FX Options Pricing & Volatility Modeling

Price currency options and structure hedging strategies, replicating the conventions used on the Bloomberg terminal.

Spot and forward exchange rates, interest rates for both currencies and implied volatilities across delta levels.

• Priced options with the Garman–Kohlhagen model, the extension of Black–Scholes to currencies with two interest rates.
• Modeled the volatility smile.
• Structured zero-cost collar strategies.
• Replicated Bloomberg OVML conventions, including spot vs. forward delta calculations.

A pricer that follows OVML conventions for spot and forward delta, and zero-cost collars built on the volatility smile.

• Garman–Kohlhagen assumes constant volatility. The smile observed in the market shows the assumption does not hold, which is why it has to be modeled separately.
• The model assumes constant interest rates over the life of the option and applies to European options.
• A collar is zero-cost only at inception: its value moves with the spot rate and with volatility.

Conventions matter as much as the model. The same delta means different things in spot or forward terms, and a convention error produces a wrong price even with a correct model.