Factor HJM Yield Curve Modelling for Pricing of Danish Callable Mortgage Bonds
(2024) In Master's Theses in Mathematical Sciences FMSM01 20241Mathematical Statistics
- Abstract
- A distinguishing component of the mortgage bond market in Denmark is the option to prepay a loan before its maturity date. From the debtors perspective, this is often done with the purpose of refinancing to a lower lending rate. Thus, interest rate modelling becomes a natural part of the pricing process of Danish callable mortgage bonds. Today, yield curves are modelled and thought of differently in real world versus pricing applications, creating a divide between the two. In this thesis, a factor modelling approach was combined with the Musiela HJM framework, as a means of bridging the divide.
The interest rate model was calibrated to forward rates and swaption premiums. Subsequently, yield curves were simulated and used in the... (More) - A distinguishing component of the mortgage bond market in Denmark is the option to prepay a loan before its maturity date. From the debtors perspective, this is often done with the purpose of refinancing to a lower lending rate. Thus, interest rate modelling becomes a natural part of the pricing process of Danish callable mortgage bonds. Today, yield curves are modelled and thought of differently in real world versus pricing applications, creating a divide between the two. In this thesis, a factor modelling approach was combined with the Musiela HJM framework, as a means of bridging the divide.
The interest rate model was calibrated to forward rates and swaption premiums. Subsequently, yield curves were simulated and used in the calculation of refinance gains. Comparing with historical data, the factor HJM model showcased a good calibration to market volatility and rates.
The refinance gain, as well as a selection of other explanatory variables, were tested for significance in a probit model. The optimisation used a maximum likelihood estimation with historical prepayment rates as targets. The different model variations demonstrated predictive power albeit with some systematic biases and areas of improvement. Notably, the best model achieved an R-squared value of around 0.45, indicating a substantial portion of the variability in prepayment rates could be explained by the model. However, better calibration and further data exploration, including individual bond and debtor group data alongside macroeconomic factors, could enhance predictive accuracy.
While the factor HJM model exhibited strong calibration to the market, its utility for pricing callable mortgage bonds remains uncertain. The thesis highlights that a complex interest rate model may not significantly impact results when coupled with a relatively simple prepayment model. Nevertheless, the attempt at bridging the gap between real world and pricing applications represents a theoretical advancement, albeit one that may not yet be widely adopted in practice. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9157310
- author
- Fagerfjäll, Ivar LU and Hu, Erik LU
- supervisor
- organization
- course
- FMSM01 20241
- year
- 2024
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Factor HJM, Yield Curve Modelling, Callable Mortgage Bonds, Mortgage Prepayment, FHJM, Pricing Danish Callable Bonds, Interest Rate Model
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUTFMS-3496-2024
- ISSN
- 1404-6342
- other publication id
- 2024:E39
- language
- English
- id
- 9157310
- date added to LUP
- 2024-06-05 09:43:56
- date last changed
- 2025-01-22 14:07:22
@misc{9157310,
abstract = {{A distinguishing component of the mortgage bond market in Denmark is the option to prepay a loan before its maturity date. From the debtors perspective, this is often done with the purpose of refinancing to a lower lending rate. Thus, interest rate modelling becomes a natural part of the pricing process of Danish callable mortgage bonds. Today, yield curves are modelled and thought of differently in real world versus pricing applications, creating a divide between the two. In this thesis, a factor modelling approach was combined with the Musiela HJM framework, as a means of bridging the divide.
The interest rate model was calibrated to forward rates and swaption premiums. Subsequently, yield curves were simulated and used in the calculation of refinance gains. Comparing with historical data, the factor HJM model showcased a good calibration to market volatility and rates.
The refinance gain, as well as a selection of other explanatory variables, were tested for significance in a probit model. The optimisation used a maximum likelihood estimation with historical prepayment rates as targets. The different model variations demonstrated predictive power albeit with some systematic biases and areas of improvement. Notably, the best model achieved an R-squared value of around 0.45, indicating a substantial portion of the variability in prepayment rates could be explained by the model. However, better calibration and further data exploration, including individual bond and debtor group data alongside macroeconomic factors, could enhance predictive accuracy.
While the factor HJM model exhibited strong calibration to the market, its utility for pricing callable mortgage bonds remains uncertain. The thesis highlights that a complex interest rate model may not significantly impact results when coupled with a relatively simple prepayment model. Nevertheless, the attempt at bridging the gap between real world and pricing applications represents a theoretical advancement, albeit one that may not yet be widely adopted in practice.}},
author = {{Fagerfjäll, Ivar and Hu, Erik}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Theses in Mathematical Sciences}},
title = {{Factor HJM Yield Curve Modelling for Pricing of Danish Callable Mortgage Bonds}},
year = {{2024}},
}