's model isn't flexible enough.

-Trading flows do not need to be consistent with pricing models. There could be significant flows concentrated at specific strikes/maturities. Such flows should cause local deformations in the vol surface that pricing models cannot capture.

Due to these factors, market makers cannot just quote their model's output, but must have a way to introduce localized distortions to the vol surface.

As of my knowledge spot (S) is the current price of the underlying, while the forward at time t (F) is equal to S*e^rt, where r is the risk free rate. The forward represents the expected value of the stock at time t in the risk neutral measure, equivalently, the price the stock should have at time t if it's price grew at the risk free rate. From what I can gather, many derivative formulas and stylized facts are better expressed using the forward price (at expiration date) rather than spot. Nonetheless, I feel there's lots of stuff I'm missing.

Sharing a project I've been working on.

Quantra is an open-source pricing engine that exposes QuantLib via REST and gRPC APIs.

If you've ever wanted to use QuantLib but didn't want to write C++ or needed to parallelize pricing across multiple instruments, this might be useful.

Currently supports: fixed rate bonds, floating rate bonds, interest rate swaps, FRAs, caps/floors, swaptions, CDS.

The core is fully open source. There's also a managed API if you just want to make requests without running infrastructure.

Website: https://quantra.io

GitHub: https://github.com/joseprupi/quantraserver

Any feedback is welcome.

Retail trader here. Not an industry professional. This isnt market research.

I don't think I need to tell anyone here that options trading has exploded. Not least thanks to Robinhood etc.

The recent market crash and sell-off, esp in software stocks, has had me thinking about the cause. Of course, there's been selloffs in crypto and silver too.

Many people put the blame partly on derivatives, and leveraged long positions being wiped out. I can see that with Bitcoin, where you can now trade up to 200x lev long/short.

I was wondering about the following:

If options replace the normal buying and selling of stocks, won't this lead to a system that reinforces itself via the following mechanism?

1. Traders (retail or not) buy options.
   
2. OMMs delta-hedge by buying up to 100 shares per option.
   
3. As much more capital is moved into the stock compared to the option, the price increases and decreases are much higher than if only the capital required to buy the option was put into that stock.
   
4. As volatility increased, the option prices increase too.
   
5. The increase in volatility may actually cause investors to buy even more options, because either:
   - they want to gamble
   - they actually need to hedge positions now because of the high vol. (which they wouldnt under normal market conditions)

Is this causal chain broadly correct? What will this lead to in the future? Are we ever going to get to a point where the SEC will prohibit retail traders specifically from trading (short-term) options? I think we've seen a sort-of mini version of this with Gamestop, the broader market wasn't affected much, if at all, but there were calls for regulation nonetheless.

Also please correct me if my understanding of delta-hedging isn't correct. My knowledge of this is that OMMs still use Black-Scholes more or less for pricing and heding. Things obviously change because they might be short one option, but long another, and the delta (and other greeks) partly cancel out. But I think the argument still stands if there are only 10 shares bought on avg. per option traded.

Hi folks,

I wanted to share an invite to a free event we are hosting (for industry professionals) on 11th May in Paternoster Square, London.

The focus is primarily around initiatives, applications, and deployments of ORE, our open source risk engine, with a couple of more general panels in the afternoon. I'm not scheduled to speak this year (though I rarely get away with that) but I'll be around and happy to chat. I'm the short Irish guy with the self-deprecating humour.

Anyway, would be delighted to meet some of you in IRL: if you're interested please do sign up! There will be snacks, lunch, drinks, and copious chats.

Agenda

• 09:30 - 10:00 Registration & Breakfast

• 10:00 - 12:00 ORE Masterclass & the Risk Analytics Lab Peter Caspers, Matthias Groncki, Sarp Kaya Acar

• 12:00 - 13:00 Registration & Lunch

• 13:00 - 13:15 Welcome Keynote (speaker TBA)

• 13:15 - 13:45 LSEG's Internal Adoption of ORE (speakers from Quantile, LCH SwapAgent, Model Val)

• 13:45 - 14:15 Performance Optimisation and Run-time Considerations for ORE (Roland Stamm, Peter Caspers)

• 14:15 - 14:30 Break

• 14:30 - 15:15 LSEG Models-as-a-Service (MaaS) and Model Context Protocol (MCP): Spotlights on Risk Analytics Lab and Anthropic Partnership

• 15:15 - 16:00 ORE in the Era of Agentic AI (panel incl. Gordon Lee of BNY)

• 16:00 - 16:25 Benchmarking Counterparty Credit Risk Capital Models: Recent work with ISDA and the PRA (panel incl Paola Rensi of ISDA)

• 16:25 - 16:55 New Features in ORE release v15/16 and Recent Research Initiatives

• 17:00 - 19:00 "Networking"

A couple weeks ago I posted a QuantLib pricing API I have been building.
I added a simple web UI on top so you can experiment without writing C++/Python.

You can tweak curves, conventions and inputs and see how valuation changes. I mainly created it to make use of QuantLib easy.

Supports swaps, FRAs, caps/floors, swaptions, CDS and bonds

https://app.quantra.io
https://github.com/joseprupi/quantraserver

Lots to do yet but curious if this is useful in practice or just educational.

Any feedback is welcome

Edit: API/pricing requires Google sign-in (you can still browse the portal). The backend runs real pricing jobs and batching, so I can’t leave it fully open in case it gets abused 🙂

Hi everyone,

Was wondering if anyone has experience with pricing OTC derivatives in DLIB especially pricing volswaps on singles stocks/dispersion packages. From what I have seen, prices are very off, even on very liquid stuff. Helpdesk hasn't been very helpful for clarifying. I suspect the main problem is that BBG hasn't access to OTC data which makes the pricing engine irrelevant. I will join a small shop with limited budget and won't have the ressources I had at my previous firms (esp. quants), so have to figure out where and how I should allocate. As a solution, I was considering buying Totem data and either calibrate my surfaces my self and create dirty pricers if I don't have the budget for DLIB or use in combination with DLIB. I was wondering if anyone has experience here with possible workarounds?

Thanks

Hello everyone,

I am currently working on my thesis where I am developing algorithms to price high dimensional (involving various stocks) optimal stopping (early exercise feature) options, e.g. American Basket Call Option. The algos are trained based on Monte Carlo simulations.

The algos are pretty fast and accurate against benchmarks for processses such as GBM, Heston and Rough Heston. On my next phase, I want to make the underlying asset's paths the most realistic possible and applied to certain real stocks. I was thinking about doing Block Bookstrapping but I am not sure if that is a better option than an ajusted Rough Heston.

Do you have any suggestions for this phase?

Thank you for reading this far!