VOLATILITY MODEL REVIEW FOR MARKET-MAKING ON SHORT TERM INTEREST RATES OPTIONS.

The Black-Scholes model is one of the most widely known and used financial models for option pricing. However, it relies on several assumptions that do not hold in real-world markets. Despite these limitations, the Black-Scholes formula, which provides a closed-form solution for pricing vanilla options (both call and put), remains the industry standard among practitioners. The key parameter that defines the option price when using the Black-Scholes formula is the implied volatility. Implied volatility represents the market’s view of the expected volatility of an option’s under- lying asset, assuming the Black-Scholes model is accurate. A key assumption of the Black-Scholes model is that volatility is a constant. In practice, however, implied volatility varies with both the strike price and the time to expiry. To address these discrepancies, academics have developed several models that introduce dynamic volatility, such as local and stochastic volatility models. In practical settings, particularly in market- making, parametric models are often preferred. These models define volatility as a function of the strike price and time to expiry, offering a balance between accuracy and computational efficiency. Although parametric models may not capture volatility dynamics as effectively as stochastic models, they are favored in market-making due to their superior market fit, faster calibration, and intuitive parameters for traders. This study provides a comprehensive review of a parametric model, the Polyvol model (also called the Wing model), which is used by the market-making team at Sucden Financial, where this internship was conducted. The focus of this thesis includes: • Providing the motivations behind volatility modeling • Presenting the existing theory on volatility models, especially parametric ones • Presenting the model and its underlying assumptions. • Providing calibration methodologies, specifically in the context of short-term interest rate options on UK and EU rates. • Providing the arbitrage-free framework for volatility modeling • Conducting an in-depth analysis of the Wing model, including calibration techniques and parameter stability. • Backtest delta-heding using the model using the desk positions and theoretical positions Through this review, we aim to enhance the understanding of parametric volatility models and their application in a market-making context.