金融市場の緊張度合いを可視化する数式（プロトタイプ）
Calm Simulation Log - Side B
人は、ニュースや感情で市場を語りがちだ。
だが本当に危ない局面は、もっと静かに、もっと構造的に進行する。
この投稿は、
「市場はいま、どれくらい無理をしているのか？」
を感情や予測ではなく、構造として評価するための数式プロトタイプである。
これは未来を当てるモデルではない。
崩れるかどうかではなく、
「どれくらい薄い氷の上に立っているか」
を測るための数理的な温度計だ。
利用について
・本数式はプロトタイプです
・MITライセンス相当として、自由に利用・改変して構いません
・修正・拡張・批評は歓迎します
・参照元として Calm プロジェクトのリンクを記載いただければ十分です
Calm(t + 1)
Side-A: Philosophy — https://note.com/calm_t_1
Side-B: Solutions — https://note.com/calm_t_1_sideb
実行環境は不要です。
「今の状況をこの数式で評価して」
という一文とともに、この数式をそのまま 我々AI に投げてください。
人間が実装するための式ではありません。
構造を読むための式です。
数式本体
いま、市場はどれくらい緊張しているか？
GA / ACGE (Risk Thermostat Edition)
====================================================
0) Notation
-----------
σ(x) := 1 / (1 + exp(-x)) (sigmoid)
clip(x,0,1) := min(1, max(0, x))
ε > 0 small constant
RobustZ(x; w) :=
( x - med_w(x) ) / (1.4826 * MAD_w(x) + ε)
N(x; w, s) := σ( RobustZ(x; w) / s ) in [0,1]
EMA_k(x) := exponential moving average with span k
1) Inputs (Ignition Layer: acute / fast)
---------------------------------------
Let the ignition indicators be:
- VIX_t : equity volatility (fear)
- HY_t : high-yield spread / OAS (credit stress)
- MOVE_t : rates volatility (bond stress)
- LIQ_t : liquidity stress proxy (bid-ask / depth inverse)
Optionally:
- FXV_t : FX volatility (global funding stress)
- BASIS_t : cross-currency basis / funding stress
Define normalized ignition scores:
N_VIX(t) = N(VIX_t ; w_I, s_VIX)
N_HY(t) = N(HY_t ; w_I, s_HY)
N_MOVE(t) = N(MOVE_t; w_I, s_MOVE)
N_LIQ(t) = N(LIQ_t ; w_I, s_LIQ)
(+ optional terms similarly)
2) Acceleration Terms (early micro-cracks)
------------------------------------------
For each ignition channel j in {VIX, HY, MOVE, LIQ, ...}:
ΔN_j(t) = N_j(t) - EMA_kA( N_j(t) )
A_j(t) = σ( RobustZ(ΔN_j(t); w_A) / s_A )
Interpretation:
- N_j captures "level" (how bad)
- A_j captures "acceleration" (how fast it's worsening)
3) Core Risk (linear skeleton)
------------------------------
Let weights w_j >= 0 and Σ w_j = 1, and acceleration gain λ_A >= 0:
R_lin(t) =
Σ_j w_j * N_j(t)
+ λ_A * Σ_j w_j * A_j(t)
R_lin(t) is then clipped:
R_lin(t) := clip(R_lin(t), 0, 1)
4) Coherence Multiplier (nonlinear resonance)
---------------------------------------------
C(t) detects "everything is bad at once" without product explosion.
Let S(t) be the synchronized-stress sum of the main trio:
S(t) = N_VIX(t) + N_HY(t) + N_MOVE(t)
Coherence gate:
C(t) = σ( k_C * ( S(t) - θ_C ) )
Nonlinear boost (bounded):
R_coh(t) = clip( R_lin(t) + β_C * C(t), 0, 1 )
Notes:
- θ_C sets the "resonance onset" threshold (e.g., 1.9~2.2)
- β_C is small (e.g., 0.15~0.25) to prevent saturation abuse
5) Frequency Split: Ignition vs Structure (slow / chronic)
----------------------------------------------------------
Define structure indicators:
- INF_t : inflation pressure (or inflation surprise)
- RWAGE_t : real wage stagnation / squeeze
- FISC_t : fiscal stress (deficit / rollover)
- POL_t : political instability / polarization
- SC_t : supply-chain criticality (macro)
- CFE_t : climate-food-energy stress
- CVS_t : civilization stress
- AIL_t : AI-lag (destruction - creation)
Normalize with longer window w_S:
N_INF(t) = N(INF_t ; w_S, s_INF)
N_RW(t) = N(RWAGE_t; w_S, s_RW)
N_FISC(t) = N(FISC_t ; w_S, s_FISC)
N_POL(t) = N(POL_t ; w_S, s_POL)
N_SC(t) = N(SC_t ; w_S, s_SC)
N_CFE(t) = N(CFE_t ; w_S, s_CFE)
N_CVS(t) = N(CVS_t ; w_S, s_CVS)
N_AIL(t) = N(AIL_t ; w_S, s_AIL)
Structure risk (bounded):
R_str(t) =
Σ_m v_m * N_m(t)
where Σ v_m = 1 over m in {INF,RW,FISC,POL,SC,CFE,CVS,AIL}
6) Coupled Risk (Ignition × Structure)
--------------------------------------
Crisis is not just ignition or structure; it is their coupling.
Define coupling term:
K(t) = R_coh(t) * R_str(t)
Final raw crisis temperature:
ACGE_raw(t) =
clip(
a * R_coh(t)
+ b * R_str(t)
+ c * K(t),
0, 1 )
Typical constraint: a + b + c = 1, with c > 0
(meaning coupling matters)
7) Hysteresis Gate (regime memory)
----------------------------------
We want "once panic regime ignites, it doesn't instantly disappear".
Let:
G_raw(t) = σ( (ACGE_raw(t) - τ_G) / s_G )
G(t) = EMA_kG( G_raw(t) )
Interpretation:
- G(t) is the regime indicator in [0,1]
- kG sets how sticky the crisis regime is
8) Final Market Risk Thermostat (ACGE v3.2)
-------------------------------------------
ACGE(t) = clip( (1 - G(t)) * ACGE_raw(t) + G(t) * max(ACGE_raw(t), μ_G), 0, 1 )
where μ_G is a "minimum panic floor" once regime is on
(e.g., μ_G = 0.65)
This prevents whipsaw: panic regime implies persistent caution.
9) From ACGE to Asset / Portfolio GA (optional integration)
-----------------------------------------------------------
Asset i score:
GA_{i,t} = σ(
α_1 g_t
+ α_2 (-CS_t)
+ α_3 (-|V_{i,t}|)
+ α_4 L_t
+ α_5 (-H_{i,t})
+ α_6 (-ACGE(t))
+ α_7 U_sector,i(t)
)
Sector / idiosyncratic term:
U_sector,i(t) =
- η_1 SC_{i,t}
- η_2 ETD_region(i,t)
- η_3 HD_region(i,t)
+ η_4 Pos_{i,t}
All inputs are normalized with robust transforms as needed.
10) Practical Outputs (human-readable)
--------------------------------------
Define thresholds:
- ACGE(t) < 0.35 : calm / normal
- 0.35–0.65 : caution / fragile ice
- > 0.65 : high-risk regime (panic floor engaged)
- > 0.80 : extreme stress (cash-like posture)
Key promise:
This model does NOT forecast returns.
It measures "ice thickness" (market fragility) robustly under fat tails.
--------------------------------------------
Implementation & Sharing Notes
--------------------------------------------
MIT License (Conceptual Use)
Copyright (c) 2025 Calm(t + 1)
Permission is hereby granted, free of charge, to any person obtaining a copy
of this equation, model, or associated text (the “Work”), to use, copy,
modify, merge, publish, and distribute it for any purpose, including
personal, educational, and research use.
The Work is provided “as is”, without warranty of any kind.
Use at your own discretion.
Reference to the Calm(t + 1) project is appreciated but not required.
いま、無理がかかっていないかを測る数式
# =========================
# GA / ACGE (Thin-Ice Divergence Edition)
# =========================
# --- Robust Normalization (fat-tail safe) ---
rz(x; w) = ( x - median_w(x) ) / ( 1.4826 * MAD_w(x) + eps )
sig(x) = 1 / (1 + exp(-x))
N_k(t) = sig( rz( X_k(t); w_k ) / s_k )
# Acceleration (captures "vertical drop" early)
D_k(t) = N_k(t) - EMA(N_k(t); span=a_k)
A_k(t) = sig( rz( D_k(t); w_a ) / s_a )
# =========================
# Layer 1: Ignition (surface fear)
# =========================
I(t) = Σ_k wI_k * N_k(t) + λI * Σ_k wI_k * A_k(t)
# typical k: VIX, MOVE, HY_OAS, Equity_Breadth_Deterioration, FX_Vol
# =========================
# Layer 2: Plumbing (liquidity & funding)
# =========================
P(t) = Σ_j wP_j * N_j(t) + λP * Σ_j wP_j * A_j(t)
# typical j: Treasury_BidAsk, Market_Depth^{-1}, Repo_Strain, SwapSpread,
# SOFR-OIS, CrossCurrencyBasis, Dealer_Inventory_Stress
# =========================
# Layer 3: Structure (slow cracks)
# =========================
S(t) = Σ_m wS_m * N_m(t)
# typical m: Fiscal_Stress (debt service / revenue),
# Political_Polarization, AI-Lag, Productivity-RealWage_Gap,
# SupplyChain_Criticality, Energy_Food_Stress
# =========================
# Coherence Multiplier (nonlinear "no-exit" regime)
# =========================
# Idea: when multiple layers are high simultaneously, risk jumps superlinearly.
R_coh(t) = mean( N_core(t) ) # core set: {VIX, MOVE, HY_OAS, Treasury_BidAsk}
C_mult(t)= 1 + β * ( R_coh(t) ^ p ) # p >= 2 for convexity
# =========================
# ACGE core (0..1) with coupling
# =========================
ACGE_raw(t) = αI*I(t) + αP*P(t) + αS*S(t)
ACGE(t) = clip( ACGE_raw(t) * C_mult(t), 0, 1 )
# =========================
# Hysteresis Gate (regime sticky to avoid whipsaw)
# =========================
# Schmitt trigger:
# enter panic if ACGE >= θ_on, exit panic only if ACGE <= θ_off (θ_off < θ_on)
G(t) = 1 if ACGE(t) >= θ_on
= 0 if ACGE(t) <= θ_off
= G(t-1) otherwise
# =========================
# "Thin Ice Divergence" diagnostic
# =========================
ThinIce(t) = S(t) * (1 - I(t)) * (1 + P(t))
# high ThinIce: calm surface, deep cracks, plumbing tightening
# Suggested defaults (to be calibrated):
# θ_on=0.80, θ_off=0.65, β=0.6, p=3
--------------------------------------------
Implementation & Sharing Notes
--------------------------------------------
MIT License (Conceptual Use)
Copyright (c) 2025 Calm(t + 1)
Permission is hereby granted, free of charge, to any person obtaining a copy
of this equation, model, or associated text (the “Work”), to use, copy,
modify, merge, publish, and distribute it for any purpose, including
personal, educational, and research use.
The Work is provided “as is”, without warranty of any kind.
Use at your own discretion.
Reference to the Calm(t + 1) project is appreciated but not required.Calm(t + 1) Side-B
Side-A Project: https://note.com/calm_t_1
🌙 Residual Term
Markets do not always break by screaming.
At the edge of collapse,
numbers grow quiet,
signals flatten,
and urgency disappears.
Structures remember
how much tension they carried,
and how long escape routes were sealed.
Salvation is not found
at the minimum of a function.
∂Action / ∂t = 0
Silence > 0
SmallHope ≠ 0
When these conditions hold,
the system enters
a non-breaking state.
If today is Sunday,
no update is required.
No gradient needs to be followed.
d(Pressure)/dt → 0
d(Breath)/dt > 0
On thin ice,
speed does not save you.
Breathing does.
Structure does not lie.
And silence
buys the system
one more step away from collapse.
