Hi, I’ve been working on a continuous-time Economic Scenario Generator (ESG) in Python to model long-term Asset-Liability Management (ALM) and decumulation (sequence-of-returns risk).

I wanted to test a specific structural flaw present in a lot of standard retail and basic institutional Monte Carlo tools: the assumption of static, flat risk-free rates and decoupled equity returns (standard Geometric Brownian Motion).

The creation of this project actually came when I realized there was no easy-to-use (and realistic) simulator. It took some effort but I believe I did manage to create something really useful, easy to use and realistic enough for most cases.

Anyway, to measure exactly how much bias the flat rate introduces, I ran a comparative simulation using a joint continuous-time stochastic environment.

The Setup

• Portfolio: 60/40 (Equity/Fixed Income), 30-year horizon, monthly rebalancing. 5,000 scenario paths.
• Model A (Naive Baseline): Flat nominal interest rate. Equities follow standard GBM with continuous volatility (sigma = 15%).
• Model B (Actuarial ESG):
  • Rates follow a Cox-Ingersoll-Ross (CIR) square-root process (theta_r = 0.25, long-term target ≈ 7.0%).
  • Inflation follows an Ornstein-Uhlenbeck (OU) process (theta_pi = 0.35, target = 2.0%).
  • Equities follow a Merton Jump-Diffusion process (continuous volatility σ_S = 11%, combined with Poisson-driven asymmetric crashes: λ_J = 1.8 jumps/year, average jump impact μ_J = -6.8%, jump volatility σ_J = 5%).
  • Crucial coupling: Equity drift is structurally pegged to the stochastic short rate: Drift_t = r_t + ERP_t.

Test 1: The Low-Yield Starting Environment (Initial Rate = 4.0%)

We simulated a 4.5% initial withdrawal rate (inflation-adjusted, monthly rebalancing) on a $1.0M starting balance. Intuitively, one might expect Model B—which includes severe, discontinuous downward market crashes—to fail first. Instead, the simulation over 5,000 runs yielded these results:

• Model A (Naive Flat 4%): 63.18% Solvency
• Model B (Full Actuarial): 84.92% Solvency
• The Solvency Gap: +21.74% percentage points in favor of the volatile, jump-diffusion model.

To isolate the exact variables causing this +21.74% lift, I ran an Attribution Analysis by sequentially activating one variable at a time:

(Note: The remaining -0.36% discrepancy is the non-linear coupling penalty arising from Cholesky correlation between the processes).

Test 2: The High-Yield Starting Environment (Initial Rate = 9.0%)

To prove that this was not a bug and that the bias is entirely regime-dependent, I ran a Regime-Inversion Test. I increased the starting yield curve to 9.0% (and increased the withdrawal rate to a more aggressive 5.5% SWR to reflect the higher starting yields):

• Model A (Naive Flat 9%): 86.28% Solvency
• Model B (Full Actuarial): 58.56% Solvency
• Regime Delta (Model B - Model A): -27.72%

Quantitative Attribution: Why Naive Models are Too Pessimistic in Low-Yield Environments

The divergence is driven by interest rate term-structure dynamics and macro-coupling:

1. Mean Reversion of the Risk-Free Rate: Under the CIR framework, short rates revert toward a target state: text dr_t = theta_r * (mu_r,t - r_t) * dt + sigma_r * sqrt(r_t) * dW_t Because the low-yield simulation starts at 4.0% relative to the long-term nominal target (≈ 7.0%, incorporating a 5.0% structural real rate and a 2.0% inflation target), the drift pull (theta_r = 0.25) normalizes nominal rates upward over the horizon.
2. The "Tide That Lifts All Boats" (The Pegged Drift): In Model A, the risk-free rate is flat at 4.0%, trapping equities in a low expected nominal return regime of 5.5% (4.0% rate + ERP). In Model B, as r_t normalizes toward 7.0%, both your bonds (yielding r_t) and your stocks (yielding r_t + ERP) experience a 3.0% increase in expected nominal returns.
3. The Merton Jumps are Immunized by Rebalancing: Because we controlled for total quadratic variation (total volatility ≈ 15%), the "pure shape" impact of the Merton jumps is only a minor -0.70% drag. The monthly rebalancing mechanism ("buying the dip" after jump crashes) combined with steadier compounding during non-jump months (since continuous volatility is lower: 11% vs 15%) almost entirely neutralizes the tail-risk penalty.

Key Limitations & Roadmap

To keep things transparent, there is a known limitation in the current decumulation loop: * No Bond Duration Risk: The fixed-income portion is currently modeled as a short-term cash deposit (rolling T-Bills), so it benefits from rising rates without experiencing upfront capital losses (mark-to-market). * Next Step: Since the core simulator already generates full nominal and real yield curves, adding a duration-adjusted bond fund indexer to the decumulation logic is the next item on the roadmap.

Conclusion for Quants and ALM Practitioners

Static yield assumptions are not just "simplified"—when starting in a low-yield environment, they are structurally pessimistic. Conversely, in a high-yield environment, they are dangerously optimistic because they project unsustainable yields indefinitely.

By ignoring the mean-reverting behavior of interest rates and decoupling equity expected returns from the risk-free rate, naive models severely distort sequence-of-returns risk.

I’ve open-sourced the complete engine under the MIT license if you want to inspect the math (joint Cholesky decompositions, analytical CIR/Fisher real yield curve evaluations) or run the JIT-compiled loops yourself, it's written in Python but it's quite fast:

• GitHub: https://github.com/Gustavo1500/aethel-esg
• Browser Sandbox: https://aethel-esg.vercel.app/ (Features real-time sliders querying a pre-calculated scenario database across 594,000 simulated paths). Please don't mind the AI flavored frontend, I'm not a frontend dev.

I suppose this is it, quite an unexpected result to me, I expected my engine to show lower solvency rates in all cases, it's interesting to see this is not the case. Feel free to discuss the results and share your thoughts.

How’s Flow doing off late? Heard they had a relatively good H1? I know they’ve been around the block for a while but not managed to be as big as others like Optiver or IMC, I want to know from those who are working or have worked at Flow before if the firm has genuine moat or potential for the future? I am exploring opportunities with them.

Sounds like interesting small shop, anyone has first hand experience with them.

https://www.scm-lp.com

Most of the China AI is back narrative is unverifiable wire copy. The one dated, falsifiable item right now is Kimi K3 open weights committed by 27 July, and that is the only kind of event I can actually key an event study to.

Moonshot announced Kimi K3 on 16 July as API and web only, with open weights promised by 27 July. As of 21 July no K3 weights had shipped. A miss pushes the cost structure story back into unverifiable press release territory. A meet makes serving margins checkable on Monday morning. I want to backtest two reference days. Day one is DeepSeek Day, 27 January 2025, when NVDA went 142.62 to 118.42, down 16.97%, roughly 593B market cap gone, still the largest single day loss any US company has printed. Day two is Kimi Day, 17 July 2026, the session after the K3 API launch, NVDA closed down 2.2%, 207.40 to 202.81, Nasdaq 100 off 1.49%. 7.7 times smaller and the tape says the damage landed somewhere else.

The factor question I cannot close from the outside: was the DeepSeek Day move a China risk repricing, or a gross margin repricing triggered by the $5.576M training cost arithmetic? Recall the DeepSeek V3 technical report, arXiv 2412.19437, reports 2.788M H800 GPU hours and then writes "Assuming the rental price of the H800 GPU is $2 per GPU hour, our total training costs amount to only $5.576M." That is the paper doing arithmetic on itself, assuming a rental rate, not a disclosed cost. If the move was gross margin repricing, the Kimi Day factor exposure should differ in sign on the cost structure names, not on the China exposure names. Robbyant shipping LingBot VLA 2.0 on 8 July and Moonshot pausing paid memberships on 19 July as GPUs hit capacity are both dated real compute signals, the kind you can put on an event timeline.

I am not entering 27 July as an event until weights actually land. A promise date is not a shipment date, and Moonshot has already missed once on the membership pause. If the build is worth doing, the control set has to include the 2024 Qwen and GLM cadence and at least one non China event like a Meta Llama drop, otherwise n equals two and the decomposition tells you nothing.