How afterhours.fi works, and how we know it does

US equities stop trading from Friday 16:00 to Monday 09:30 New York, yet tokenized versions of those stocks (Binance bStocks, Ondo Stocks) trade on-chain all weekend. A holder carries the full weekend gap and has no instrument to shed it. We propose a weekly, fully collateralised protection contract: the holder pays a small fee on Friday and is paid the part of any Monday-open drop beyond a chosen line (capped at 20% of the protected amount), funded by a pool of liquidity providers.

Using 61,815 ticker-weekends across 50 underlyings, we show that weekend gaps are extremely fat-tailed (excess kurtosis 198), that textbook option pricing is mis-calibrated for them, and that a pooled, volatility-scaled empirical engine prices them out of sample with a loss ratio of 0.57 (target 0.67), stable across volatility regimes. Buyers who are even moderately risk-averse are better off insured on volatile names; liquidity providers earn about 7.3% a year on capital with a weekly Sharpe of 0.90, at a one-year ruin probability of 0.4% under the capital rule we enforce.

1. Hunch
   Nobody trades time

   Commodity traders make money on three dimensions: space (the same barrel is worth more in Rotterdam), form (blending off-spec crude) and time (storing it and selling forward). For stocks, the time dimension has a hole in it every weekend. Tokenization is the first thing that makes that hole tradable. Our first spec, “Weekend Market”, put the idea in three steps: closed-session risk is universal and unpriced; tokenization makes it transferable; and the closed session is where equity returns are made, so whoever carries the risk is “paid twice”: the fee plus the overnight drift.

2. First pricing
   A textbook formula

   We first priced protection with the at-the-money approximation P ≈ 0.4 · σ · S · √T. For Nvidia at 45% volatility over a 65-hour weekend that gives 1.55% of the position: too expensive to buy every week, which told us the product had to be out-of-the-money tail cover, not full hedging.

3. Test 1
   The first backtest killed two ideas

   One stock (Apple), 2015–2017, 104 weekends. (a) A weekend carried 0.75 of a full trading day’s variance, not the ~0.2 the index literature suggested, so the “retail overestimates weekend risk and we pocket the difference” margin story shrank from 3× to 1.58×. (b) Weekend returns were slightly negative (−1.9% a year, t = −0.28), so “paid twice” was rejected. What survived was stronger: weekend gaps had excess kurtosis 43, and the lognormal model under-priced a 7% drop by a factor of thousands. We repositioned from “a carry trade on a quiet session” to “tail insurance on a risk textbook models cannot price”.

4. Constraints
   Two rules we committed to

   From test 1 we wrote two hard constraints into the log: the price must come from data (empirical or extreme-value), never Black-Scholes; and the pool must hold capital of at least 10% of what it covers, with per-stock limits, because one weekend on one stock can exceed any thin buffer.

5. Test 2
   The full backtest

   50 stocks and ETFs with bStock or Ondo wrappers, 61,815 weekends, four pricing engines, strictly out of sample. Section 5 and 6 describe it. It confirmed the tail, overturned test 1’s claim that Black-Scholes is uniformly too cheap (it is wrong by regime, not in one direction), and picked the engine we ship.

6. Research
   Is it wanted, and is it new?

   A market and literature review (section 2) before any code: who carries weekend risk today, what they pay, what already exists, and what 58 academic papers say about pricing it.

7. Structure
   Making both sides work

   Simulations of protection structures for buyers (fixed lines, spreads, yield-funded, fixed budgets) and capital structures for the pool (T-bill collateral, payout caps, junior/senior tranches, dynamic sizing). Tranches were rejected; dynamic sizing was adopted (section 4).

8. Build
   Live on a test network

   Contracts, pricing server and app, with a full Friday-to-Monday cycle settled on-chain: a −7% Monday paid exactly the $40 the formula says on $1,000 protected at a 3% line.

The risk is real, and it lives in the closed session

The most remembered equity losses of 2024–2025 were Monday gaps: Nvidia’s −17% on 27 Jan 2025 after DeepSeek news broke over the weekend (−$589 bn, the largest one-day loss in market value on record), the April 2025 tariff weekend (S&P futures limit-down, VIX 60), and the August 2024 yen carry unwind. The academic literature since French (1980) and Cooper, Cliff & Gulen (2008) finds that most of the equity premium and a large share of variance are realised while the market is closed.

Retail takes the hit; institutions pay, but not for weekends

• In a sample of $15 bn of retail option trades (Bogousslavsky & Muravyev), protective puts are close to absent. Stop-loss orders cannot help against a gap: they execute at the first price after it.
• Institutions spend heavily on downside protection: about $78–87 bn sits in buffer/defined-outcome ETFs, $79.5 bn of buffered annuities were sold in 2025, and roughly $225 bn of US structured notes were issued. All of it is annual and index-level. No listed product isolates Friday close to Monday open.
• Option markets over-charge the weekend: selling Friday-to-Monday index puts earned about two-thirds of a one-day put-writing strategy’s profit (OptionMetrics), and Jones & Shemesh (2018) show equity options are systematically overpriced across non-trading periods. That over-pricing is the margin a well-priced pool can share with buyers.

On-chain, the weekend is where tokenized stocks actually trade

• 92% of on-chain bStock volume in a July 2026 week happened while the US market was closed (Binance Research). Weekend liquidity falls 70–90% and spreads widen 19–33×, and Chainlink equity feeds publish nothing over the weekend by design.
• The institutions already carrying this risk pay for it themselves: Venus keeps a $200,000 “bStock liquidation buffer” for weekends and listed bStocks with zero borrowing; Ethena’s framework for its bStock trade demands 10% extra margin over weekends or flattening before Friday’s close.
• Ondo Stocks mostly cannot be minted or redeemed between Friday evening and Sunday evening, so a holder often has no way out at all. bStocks can be traded 24/7, but the token itself finds almost none of Monday’s move before Monday morning (section 6.6), so selling on Sunday doesn’t help either.

Three patterns matter for design. First, the damage is concentrated: across the 99 stock-weekends we priced, the 43 that breached a 5% line account for nearly all of the losses. Second, the fee the engine asked the Friday before was usually small, because a quiet Friday looks quiet (DeepSeek: $5.50 per $10,000), which is exactly why protection has to be bought before you know you need it. Third, some crashes happen during Monday rather than at the open (Volmageddon, February 2018: SPY opened −0.7% and closed −4.2%), so a product that settles at the open must say so plainly.

Figure 3.1

backtest/scripts/30_famous_weekends.py

Every stock in our famous-weekend set: Friday close to Monday open

The payoff

The price (the engine we ship)

Every historical weekend gap in the universe is divided by that stock’s daily volatility over the previous 20 trading days, which puts a quiet utility and a meme stock on the same scale. The resulting pool of 61,815 standardised moves is the engine’s picture of what a weekend can do. To price a stock this week, we rescale that picture by the stock’s current volatility and average the payoff:

The 50% margin is not profit for its own sake: the backtest says the engine’s expected payout is right on average but noisy weekend to weekend, and the margin is what keeps the pool solvent through the bad years (section 6.3). This is the same idea as Kelly & Jiang’s (2014) pooled estimate of tail risk across stocks, applied to weekend gaps.

The rules that keep it fair

• Sales close at the Friday bell. After 16:00 New York, futures and the overnight session start to reveal the weekend’s news; anyone buying later would be buying with information.
• Settlement uses the official Monday opening price, never the thin weekend token price, which could be pushed around for less than a payout is worth.
• You can only protect what you hold, and corporate actions (splits, halts) cancel the weekend and refund the fee.
• The pool sizes itself. Half of it is a safety reserve that is never put at risk. It can only sell protection whose maximum payout fits inside the other half, so after a bad weekend it automatically sells less until it recovers (constant-proportion portfolio insurance).

Construction

• Universe. Every underlying that has an Ondo or bStock token on BNB Chain and enough price history: 50 names, 28 of them with a bStock wrapper, 10 ETFs.
• Weekend definition. A closed session that spans a weekend (Friday close → Monday open, or a longer holiday weekend). 61,815 such ticker-weekends; 50,059 single names and 11,756 ETFs.
• Data hygiene. Gaps below −75% were treated as unadjusted corporate actions in the vendor feed and removed (one case, a reverse split). Real distributions such as AMC’s APE units were kept and flagged.
• Out of sample, walk-forward. Every price for a weekend in year Y uses only data from before 1 January of Y; models are refitted yearly. The backtest runs 2005–2026 so that every engine has at least 15 years of history behind its first quote.
• Four engines. Textbook Black-Scholes (two clocks), each stock’s own history, an extreme-value (generalised Pareto) tail fitted per stock, and the pooled volatility-scaled engine.
• Buyer utility. We score protection by the certainty-equivalent return of a buyer with constant relative risk aversion γ = 4: a moderately cautious person. Positive means they’d rather have the protected weekend, fee included.
• Pool risk. 20,000 simulated years made of randomly drawn 4-week blocks of real history (block bootstrap, which keeps the clustering of bad weeks), for pools of different sizes and compositions.

6.1 Weekend gaps are extremely fat-tailed

Pooled over all stocks, the typical weekend gap has a standard deviation of 1.8%. If gaps followed a normal curve with that spread, a 3% drop would be common and a 10% drop essentially impossible. Reality is the opposite at both ends: fewer small drops, far more large ones. Excess kurtosis is 198 (a normal curve has 0).

Figure 6.2

backtest/scripts/10_universe_stats.py

Distribution of weekend gaps, log scale

6.2 Which pricing engine survives out of sample

The loss ratio is what the pool paid out divided by what it charged. With a 50% margin, a perfectly calibrated engine lands at 1 / 1.5 = 0.67. Below that it over-charges (buyers overpay); above 1 the pool loses money.

6.3 Is the shipped engine calibrated?

6.4 The buyer: twelve people who held a stock

Figure 6.6

backtest/scripts/40_hermee.py

Cumulative weekend profit and loss, protected vs not

6.5 The pool: 22 years of underwriting

A static pool at 10% capital survives every historical start date, but 13 March 2020 (the Sunday emergency rate cut) cost it 62% of its capital in one weekend. With the dynamic sizing we enforce (sell at most 10× the cushion above a 50% reserve), the same pool’s value never fell below 100% of its starting capital in the historical run, the reserve held in all 20,000 simulated years, and the median year returned 10.6%. We also tested splitting the pool into senior and junior slices; the senior slice was still hit in about 4% of years at every split, because a 2020-type year exceeds any junior slice. We rejected it.

Figure 6.7

backtest/scripts/50_keeper.py

Pool value by composition, 2005–2026

6.6 What the token does while the market is shut

Across 165 bStock weekends, the token’s move by Monday 13:00 UTC (30 minutes before the open) explained Monday’s gap almost perfectly (slope 0.95, correlation 0.96), but its move by Sunday night explained essentially none of it (slope 0.02). Price discovery happens in Monday pre-market, when futures and the overnight session trade. Thirty minutes before the bell the token sat within 0.31% of the official open on a typical weekend and within 0.84% at the 90th percentile.

Figure 6.8

backtest/scripts/60_token_weekend.py

Token move before the open vs the actual Monday gap

The server runs the same pooled, volatility-scaled formula as the backtest, from the same 61,815-weekend history, with this week’s volatility measured live from the bStock’s own trading. Each price is signed, so the contract accepts only prices the engine produced, and only before the Friday bell.

Validated

• Out of sample. No price in any table was fitted on the payouts it is scored against; every engine is refitted once a year on prior data only.
• Calibration. The shipped engine’s predicted and realised payouts line up by decile (figure 6.4), and its loss ratio is level across volatility regimes from the second quintile up.
• Stress. Pool results come from 20,000 bootstrapped years and from starting the pool on the worst historical dates (just before 2008, 2015, 2020 and 2024).
• On-chain. A full cycle was run on the live contracts: $1,000 protected at a 3% line, Monday −7%, payout exactly $40.00 as the formula says.
• Consistent with the literature. Pooling tails across stocks (Kelly & Jiang 2014), scaling by current volatility (McNeil & Frey 2000), treating the weekend as roughly one trading day of variance (French & Roll 1986), and the finding that weekend options are overpriced (Jones & Shemesh 2018) all match what we built.

Corrected along the way

While testing the live app we found the server was measuring a bStock’s volatility over all seven days of its 24/7 trading and annualising it as if every day were a trading day. Quiet Saturdays and Sundays pulled the estimate down (Nvidia read 21% against 46% on the exchange), which would have under-priced protection by up to half. The live estimate now uses weekday closes only, matching how the engine was calibrated. We report it because this is the kind of error a backtest cannot catch and only a live system can.

Known limitations

• Survivorship. The universe is today’s tokenized list, so stocks that failed (SVB, First Republic, Lehman) are missing. The measured tail is therefore a lower bound on the real one.
• Few extreme events. Most of the pool’s losses come from a handful of weekends; any figure that depends on them (worst weekend, ruin) has wide uncertainty even with 22 years of data.
• Opening prints are noisy. The official open is the reference the market publishes, but opening auctions are noisier than closes. A 15-minute average is the next thing to test.
• Scheduled events. Earnings weekends are known jumps, not tail risk; the production rules refuse or surcharge them rather than rely on the model.
• Token history is short. bStocks launched in June 2026; the token-behaviour results rest on 165 weekends, and Ondo’s on-chain history could not be retrieved.
• Vendor data. Daily prices come from a free vendor with occasional corporate-action errors; we removed the one we found and flagged the rest.

1. French, K. (1980). Stock returns and the weekend effect. Journal of Financial Economics 8(1).
2. French, K. & Roll, R. (1986). Stock return variances: the arrival of information and the reaction of traders. Journal of Financial Economics 17(1).
3. Cooper, M., Cliff, M. & Gulen, H. (2008). Return differences between trading and non-trading hours: like night and day. SSRN 1004081.
4. Lou, D., Polk, C. & Skouras, S. (2019). A tug of war: overnight versus intraday expected returns. Journal of Financial Economics 134(1).
5. Boyarchenko, N., Larsen, L. & Whelan, P. (2023). The overnight drift. Review of Financial Studies 36(9); and (2026) The disappearing overnight drift, Liberty Street Economics.
6. McNeil, A. & Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. Journal of Empirical Finance 7.
7. Kelly, B. & Jiang, H. (2014). Tail risk and asset prices. Review of Financial Studies 27(10).
8. Jones, C. & Shemesh, J. (2018). Option mispricing around nontrading periods. Journal of Finance 73(2).
9. Black, F. & Perold, A. (1992). Theory of constant proportion portfolio insurance. Journal of Economic Dynamics and Control 16.
10. Balder, S., Brandl, M. & Mahayni, A. (2009). Effectiveness of CPPI strategies under discrete-time trading. Journal of Economic Dynamics and Control 33.
11. Sydnor, J. (2010). (Over)insuring modest risks. American Economic Journal: Applied Economics 2(4).
12. Bogousslavsky, V. & Muravyev, D. An anatomy of retail option trading. SSRN 4682388.
13. Binance Research (2026). Tokenized stocks: weekend price discovery analysis.

Nothing here is investment advice. Figures are historical and hypothetical; the product runs on test networks. Back to the plain-English story.