TWAP Scheduling & Cost Estimation Model

Interactive TWAP scheduling and execution cost estimation tool using intraday equity data.
This model does not execute trades — it only generates an execution schedule, estimates expected trading costs, and compares expected TWAP performance versus VWAP.

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Purpose

Simulate a TWAP-style execution plan for a user-defined equity order and estimate the expected trading cost per slice and in total, subject to participation and liquidity constraints. Benchmark expected TWAP execution performance against VWAP.

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User Inputs (Interactive Prompt)

Input	Description	Example
ticker	Equity ticker	AAPL
Q	Parent order size (shares)	50,000
direction	Trade direction	Long or Short
start_time	Start time of execution	10:00
bin_minutes	Time bucket size	5, 10, or 15
p_max	Max participation rate	0.02 – 0.10

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Data Source

• yfinance intraday OHLCV data
• Intraday bars are resampled to the selected time bucket size (bin_minutes)
• VWAP is computed using an OHLCV-based approximation, not true trade-level VWAP

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Core Rules & Constraints

• Max participation per bucket: p_max (2%–10%)
• Scheduling & cost estimation only (no execution)
• No persistence — all results are displayed immediately
• Execution runs from start_time until order completion or market close

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Volume per Slice (V_i) — 20-Day Rolling Intraday Estimate

Definition

V_i is the expected market trading volume for time bucket i, estimated using a 20-day rolling window of historical intraday volume for the same time-of-day bucket.

This mirrors the methodology used to estimate volatility.

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How V_i Is Calculated

1. Pull intraday OHLCV data for the last ≥20 trading days
2. For each trading day, resample volume into bin_minutes buckets
3. Label buckets by time-of-day (e.g. 10:00–10:05)
4. For each bucket i, collect historical volumes:

[ {V_{d-1,i}, V_{d-2,i}, \ldots, V_{d-20,i}} ]

5. Compute expected bucket volume:

[ V_i = \text{mean}\left(V_{d-k,i}\right), \quad k = 1 \ldots 20 ]

If fewer than 20 observations exist:

• Use available data if ≥10 observations
• Otherwise return a warning:
  Insufficient intraday history to estimate bucket volume

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Usage of V_i

The same V_i is used consistently for:

• Participation caps
• POV reporting
• Trading cost model

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Liquidity Feasibility Check (Pre-Schedule)

Before scheduling, check whether the parent order can be completed under the participation constraint using expected intraday liquidity.

Maximum Executable Shares

[ q^{max}i = p{\text{max}} \times V_i ]

[ Q_{max} = \sum_i q^{max}_i ]

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Behavior

• If ( Q \le Q_{max} ): proceed with full schedule
• If ( Q > Q_{max} ):
  • Generate a partial schedule only (through market close)
  • Display a feedback box below user input:

Feedback Box

• Status: Cannot complete order within participation constraint
• Requested shares: Q
• Max executable shares today: Q_max
• Unfilled shares: Q - Q_max

Cost and VWAP comparisons are calculated only on executed shares.

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Scheduling Logic

Step 1: Estimate Time to Completion

[ T = \left(\frac{Q}{p_{\text{max}} \times ADV}\right) \times 390 ]

Where:

• T = minutes to complete trade
• Q = parent order size
• ADV = average daily volume
• p_max = max participation rate
• 390 = minutes per trading day

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Step 2: Number of Slices

[ N = \left\lfloor \frac{T}{\text{bin_minutes}} \right\rfloor ]

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Step 3: Child Order Size

[ q = \frac{Q}{N} ]

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Step 4: Per-Bucket Execution

For each bucket i:

[ q_{\text{executed},i} = \min\left(q,\ p_{\text{max}} \times V_i,\ \text{remaining shares}\right) ]

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Step 5: Participation Rate (POV%)

[ POV_i = \frac{q_{\text{executed},i}}{V_i} ]

This realized POV% is reused directly in the trading cost model.

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VWAP (Single Benchmark Over Execution Window)

Representative Price per Bar

For each intraday bar j:

[ \text{price}_j = \frac{H_j + L_j + C_j}{3} ]

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VWAP Over Execution Window

Compute VWAP using all intraday bars from start_time through the final executed slice end time:

[ VWAP_{\text{window}} = \frac{\sum_j (\text{price}_j \times \text{volume}_j)} {\sum_j \text{volume}_j} ]

This is the only VWAP used for benchmarking.

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Expected Trading Cost Model

Cost Per Slice (bps)

[ C_i = \text{halfspread} + G \times S \times POV_i ]

Where:

Variable	Description
halfspread	Half of quoted bid-ask spread (bps)
G	Impact coefficient
S	Volatility over the time slice
POV_i	Realized participation rate from schedule

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Volatility Over Slice

1. Compute log returns over matching intraday intervals for the last 20 trading days:

[ L_x = \ln\left(\frac{P_x}{P_{x-1}}\right) ]

2. Compute standard deviation:

[ S = \text{stdev}(L_x) ]

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Impact Coefficient ( G ) (by ADV)

Liquidity Bucket	ADV	G
MEGA	> 50M	0.10
LARGE	10–50M	0.25
MID	2–10M	0.50
SMALL	0.5–2M	0.90
MICRO	≤ 0.5M	1.50

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Half-Spread (bps) (by ADV)

Liquidity Bucket	Halfspread
MEGA	0.5
LARGE	1.0
MID	2.0
SMALL	5.0
MICRO	7.5

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Converting Costs to Price Terms (VWAP Comparison)

Costs are computed in basis points and converted using the single VWAP benchmark.

Total Expected Cost (Dollars)

[ \text{TotalCost}{$} = \sum_i \left( q{\text{executed},i} \times \frac{C_i}{10{,}000} \times VWAP_{\text{window}} \right) ]

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Expected All-In Execution Price

Let:

[ \Delta P = \frac{\text{TotalCost}{$}}{\sum_i q{\text{executed},i}} ]

• Long (Buy): [ P_{\text{TWAP,allin}} = VWAP_{\text{window}} + \Delta P ]

• Short (Sell): [ P_{\text{TWAP,allin}} = VWAP_{\text{window}} - \Delta P ]

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Outputs (Displayed Below User Input)

1. Feedback Box (if insufficient liquidity)

   • Requested shares Q
   • Max executable shares Q_max
   • Unfilled shares Q - Q_max

2. Execution Schedule Table

   • Time bucket
   • Slice size
   • Cumulative shares
   • Expected bucket volume V_i
   • POV%
   • Expected slice cost (C_i, bps)

3. Schedule Chart

   • Bars: shares executed per slice
   • Optional cumulative overlay

4. Expected Cost Summary

   • Total expected cost (bps and $)
   • Expected cost per share

5. Benchmark vs VWAP

   • ( VWAP_{\text{window}} )
   • ( P_{\text{TWAP,allin}} )
   • Relative performance (bps and $), direction-aware:
     • Long: lower than VWAP is better
     • Short: higher than VWAP is better

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Assumptions & Limitations

• Intraday volume is estimated from historical data (expected liquidity)
• VWAP is OHLCV-approximated
• No order book, queue priority, or adverse selection modeling
• Expected costs, not realized outcomes

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Intended Use

• Execution research and education
• Strategy prototyping
• Market impact intuition

Not intended for live trading or production execution.