unit tests for threshold pricing model lead to error

[bayareacoder]

First off, fantastic library!

I think I found an issue though in the pricing/telegraph.py file. The function estimate_telegraph_parameters raises a DecimalError if called with a threshold=0 parameter. But the telegraph function does exactly that when it is called with a None parameter on either lambda_up or lamba_down and this is what the unit test test_telegraph_with_estimated_parameters does so I don't see how this can pass the unit tests.

Also what is the article or book reference for this telegraph pricing model?

[joaquinbejar]

Hi there! Thank you for the detailed bug report and for the kind words about the library!

You were absolutely correct - there was indeed a bug in the telegraph pricing model. The issue was in the estimate_telegraph_parameters function in src/pricing/telegraph.rs.

The Problem

The function had an unnecessary validation that rejected threshold = 0:

if threshold == Decimal::ZERO {
    return Err(DecimalError::InvalidValue { ... });
}

But the telegraph() function was calling it with exactly that value when lambda_up or lambda_down parameters were None:

estimate_telegraph_parameters(&returns, Decimal::ZERO)?  // This always failed!

The Fix

I've just pushed a fix that:

1. Removed the invalid threshold validation - Zero is a perfectly valid threshold for classifying returns as +1 (above threshold) or -1 (below/equal to threshold)
2. Added proper error handling for edge cases where all returns fall on one side of the threshold
3. Improved error messages for better debugging
4. Updated tests to reflect the corrected behavior

All 18 telegraph-related tests now pass, including test_telegraph_with_estimated_parameters.

Telegraph Process References

Regarding your question about references, the Telegraph Process (two-state Markov chain) is covered in several academic sources:

• Nikita Ratanov , Alexander D. Kolesnik (2022) - "Telegraph Processes and Option Pricing"
• Kijima, M. (2003) - "Stochastic Processes with Applications to Finance"
• Elliott, R.J. & Kopp, P.E. (2005) - "Mathematics of Financial Markets"
• Buffington, J. & Elliott, R.J. (2002) - "American options with regime switching"

The model is particularly useful for capturing regime-switching behavior in financial markets.

Thanks again for the thorough bug report - this kind of feedback really helps improve the library!

[joaquinbejar]

Also, I have implemented the Telegraph process integration into the OptionStratLib Monte Carlo simulation framework. The implementation includes:

Changes Made

1. New Telegraph Variant: Added to the WalkType enum in src/simulation/model.rs with complete parameters:

   • dt: Time step
   • drift: Drift coefficient
   • volatility: Base volatility
   • lambda_up/lambda_down: Transition rates between regimes
   • vol_multiplier_up/vol_multiplier_down: Optional volatility multipliers per state

2. Process Logic: Implemented in src/simulation/traits.rs with:

   • Two-state Markov chain (+1/-1) for regime alternation
   • Correct transition probability calculations using exp(-λΔt)
   • Geometric Brownian motion with regime-dependent volatility
   • Robust error handling and parameter validation

3. Complete Integration: Updated pattern matching in:

   • src/chains/generators.rs
   • src/series/generators.rs

4. Comprehensive Testing:

   • Unit tests for creation, serialization, and process generation
   • Display trait implementation for readable formatting
   • Full JSON serialization/deserialization support

Functionality

The Telegraph process now enables modeling regime-switching behaviors in financial markets where volatility can suddenly alternate between high and low volatility states, capturing common phenomena during periods of market stress or calm.

Usage Example:

WalkType::Telegraph {
    dt: pos!(1.0),
    drift: Decimal::new(5, 2), // 0.05
    volatility: pos!(0.2),
    lambda_up: pos!(0.5),      // Transition to high regime
    lambda_down: pos!(0.3),    // Transition to low regime  
    vol_multiplier_up: Some(pos!(1.5)),   // 150% volatility in high regime
    vol_multiplier_down: Some(pos!(0.8)), // 80% volatility in low regime
}

The Telegraph process is now fully integrated and ready for Monte Carlo option pricing simulations with regime-switching capabilities.