Interest rate models on Lie groups

Park, F. C.; Chun, Changmook; Han, Cheol E.; Webber, Nick

doi:10.1080/14697680903468963

Cited by 16 publications

(24 citation statements)

References 11 publications

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“…Lo and Hui [13] and Carr et al [14] constructed a concrete example of a short-rate model on the circle S 1 . Park et al [15] tested the proposition that nonlinear and random behavior of interest rates is governed by a stochastic differential equation model on a curved state space. They developed short-term interest rate models on S 1 and S 2 manifolds using matrix representations instead of differential operator representations of Lie groups.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we employ a model on S 2 manifolds that uses matrix representations instead of differential operator representations of Lie algebras. As accented by [15], the drift and noise volatility terms of the stochastic state equations are worked out to reflect various observed phenomena. We try to keep these terms simple and instead choose an underlying state space that is curved.…”

Section: Introductionmentioning

confidence: 99%

“…We try to keep these terms simple and instead choose an underlying state space that is curved. Park et al [15] and Goard [16] used the ordinary least square (OLS) estimation method for parameter estimation. We preferred the nonlinear least square (NLS) method for parameter estimation due to the nonlinear behavior in the specified period.…”

Section: Introductionmentioning

confidence: 99%

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Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks

2021

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In this paper, we propose hybrid models for modelling the daily oil price during the period from 2 January 1986 to 5 April 2021. The models on S2 manifolds that we consider, including the reference ones, employ matrix representations rather than differential operator representations of Lie algebras. Firstly, the performance of LieNLS model is examined in comparison to the Lie-OLS model. Then, both of these reference models are improved by integrating them with a recurrent neural network model used in deep learning. Thirdly, the forecasting performance of these two proposed hybrid models on the S2 manifold, namely Lie-LSTMOLS and Lie-LSTMNLS, are compared with those of the reference LieOLS and LieNLS models. The in-sample and out-of-sample results show that our proposed methods can achieve improved performance over LieOLS and LieNLS models in terms of RMSE and MAE metrics and hence can be more reliably used to assess volatility of time-series data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks

2021

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“…(91) 37 Here we focus on the solution with only one (lower) boundary. The solution with both (lower and upper) boundaries can also be readily constructed and involves both Ai(y) and Bi(y).…”

Section: B Reflecting Barriers For the Short-rate Processmentioning

confidence: 99%

Coping With Negative Short Rates

Kakushadze¹

2016

Wilmott

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We discuss a simple extension of the Ho and Lee model with generic timedependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the short-rate process. Our extension amounts to introducing one or two reflecting barriers for the underlying Brownian motion (as opposed to the short-rate), which allows to have more realistic time-dependent drift (as opposed to constant drift). In our model the spectrum -or, roughly, the set of short-rate values contributing to bond and other claim prices -is discrete and positive. We discuss how to calibrate our model using empirical yield data by fitting three parameters and then read off the time-dependent drift.

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“…The method in Park et al (2011) is used here to obtain the model parameters by optimizing the variance…”

Section: Contribution Of the Thesismentioning

confidence: 99%

Fredholm, chaos-based and Gram-Charlier methods in fixed income derivative pricing

Wu¹

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have been so grateful to have a supervisor who cared so much about my work, and who responded to my questions and queries so promptly. I would also like to thank the Division of Mathematical Sciences at Nanyang Technological University, not only for providing the funding which allowed me to undertake this research, but also for giving me the opportunity to attend conferences and meet so many interesting people. Finally, I would like to thank my family for always being there and believing in me. Completing this work would have been all the more difficulty were it not for the support and care provided by them.

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Interest rate models on Lie groups

Cited by 16 publications

References 11 publications

Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks

Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks

Coping With Negative Short Rates

Fredholm, chaos-based and Gram-Charlier methods in fixed income derivative pricing

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