Interactive Charts

Strategy Performance Comparison

The following charts illustrate typical simulation results. Run the app to generate your own interactive visualizations.

Performance Distribution

Strategy performance follows approximately normal distributions, with adaptive strategies shifted positively:

Strategy	Mean	Std Dev	Skew
S1 Uniform	0	~50	0
S2 Adaptive	+20	~65	+0.1
S3 Discount	+25	~60	+0.1
S4 Convex	+35	~80	+0.2
S5 Flexible	+40	~90	+0.3

Volatility Sensitivity

Higher volatility amplifies strategy differences:

Volatility	S1	S2	S3	S4	S5
15%	0	+10	+12	+15	+18
25%	0	+20	+25	+35	+40
35%	0	+30	+38	+55	+65
50%	0	+45	+55	+85	+100

Key insight

Adaptive strategies perform best in volatile markets where discounts are larger and more frequent.

Duration Distribution

Strategy 4 and 5 tend to complete earlier due to aggressive buying at discounts:

Strategy	Mean Duration	Std Dev	Range
S1	100 (fixed)	0	100-100
S2	95	15	75-125
S3	93	14	75-125
S4	88	18	75-125
S5	85	20	75-125

Execution Path Example

A typical execution path shows:

1. Early phase (days 1-10): Constant execution to establish baseline
2. Adaptive phase (days 11-74): Variable execution based on price
3. Completion phase (days 75+): Urgency-driven execution to meet deadline

Generate Your Own Charts

The Streamlit app generates interactive Plotly charts that you can:

• Zoom and pan
• Hover for data points
• Export as PNG
• Toggle strategy visibility

# Example: Generate performance comparison
import plotly.graph_objects as go

fig = go.Figure()
for strategy, data in results.items():
    fig.add_trace(go.Histogram(
        x=data['performances'],
        name=strategy,
        opacity=0.7
    ))
fig.update_layout(barmode='overlay')
fig.show()

API for Custom Analysis

Use the vectorized strategy functions for batch analysis:

from modules.gbm import generate_gbm_paths
from modules.strategies_vectorized import (
    precompute_benchmarks,
    strategy_4_vectorized
)

# Generate 10,000 price paths
prices = generate_gbm_paths(S0=100, mu=0, sigma=0.25,
                            n_days=125, n_sims=10000)

# Precompute benchmarks
benchmarks = precompute_benchmarks(prices)

# Run Strategy 4 on all paths
perf, dur, vwap, bench = strategy_4_vectorized(
    prices, benchmarks,
    total_usd=1e9,
    min_duration=75,
    max_duration=125,
    target_duration=100
)

print(f"Mean performance: {perf.mean():.2f} bps")
print(f"Mean duration: {dur.mean():.1f} days")

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(c) Joerg Osterrieder 2025