Models of negative interest rates
Team:
Dalma Tóth-Lakits, Miklós Arató, András Ványolos
Student level:
PhD
Our research focuses on the parameter estimation and calibration of negative interest rate models. In the 2010s, negative interest rates appeared as a new phenomenon which caused significant difficulties for the financial markets. We examined the extension of a large number of models labelled as industry standards (SABR, HJM and Black model) into the negative range, as well as models that were specifically developed to deal with negative interest rates. Based on their distributional properties, we compared the models and set up an order of which one is best used for pricing financial instruments and developing risk management strategies.
Last year, our main focus was on a model based on Gaussian random fields proposed by Kennedy in the 1970s which naturally handles negative rates. The so-called Kennedy field is normally distributed due to the properties of the Gaussian distribution, therefore analytical maximum likelihood estimations were derived for the parameters of the field. An analytical Black-Scholes-like pricing formula for the European call option on interest rate swaps was also calculated.
A priority was to pay a lot of attention to implement the fastest and most accurate simulation possible. Hence, we generated forward rates from the Kennedy field with the help of the fastest generation of the Brownian sheet in Python. Simulated financial swap prices were also generated using the Kennedy field with Monte Carlo simulation, on which we were able to test the previously derived parameter estimations and pricing formulas with numerical extreme value analysis.
In the next phase, our plan is to build different artificial intelligence based models for parameter estimation and calibration to provide more accurate and fast estimations. Also, we plan to compare the calibration and parameter estimation between different models. Therefore, we started working with the extended SABR model (shifted SABR, free-boundary SABR) to examine whether analytical parameter estimations or pricing formulas can be derived and compared.
We have already started to examine how the analytical parameter estimations and pricing formulas work on real financial data. Our ultimate goal is to compare the analytical and AI based estimation and build a calibration engine which can be effectively used in practice.
Our research focuses on the parameter estimation and calibration of negative interest rate models. In the 2010s, negative interest rates appeared as a new phenomenon which caused significant difficulties for the financial markets. We examined the extension of a large number of models labelled as industry standards (SABR, HJM and Black model) into the negative range, as well as models that were specifically developed to deal with negative interest rates. Based on their distributional properties, we compared the models and set up an order of which one is best used for pricing financial instruments and developing risk management strategies.
Last year, our main focus was on a model based on Gaussian random fields proposed by Kennedy in the 1970s which naturally handles negative rates. The so-called Kennedy field is normally distributed due to the properties of the Gaussian distribution, therefore analytical maximum likelihood estimations were derived for the parameters of the field. An analytical Black-Scholes-like pricing formula for the European call option on interest rate swaps was also calculated.
A priority was to pay a lot of attention to implement the fastest and most accurate simulation possible. Hence, we generated forward rates from the Kennedy field with the help of the fastest generation of the Brownian sheet in Python. Simulated financial swap prices were also generated using the Kennedy field with Monte Carlo simulation, on which we were able to test the previously derived parameter estimations and pricing formulas with numerical extreme value analysis.
In the next phase, our plan is to build different artificial intelligence based models for parameter estimation and calibration to provide more accurate and fast estimations. Also, we plan to compare the calibration and parameter estimation between different models. Therefore, we started working with the extended SABR model (shifted SABR, free-boundary SABR) to examine whether analytical parameter estimations or pricing formulas can be derived and compared.
We have already started to examine how the analytical parameter estimations and pricing formulas work on real financial data. Our ultimate goal is to compare the analytical and AI based estimation and build a calibration engine which can be effectively used in practice.