feat: Implement Power option pricing model

[joaquinbejar]

Summary

This PR implements pricing support for Power options as described in issue #248. Power options have payoffs that are a power function of the underlying asset price, providing leveraged exposure.

What was implemented

Pricing Implementation

Created src/pricing/power.rs with the adjusted Black-Scholes formula for power options:

Pricing Formula

For a power option, S^n is log-normal with adjusted parameters:

• Expected value: E[S^n] = S^n × e^(n×(r-q)×T + n×(n-1)×σ²×T/2)
• Adjusted volatility: σ_adj = n × σ
• Forward price: F = S^n × e^(drift_adjustment × T)
• d1 = (ln(F/K) + σ_adj²×T/2) / (σ_adj×√T)
• d2 = d1 - σ_adj×√T

Payoff Structure

• Standard Power Call: max(S^n - K, 0)
• Standard Power Put: max(K - S^n, 0)

Why This Implementation?

Power options require special handling because:

1. Non-linear payoffs: S^n is not normally distributed, but log-normal with adjusted parameters
2. Drift adjustment: The expected value of S^n includes an additional term n×(n-1)×σ²×T/2
3. Volatility scaling: The effective volatility scales linearly with the exponent

Technical Decisions

• Uses f64 arithmetic for power calculations to avoid Decimal overflow issues with large exponents
• Validates exponent > 0 (negative or zero exponents are rejected)
• Supports fractional exponents (e.g., n=0.5 for square root options)
• For n=1, the formula reduces to standard Black-Scholes

Common Applications

• Leveraged exposure: Higher exponents amplify both gains and losses
• Structured products: Non-linear payoff profiles
• Speculative trading: Betting on large price movements

Tests

12 comprehensive unit tests covering:

• Power call pricing (n=2, squared)
• Power put pricing (n=2, squared)
• Different exponents (n=1, n=2, n=3)
• Fractional exponents (n=0.5)
• Invalid exponent handling (n ≤ 0)
• Short position pricing
• Deep ITM/OTM scenarios
• Higher exponent gives higher value verification

Files Changed

• src/pricing/power.rs: NEW - Power option pricing implementation
• src/pricing/mod.rs: Added power module export
• src/pricing/black_scholes_model.rs: Routed Power to new module

Closes #248

[codecov]

Codecov Report

❌ Patch coverage is 82.60870% with 12 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/pricing/power.rs	83.82%	11 Missing ⚠️
src/pricing/black_scholes_model.rs	0.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/pricing/black_scholes_model.rs	66.07% <0.00%> (+2.27%)	⬆️
src/pricing/power.rs	83.82% <83.82%> (ø)

... and 2 files with indirect coverage changes

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