Fair value of an interest rate Cap for financial risk management in a company

Abstract

This study aims to calculate the price of interest rate caps for a fictitious company, ACN, using both the SABR and Hull-White models. The study provides a comprehensive overview of the theoretical foundations of each model, details their implementation in MATLAB, and compares the resulting cap prices. The SABRmodeliswidely used in the pricing of interest rste derivatives, and it is known for its ability to capture the stochastic volatility of financial assets. Conversely, the Hull-White model uses a different approach to model interest rate dynamics and volatilities. The models were calibrated using parameters generated by a custom algorithm, and the pricing calculations were conducted using MATLAB. The results compares the price obtained using the two models. The two different prices highlight the sensitivity of cap pricing to the underlying assumptions and numerical implementations of each model. Also, the observed price difference underscores the importance of understanding the unique characteristics and limitations of each model when applied to interest rate cap pricing. This study contributes to the knowledge of the field by showing the strengths and limitations of the pricing methodologies used as it explored practical considerations in implementing pricing techniques, including data requirements, computational complexity, and calibration processes.