Advanced Algorithms - HFThot Research Lab

🎯 Algorithm Suite

Our trading platform implements three complementary algorithm families optimized for different market conditions:

📊 Regime Detection

Hidden Markov Models identify market states (trending, mean-reverting, volatile) in real-time.

→ Adapts strategy selection dynamically

🤖 Agent-Based Models

Chiarella Multi-Agent simulates heterogeneous traders (fundamentalists, chartists, noise).

→ Predicts price impact & volatility

⚡ Adaptive Execution

CARA/Risk Parity/Sparse optimize portfolio allocation under risk constraints.

→ Maximizes Sharpe with controlled drawdowns

🔍 Regime Detection via HMM

We use a 3-state Hidden Markov Model to classify market conditions:

\[ P(S_t | r_{1:t}) = \frac{P(r_t | S_t) \cdot \sum_{S_{t-1}} P(S_t | S_{t-1}) P(S_{t-1} | r_{1:t-1})}{\sum_{S_t} P(r_t | S_t) \cdot \sum_{S_{t-1}} P(S_t | S_{t-1}) P(S_{t-1} | r_{1:t-1})} \]

States

📈 Trending

Characteristics:

High autocorrelation
Low mean reversion
Positive momentum

Strategy: Breakout/Momentum

↔️ Mean-Reverting

Characteristics:

Negative autocorrelation
Fast reversion (τ < 5 min)
Stable volatility

Strategy: Pairs/Stat Arb

💥 Volatile

Characteristics:

High variance
Low predictability
News/event-driven

Strategy: Reduce exposure

Implementation

📊 Market Returnsr₁, r₂, …, rₜ

↓

Forward Passα[s,t] = P(rₜ | Sₜ=s) × Σ P(Sₜ=s|Sₜ₋₁=s′) α[s′,t−1]

↓

Backward Passβ[s,t] = Σ P(rₜ₊₁|Sₜ₊₁=s′) × P(Sₜ₊₁=s′|Sₜ=s) × β[s′,t+1]

↓

Most Likely Statearg max_s α[s,t] × β[s,t]

↓

Strategy SelectionMomentum / Mean-Reversion / Risk-Off

Performance: 85% accuracy on S&P 500 data (2018-2024), < 100μs latency per update.

🤖 Chiarella Agent-Based Model

Simulates market microstructure with 3 trader types:

\[ \frac{dp_t}{dt} = \lambda \left( \sum_{i=1}^N w_i D_i(p_t, F_t) \right) + \sigma_p dW_t \] where $ D_i $ is the demand function for agent type $i$, $ F_t $ is fundamental value, $ \lambda $ is price adjustment speed.

📚 Fundamentalists

$ D_F = \alpha_F (F_t - p_t) $

Mean revert to fair value. Stabilizing force.

📈 Chartists

$ D_C = \alpha_C (p_t - p_{t-1}) $

Follow trends. Destabilizing (momentum).

🎲 Noise Traders

$ D_N \sim \mathcal{N}(0, \sigma_N^2) $

Random demand. Liquidity providers.

Price Dynamics

📈 ChartistsTrend Following

↓

📚 FundamentalistsMean Reversion

←

Price
p(t)

→

🎲 Noise TradersRandomness

↓

Equilibrium: D_F + D_C + D_N = 0

↓

Stable Marketw_F > w_C → Reversion to F

Volatile Marketw_C > w_F → Bubbles / Crashes

Calibration: Fit $ \alpha_F, \alpha_C, w_i $ to historical order flow. Use case: Predict impact of large orders (>1% ADV).

⚡ Adaptive Portfolio Strategies

Three optimization frameworks for different objectives:

1. CARA (Constant Absolute Risk Aversion)

\[ \mathbf{w}^* = \arg\max_{\mathbf{w}} \left\{ \mathbf{w}^\top \boldsymbol{\mu} - \frac{\gamma}{2} \mathbf{w}^\top \boldsymbol{\Sigma} \mathbf{w} \right\} \] Subject to: $ \sum w_i = 1, \; w_i \geq 0 $

Closed-form solution: $ \mathbf{w}^* = \frac{1}{\gamma} \boldsymbol{\Sigma}^{-1} \boldsymbol{\mu} $ (rescaled to sum to 1).

Best for: Short-term mean-reversion strategies with stable covariance.

2. Risk Parity

\[ \text{RC}_i = w_i \frac{\partial \sigma_p}{\partial w_i} = \frac{1}{N} \sigma_p \quad \forall i \] where $ \sigma_p = \sqrt{\mathbf{w}^\top \boldsymbol{\Sigma} \mathbf{w}} $ is portfolio volatility.

Equalizes risk contribution across assets. Best for: Diversified portfolios with heterogeneous volatilities.

3. Sparse Optimization (L1 Penalty)

\[ \mathbf{w}^* = \arg\min_{\mathbf{w}} \left\{ \mathbf{w}^\top \boldsymbol{\Sigma} \mathbf{w} - \lambda \mathbf{w}^\top \boldsymbol{\mu} + \rho \|\mathbf{w}\|_1 \right\} \]

Promotes sparsity (few non-zero positions). Best for: High transaction costs, limited capital.

Without Sparse Penalty (ρ=0)

95 assets with w > 0.001 · Transaction Costs: 2.1% · Turnover: High

With Sparse Penalty (ρ=0.05)

Only 12 assets selected · Transaction Costs: 0.3% · Turnover: Low

🔄 Integration: Adaptive Pipeline

1

Data → Regime Detection (HMM)

Market Data (1-min bars) → Viterbi Algorithm → State: {Trending, Mean-Reverting, Volatile}

→ Confidence: 0.87

↓

2

Regime → Strategy Selection

Trending → Momentum · Mean-Reverting → Stat Arb · Volatile → Risk-Off

→ Selected: Mean-Reverting (confidence > 0.8)

↓

3

Strategy → Chiarella Simulation

α_F=0.5, α_C=0.3, w_F=0.6, w_C=0.3, w_N=0.1 · 1000 paths (Δt=1s, horizon=5min)

→ Expected Price: $105.23 (±0.15) · Impact: −0.08%

↓

4

Position Sizing → Adaptive Optimization

High Costs → Sparse (L1) · Low Costs → Risk Parity · Mean-Reversion → CARA (γ=2.0)

→ w* = [0.35, 0.28, 0.20, 0.12, 0.05]

↓

5

Execution → Trade Signals

Generate orders → TWAP/VWAP slicing → Send to broker → Monitor fills → Loop

📊 Performance Metrics

Sharpe Ratio

2.8

Annualized (2023-2024 backtest)

Max Drawdown

-8.2%

Controlled by risk parity

Win Rate

62%

On 10,000+ trades

Regime-Specific Performance

📈 Trending

Sharpe: 3.2

Strategy: Momentum (breakout)

Avg Hold: 12 hours

↔️ Mean-Reverting

Sharpe: 4.1

Strategy: Stat Arb (pairs)

Avg Hold: 45 minutes

💥 Volatile

Sharpe: 0.9

Strategy: Reduced exposure

Avg Hold: N/A (mostly flat)

🚀 Ressources & Documentation

📓 Interactive Notebooks

🔒 Unlock interactive Jupyter notebooks with an Educational or Professional account.

Try it out live by subscribing to a Hobbyist tier and access the interactive Streamlit platform.

Available notebooks:
• Regime Detection (HMM)
• Kalman Filter Market Making
• Mean Field Games Portfolio
• Differential Evolution
• Sparse Mean Reversion

📚 Theoretical Documentation

🔬 Regime Detection (HMM)

Hidden Markov Models theory with Forward-Backward and Viterbi algorithms

📊 Chiarella Agent-Based Model

Multi-agent market microstructure with heterogeneous traders (Fundamentalists, Chartists, Noise)

⚙️ Adaptive Portfolio Strategies

Risk Parity, Sparse L1 optimization, and CARA utility maximization

📂 Browse all theoretical documentation →

🚀 Try it Live

🎯 Streamlit Interactive Platform

Test algorithms on real market data with an interactive interface

💳 View Pricing & Subscription Tiers

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