test: Add property-based testing for mathematical invariants

[joaquinbejar]

Issue #12: Add property-based testing

Title

test: Add property-based testing for mathematical invariants

Labels

• testing
• quality
• priority-low

Description

Add property-based testing using proptest to validate mathematical invariants like Put-Call Parity and Greeks bounds.

Current State

• Tests use specific example values
• Mathematical invariants not systematically tested
• Edge cases may be missed

Target State

• Property-based tests cover key mathematical invariants
• Tests run as part of the test suite
• Higher confidence in mathematical correctness

Tasks

• Add proptest as a dev dependency
• Add property tests for Put-Call Parity:
  • C - P = S - K * e^(-rT)
• Add property tests for Greeks bounds:
  • 0 ≤ delta ≤ 1 for calls
  • -1 ≤ delta ≤ 0 for puts
  • gamma ≥ 0 for all options
• Add property tests for arbitrage-free pricing:
  • C ≥ max(0, S - K * e^(-rT))
  • P ≥ max(0, K * e^(-rT) - S)
• Add property tests for Positive type invariants:
  • Value is always > 0
  • Operations preserve positivity where expected
• Add property tests for strategy invariants:
  • Break-even points are within valid range
  • Max profit/loss are consistent
• Run make lint-fix and make pre-push to verify

Acceptance Criteria

• Property tests cover key mathematical invariants
• Tests run as part of the test suite
• No false positives in normal operation
• Edge cases are properly handled

Technical Notes

Put-Call Parity Test

use proptest::prelude::*;

proptest! {
    #[test]
    fn test_put_call_parity(
        s in 10.0f64..1000.0,
        k in 10.0f64..1000.0,
        r in 0.0f64..0.2,
        sigma in 0.05f64..1.0,
        t in 0.01f64..2.0,
    ) {
        let s = pos!(s);
        let k = pos!(k);
        let sigma = pos!(sigma);
        let t = pos!(t);
        
        let call = black_scholes_call(s, k, r, sigma, t);
        let put = black_scholes_put(s, k, r, sigma, t);
        
        let parity_lhs = call - put;
        let parity_rhs = s.to_dec() - k.to_dec() * (-r * t.to_dec()).exp();
        
        prop_assert!((parity_lhs - parity_rhs).abs() < dec!(0.0001));
    }
}

Greeks Bounds Test

proptest! {
    #[test]
    fn test_call_delta_bounds(
        s in 10.0f64..1000.0,
        k in 10.0f64..1000.0,
        sigma in 0.05f64..1.0,
        t in 0.01f64..2.0,
    ) {
        let option = create_call_option(s, k, sigma, t);
        let delta = option.delta().unwrap();
        
        prop_assert!(delta >= dec!(0.0));
        prop_assert!(delta <= dec!(1.0));
    }
    
    #[test]
    fn test_gamma_non_negative(
        s in 10.0f64..1000.0,
        k in 10.0f64..1000.0,
        sigma in 0.05f64..1.0,
        t in 0.01f64..2.0,
    ) {
        let option = create_call_option(s, k, sigma, t);
        let gamma = option.gamma().unwrap();
        
        prop_assert!(gamma >= dec!(0.0));
    }
}

Files to Create/Update

• Cargo.toml (add proptest dependency)
• tests/property/mod.rs
• tests/property/put_call_parity_test.rs
• tests/property/greeks_bounds_test.rs
• tests/property/positive_invariants_test.rs

Estimated Effort

Medium (4-6 hours)

Dependencies

None

Related Issues

• Issue Feature/positive f64 #11: Add benchmarks for critical paths