Mustard Seed Capital Automation (MSCA)

Table of Contents

1. System Architecture Overview
2. Black-Scholes Option Pricing Model
3. Statistical Volatility Analysis
4. Stock Selection and Recovery Scoring
5. Technical Indicators
6. Options Strategy Implementation
7. Risk Management Framework
8. Capital Allocation Model
9. Appendix: Formula Reference

1. System Architecture Overview

1.1 Trading Philosophy

MSCA implements a Buy-and-Hold with Covered Calls (HODL) strategy based on the following principles:

1. Long-term stock accumulation in quality equities purchased in 100-share lots
2. Income generation through systematic covered call and cash-secured put writing
3. Capital preservation via conservative delta thresholds and margin limits
4. Capital velocity optimization through early buyback strategies

1.2 Component Architecture

┌─────────────────────────────────────────────────────────────────┐
│                     MSCA Trading System                          │
├─────────────────────────────────────────────────────────────────┤
│  ┌─────────────────┐  ┌─────────────────┐  ┌─────────────────┐ │
│  │  BlackScholes   │  │  StockAnalyzer  │  │   Calculations  │ │
│  │  Option Pricing │  │  Recovery Score │  │  Tech Indicators│ │
│  └────────┬────────┘  └────────┬────────┘  └────────┬────────┘ │
│           │                    │                    │           │
│           └────────────────────┼────────────────────┘           │
│                                ▼                                │
│  ┌─────────────────────────────────────────────────────────────┐│
│  │                         Decider                              ││
│  │              Trade Decision Engine                           ││
│  └─────────────────────────────────────────────────────────────┘│
│                                │                                │
│           ┌────────────────────┼────────────────────┐           │
│           ▼                    ▼                    ▼           │
│  ┌─────────────────┐  ┌─────────────────┐  ┌─────────────────┐ │
│  │   PutAnalyzer   │  │CashReserveManager│ │ CoveredCallBuyback││
│  │  CSP Selection  │  │  Margin Control  │ │  Early Buyback    ││
│  └─────────────────┘  └─────────────────┘  └─────────────────┘ │
└─────────────────────────────────────────────────────────────────┘

2. Black-Scholes Option Pricing Model

2.1 Theoretical Foundation

The Black-Scholes model, developed by Fischer Black, Myron Scholes, and Robert Merton (1973), provides the theoretical framework for pricing European-style options. MSCA implements this model for both call and put option pricing.

2.2 Call Option Pricing

The Black-Scholes formula for a European call option:

Where:

• \(C\) = Call option price
• \(S\) = Current stock price
• \(K\) = Strike price
• \(r\) = Risk-free interest rate
• \(T\) = Time to expiration (in years)
• \(N(\cdot)\) = Cumulative standard normal distribution function

The intermediate variables are calculated as:

Where \(\sigma\) = Annualized volatility of the underlying

2.3 Put Option Pricing

The Black-Scholes formula for a European put option:

This can also be derived from put-call parity:

2.4 Implementation Details

The system handles edge cases:

2.5 Greeks Calculation: Delta

Delta measures the rate of change of option price with respect to the underlying price.

Call Delta:

Range: \([0, 1]\) - Approaches 1 for deep ITM, 0 for deep OTM

Put Delta:

Range: \([-1, 0]\) - Approaches -1 for deep ITM, 0 for deep OTM

2.6 Implied Volatility Calculation

MSCA calculates implied volatility using a binary search algorithm:

Algorithm: Implied Volatility via Bisection
Input: Market price P_market, S, K, T, r, option type
Output: Implied volatility σ

1. Set bounds: σ_low = 0.001, σ_high = 5.0
2. Set initial guess: σ = 0.30
3. For i = 1 to max_iterations:
   a. Calculate P_model = BS_Price(S, K, T, σ, r)
   b. If |P_model - P_market| < precision:
      return σ
   c. If P_model > P_market:
      σ_high = σ
   d. Else:
      σ_low = σ
   e. σ = (σ_low + σ_high) / 2
4. Return σ

Convergence parameters:

• Precision: \(10^{-4}\)
• Maximum iterations: 100

3. Statistical Volatility Analysis

3.1 Historical Volatility Calculation

MSCA calculates annualized volatility using logarithmic returns:

Where:

• \(r_i = \ln(P_i / P_{i-1})\) = Log return
• \(\bar{r}\) = Mean log return
• \(A\) = Annualization factor

Annualization Factors:

3.2 84th Percentile Maximum Move Analysis

For strike selection, MSCA uses empirical percentile analysis rather than theoretical distributions. This approach calculates the 84th percentile of historical maximum price movements within a given DTE window.

Algorithm: Percentile Max-High Calculation

For each starting bar i in historical data:
  1. Define window: bars[i] to bars[i + DTE]
  2. Find max_high = max(High[j]) for j in window
  3. Calculate move: max_move[i] = (max_high - Close[i]) / Close[i]

Sort all max_moves ascending
Return max_moves[84th percentile index]

Data Requirements:

• Minimum 3,000 hourly bars (~2 years of trading data)
• Minimum 500 rolling windows for statistical significance
• Returns -1 (invalid) if insufficient data

Application:

• Covered Calls: 84th percentile max-high determines minimum strike buffer
• Cash-Secured Puts: 84th percentile max-low determines strike distance below current price

4. Stock Selection and Recovery Scoring

4.1 Multi-Timeframe Analysis Framework

MSCA employs a 100-point scoring system to evaluate stocks for buy-and-hold suitability:

4.2 Long-Term Growth Score (25 points)

Calculates Compound Annual Growth Rate (CAGR) over full historical period:

4.3 Crash Resilience Score (20 points)

Analyzes recovery patterns from major drawdowns (>20% decline):

Recovery Definition: Price returns to 95% of pre-drawdown peak

4.4 Position Averaging Evaluation

For existing positions, MSCA evaluates averaging down opportunities using a 10-factor scoring system.

Eligibility Criteria:

• Position is underwater (current price < cost basis)
• Loss percentage: 5% ≤ loss ≤ 30%
• Minimum 1,300 hourly bars available

Decision Rule: Score ≥ 0.5 (5/10 factors positive) → Recommend averaging down

5. Technical Indicators

5.1 Exponential Moving Average (EMA)

Where \(k = \frac{2}{n + 1}\) (smoothing factor), \(n\) = period length

5.2 Moving Average Convergence Divergence (MACD)

5.3 Relative Strength Index (RSI)

Where \(RS = \frac{\text{Average Gain}}{\text{Average Loss}}\)

• RSI > 70: Overbought
• RSI < 30: Oversold

5.4 Simple Moving Average (SMA)

6. Options Strategy Implementation

6.1 Covered Call Strategy

Objective: Generate premium income while holding long stock positions.

Strike Selection Algorithm:

1. Calculate 84th percentile max-high for target DTE
2. Apply DTE-based buffer multiplier

6.2 Cash-Secured Put Strategy

Objective: Generate premium income while accumulating quality stocks at discount.

Candidate Selection (PutAnalyzer) - 0-100 Score:

6.3 SPY "Golden Child" Treatment

SPY (S&P 500 ETF) and IWM receive special handling as index ETFs:

6.4 Early Buyback Strategy

Philosophy: Capital velocity > maximum profit extraction

Where \(T_{min} = 0.40\) (40% at 1 DTE), \(T_{max} = 0.15\) (15% at 30 DTE)

7. Risk Management Framework

7.1 Option Safety Assessment

Call Option Safety Check:

Default safety factor: 0.30

7.2 Volatility Threshold

Stocks with excessive volatility are excluded from covered call writing:

7.3 Data Freshness Check

Trades require recent price data:

8. Capital Allocation Model

8.1 Margin Limit Enforcement

Standard Stocks:

Premium ETFs (SPY, QQQ, IWM, DIA, VOO, VTI):

• No margin limit
• Uses all available buying power

8.2 Collateral Calculation

For cash-secured puts:

8.3 Position Sizing

Each new stock position limited to:

Appendix: Formula Reference

A.1 Black-Scholes Formulas

A.2 System Constants