feat: Implement Quanto option pricing model

[joaquinbejar]

Summary

This PR implements pricing support for Quanto options as described in issue #246. Quanto options are derivatives where the underlying asset is denominated in one currency (foreign) but the payoff is settled in another currency (domestic) at a fixed exchange rate.

What was implemented

ExoticParams Extensions

Added quanto-specific fields to ExoticParams:

• quanto_fx_volatility: Volatility of the exchange rate
• quanto_fx_correlation: Correlation between the underlying asset and the exchange rate (-1 to 1)
• quanto_foreign_rate: Foreign risk-free interest rate

Pricing Implementation

Created src/pricing/quanto.rs with the quanto-adjusted Black-Scholes formula:

Quanto Adjustment

The key insight is that the drift of the underlying asset must be adjusted for the correlation between the asset and the exchange rate:

Adjusted drift = r_d - q - ρ × σ_S × σ_FX

Where:

• r_d: Domestic risk-free rate
• q: Dividend yield of the underlying
• ρ: Correlation between asset and FX rate
• σ_S: Volatility of the underlying asset
• σ_FX: Volatility of the exchange rate

Pricing Formula

• Quanto Forward: F = S × e^((r_d - q - ρ×σ_S×σ_FX)×T)
• Call: C = X × e^(-r_d×T) × [F × N(d1) - K × N(d2)]
• Put: P = X × e^(-r_d×T) × [K × N(-d2) - F × N(-d1)]

Where X is the fixed exchange rate.

Why This Implementation?

• Quanto adjustment: Accounts for the covariance between asset returns and exchange rate movements
• Correlation impact:
  • When ρ > 0: Asset and FX move together, reducing the quanto call value
  • When ρ < 0: Asset and FX move oppositely, increasing the quanto call value
• Exchange rate scaling: The fixed exchange rate directly scales the option value

Common Applications

• Foreign equity investments with currency protection
• Commodity options settled in a different currency
• Cross-border structured products
• International index options

Tests

12 comprehensive unit tests covering:

• Quanto call and put pricing (positive values)
• Zero correlation case
• Positive correlation reduces call value
• Negative correlation increases call value
• Invalid correlation rejection
• Missing parameters handling
• Short position pricing
• Exchange rate scaling verification
• Zero FX volatility handling
• Deep ITM/OTM scenarios

Files Changed

• src/model/option.rs: Added quanto fields to ExoticParams
• src/model/format.rs: Updated Display implementations
• src/pricing/quanto.rs: NEW - Quanto option pricing implementation
• src/pricing/mod.rs: Added quanto module export
• src/pricing/black_scholes_model.rs: Routed Quanto to new module
• src/pricing/rainbow.rs: Updated ExoticParams in tests
• src/pricing/spread.rs: Updated ExoticParams in tests
• src/pricing/cliquet.rs: Updated ExoticParams in tests
• examples/examples_exotics/src/bin/cliquet_example.rs: Updated ExoticParams

Closes #246