Repeating Christmas jump in LIBOR

Vikenty Mikheev; Serge E. Miheev

doi:10.12688/f1000research.26024.2

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Research Article

Revised

Repeating Christmas jump in LIBOR

[version 2; peer review: 2 approved]

Previously titled: Upcoming Christmas jump in LIBOR

Vikenty Mikheev ¹, Serge E. Miheev²

PUBLISHED 27 Jul 2023

Author details Author details

¹ Mathematics, Kansas State University, Manhattan, KS, 66502, USA
² Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg, 198504, Russian Federation

Vikenty Mikheev
Roles: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Project Administration, Software, Validation, Visualization, Writing – Original Draft Preparation, Writing – Review & Editing

Serge E. Miheev
Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Supervision, Validation, Writing – Original Draft Preparation

OPEN PEER REVIEW

REVIEWER STATUS

Abstract

Background: London Interbank Offered Rate (LIBOR) exists since 1986 as a benchmark interest rate.
Methods: Using two-layer linear regression method, we found a pattern of shortterm nature in LIBOR behaviour.
Results: To wit, 2-month LIBOR experiences a jump after Xmas for the last two decades. The direction and size of the jump depend on the data trend on 21 days before Xmas.
Conclusions: The obtained results can be used to build a winning strategy on the Swap Market.

Keywords

LIBOR, short term approximation, pattern, swap market, Christmas jump, linear regression

Corresponding author: Vikenty Mikheev

Competing interests: No competing interests were disclosed.

Grant information: The author(s) declared that no grants were involved in supporting this work.

Copyright: © 2023 Mikheev V and Miheev SE. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Mikheev V and Miheev SE. Repeating Christmas jump in LIBOR [version 2; peer review: 2 approved]. F1000Research 2023, 9:1221 (https://doi.org/10.12688/f1000research.26024.2) First published: 09 Oct 2020, 9:1221 (https://doi.org/10.12688/f1000research.26024.1) Latest published: 27 Jul 2023, 9:1221 (https://doi.org/10.12688/f1000research.26024.2)

Revised Amendments from Version 1

Several links to works on the transition from Libor to other benchmark systems are added.

See the authors' detailed response to the review by FAUZIA MUBARIK

Introduction

In 1986, a new benchmark interest rate was introduced, named the London Interbank Offered Rate (LIBOR). At LIBOR, major banks of the world lend to one another in the international interbank market for short-term loans. From a mathematical point of view, LIBOR is a sequence of daily changing real values. LIBOR data is in open access and can be found on multiple web-sites, for example, here¹.

In Figure 1, one can see a large scale sample of 2-month LIBOR for loans in USD. In Figure 2, the values of 2-month LIBOR 21 days before Xmas and 6 days after from 2004–2019 years were put together.

Figure 1. Data of 2-month LIBOR from 1987 to 2019.

LIBOR has a crucial role in the Swap Market, where people exchange their loan interests and can win or lose money depending on their right or wrong predictions of LIBOR dynamics. For example, person P got a one-million-dollar loan with 5% interest and person E borrowed the same amount but with the interest 2%+LIBOR. After some time, they decide to exchange their interest rates because P thinks that LIBOR will go lower than 3% but E believes that it will go higher than 3%. Both their opinions are based on some prediction methods, even if it is just an intuition. We intend to bring another prediction tool into the game. A curious reader may find more complex models and measures on LIBOR for different problems^2–5.

Figure 2. 2-month LIBOR values 21 days before Xmas and 6 days after from 2004–2019 years combined.

Thus, here we are not interested to LIBOR nature per se but in its volatility. More precisely, we study the behavior of LIBOR after Christmas from December 26 to December 31. Examples of such data are in Figure 3 and Figure 4.

Figure 3. Data from 2012 year around Xmas.

Figure 4. Data from 2004 year around Xmas.

Although LIBOR itself is going to disappear in 2021^6–11, and one can apply our results only for Xmas 2020, we think that the model we introduce here might be useful for short-term analysis in other problems.

So, how does Christmas affect dynamics of LIBOR until the next holiday?

Methods

Definition and models

The research we conducted indicates convincingly that a jump does exist. But what is a jump in a discrete sequence of numbers? The following seems to be the most acceptable:

Definition 1. There are a real number $\bar{x}$ and a real discrete function given tabularly

z = (\begin{matrix} x_{1} & \dots & x_{n} \\ y_{1} & \dots & y_{n} \end{matrix}),

where x₁ < x₂ < ... < x_n and $x_{k} < \bar{x} < x_{k + 1}$ for some natural k ∈ [2,n − 2]. One chooses approximant A : R^r × R¹ → R¹ among functions having continuous derivative by second argument notated as ${A^{'}}_{2}$ and chooses some quality criterion Q(z,A(p, ·) to minimize by parameter vector p ∈ R^r. Then we appoint

z_{0} = (\begin{matrix} x_{1} & \dots & x_{k} \\ y_{1} & \dots & y_{k} \end{matrix}), z_{1} = (\begin{matrix} x_{k + 1} & \dots & x_{n} \\ y_{k + 1} & \dots & y_{n} \end{matrix})

and consider the approximation problem with the criterion Q(z₀,A(p,·)) → min_p∈R^r. Let its solution be denoted as $\bar{A} (z_{0}, x) .$ Then we consider the next problem

Q (z_{1}, A (p, \cdot)) \to \begin{matrix} \min \\ p ∈ R^{r} \land A_{2}^{'} (p, \bar{x}) = {\bar{A}}_{2}^{'} (z_{0}, \bar{x}) \end{matrix} .

Let its solution be denoted as $\bar{A} (z_{1}, x) .$ Then the difference $\bar{A} (z_{0}, \bar{x}) - \bar{A} (z_{1}, \bar{x})$ is the jump at $\bar{x}$ .

In other words, the jump at $\bar{x}$ of a discrete function given by a tabular is the difference at $\bar{x}$ between the obtained solutions of two approximation problems of the same type, the first problem is formulated on the left part of the table, the second problem is formulated on the right part of the table and must keep at $\bar{x}$ trend (i.e. derivative) of the first problem solution. The left part corresponds to the nodes less than $\bar{x}$ , the right part corresponds to the nodes greater than $\bar{x}$ .

In our case, $\bar{x}$ =Dec 25).

It is easy to see that the so-defined jump depends on the type of approximation and on the amount of the input data. On top of that, we have to decide the amount of input data in z₀. Notice that the amount of the data in z₁ is only three pairs (date, LIBOR of this date) because there are exactly three working banking days between Xmas and New Year’s Eve (NYE). The data source is available in 1 or in many other sources.

Variability of the data due to random factors leads to the choice of the simplest approximation. We use linear approximating functions, which coefficients may be found by linear regression with its own quality criterion. We restrict ourselves to LIBOR data for the last 22 years, because it is natural to expect the evolution of LIBOR behavior over the years.

So, for year j in set J taken sequentially with no gaps from {1997, ..., 2019} data are taken for 15 banking days $x^{'}$ ₋₁₅,..., $x^{'}$ ₋₁ (corresponding to 21 calendar days) preceding Xmas of year j. Since all the days are in December, we may refer to them just by number without problem of passing days to another month: $x^{'}$ ₋₁₅,..., $x^{'}$ ₋₁ ⊂ {4,...,24}. Moreover, for simplicity of following constructions we may decrease them by 25, i.e. $x_{i} : = {x^{'}}_{i} - 25$ , i = −15,...,−1. Therefore, x₋₁₅,...,x₋₁ ⊂ {−21,...,−1}. Each x_i corresponds to y_i, which is the annual interest rate of LIBOR for 2 months on day x_i. Using them we build a linear regression

\hat{y} (x) = a_{j} x + b_{j}, (1)

or $y_{i} = \hat{y} (x) + ε_{i},$ where x is a December day minus 25 and ε_i is the error.

That is, in terms of Definition 1, $\bar{A} (z_{0}, x) = a_{j} (z_{0}) x + b_{j} (z_{0}) .$ Since the current trend of LIBOR (meaning the rate of growth or decrease) does not change a lot over a short time interval, it is almost the same before and after Xmas. Therefore, we seek an approximation after Xmas in the following form: $\hat{y} (x) = {a^{'}}_{j} x + {b^{'}}_{j},$ where x is a December day decreased by 25 and ${a^{'}}_{j} = a_{j} = \bar{A} (z_{0}, \bar{x}) .$ Hence, the second approximation has only one unknown parameter, ${b^{'}}_{j} .$ It can also be found by linear regression or can be calculated simply as the average of values y_i − a_jx_i, where i runs 1,2,3 and x_i ∈ {27 − 25,...,31 − 25} = {2,...,6} (There are exactly three bank days between Xmas and New Year.) The examples of such approximations are seen in Figure 5 and Figure 6.

Figure 5. Approximation on data of 2012 year.

Figure 6. Approximation on data of 2004 year.

Notice that on the last Figure 5 and Figure 6 with data for 2012 and 2004 years and their regressions, the y-axes have different scales.

Thus, for each selected year j there is a relationship $(b_{j}, a_{j}) \to {\hat{b}}_{j} .$ According to Definition 1 the difference $Δ_{j} := {\hat{b}}_{j} - b_{j}$ is the jump we have been looking for. Having such connections over 23 years, one can try to find a pattern. To do that, we turn to linear-quadratic regression on two-dimensional nodes. This time the approximating function has the form:

F (a, b) : = β_{0} + β_{1} a + β_{2} b + β_{3} a b (2)

with an approximation table F_J (a_j,b_j) ≈ Δ_j, j ∈ J ⊂ {1995,...,2019}. Sub index J at F points at which subset of years over the past 23 has been chosen to construct the regression. The remaining years will be used to verify the statistical reliability of the result.

Why 15 week days before and 3 week days after Xmas?

On one hand, we want as much data for our approximation as possible. On the other hand, the longer the time interval, the less accurate the trend on the end of the interval. Someone could say: ”Why don’t you take a more complex approximant to capture more complicated futures of the time series?” Well, that would require even more data for statistical power of such approximant. Since we want to detect a short-term pattern, we should avoid such approach. It made sense to take a number of days before Xmas divisible by 5, so each week day would appear evenly. After trying 25, 20, 15, 10, 5, we found the model worked best with 15 days.

Regarding 3 LIBOR days after Xmas, the same logic explained above is applicable here too. Again, empirically we have found that 3 days work the best. Notice every year has exactly 3 LIBOR days between Xmas and NYE. It is possible that NYE plays a big role in that.

Results

We conducted the process above for several different numbers of years for F regression (from 5 to 20 years), different LIBOR data (overnight, 1 month, 2 months, etc.). The most convincing results have been obtained with the following setups: 21 calendar day regression for each year from 15-year intervals; 2-month-loan values of LIBOR.

Observe the results in the Table 1.

Table 1. Model Δ ≈ β₀ + β₁a + β₂b + β₃ab and its predictions with p-values p for 2019 year.

Data	2000–14	2001–15	2002–16	2003–17	2004 – 18	2005 – 20
Pred. on	2015	2016	2017	2018	2019	2020
$\hat{β_{0}}$ $\hat{β_{1}}$ $\hat{β_{2}}$ $\hat{β_{3}}$	-2.96E-3 -9.286 1.8E-4 1.91521	4.1E-4 -9.337 -0.002209 1.99021	4.1E-4 -9.321 -0.00220 1.98676	0.00327 -9.278 -0.00204 2.02619	0.00473 -9.265 -0.00238 2.016	0.00477 (p=0.157) -9.26577 (p=1.93e-12) -0.002346 (p=0.113) 2.01876 (p=2.90e-08)
Adj R²	0.98	0.99	0.99	0.99	0.99	0.99
RSS	0.01178	0.00844	0.00844	0.00984	0.00815	0.00854
Pred. val Real val	-0.0709 -0.0599	-0.0306 -0.0269	-0.0548 -0.0291	-0.0180 -0.0228	-0.0085 -0.0188	wait for data till 12/24/2019
${\hat{L}}^{m e a n}$ L^mean	0.5024 0.5134	0.8146 0.8183	1.5967 1.6224	2.6222 2.6174	1.8509 1.8404	wait for data till 12/24/2020
Error	-0.0110	-0.0037	-0.0257	0.0048	0.0105

So, our prediction for the jump formula after Xmas 2020 are:

{\hat{Δ}}_{2020} = 0.004770 - 9.265766 a_{2020} - 0.002346 b_{2020} + 2.018758 a_{2020} b_{2020} (3)

The 95%-confidence intervals for the coefficients β₀,β₁,β₂,β₃ in (3) are (-0.00217, 0.01171), (-9.77318, -8.75835), (-0.00536, 0.00066) and (1.72466, 2.31286), respectively.

It may be activated at Dec 24 2020 as following:

At this day extract data {y_i} from 1 for bank days ${{x^{'}}_{i}}$ since Dec 21 till Dec 24 (in 2020, of course). Build 15 pairs (x_i,y_i), i = −15,...,−1, where $x_{i} = {x^{'}}_{i} - 25$ . Put them into any program to find linear regression, for example, into our code in R, which is available as Extended data¹². The result of the regression is two numbers: that corresponding to free term is b₂₀₂₀, the other is a₂₀₂₀. Substitution of them to (3) yields the jump.

The prediction of the jump can be used to predict the mean LIBOR after Xmas and before NYE ( $L_{j}^{m e a n}) .$ Let us show some formulas.

According to Definition 1 the jump with approximations above is $Δ_{j} = {\hat{b}}_{j} - b_{j}$ , where ${\hat{b}}_{j}$ = arg min_b ${\sum_{i = 1}^{3} {(a_{j} x_{i} + b - y_{i})}^{2}},$ which is equivalent to ${\hat{b}}_{j} = \frac{1}{3} \sum_{i = 1}^{3} (y_{i} - a_{j} x_{i}) .$ Hence

Δ_{j} = \frac{1}{3} \sum_{i = 1}^{3} (y_{i} - a_{j} x_{i}) - b_{j} = \frac{1}{3} \sum_{1}^{3} y_{i} - \frac{1}{3} \sum_{i = 1}^{3} (a_{j} x_{i} + b_{j}) . (4)

Notice that the last term in (4) is just a predicted mean value of LIBOR between Xmas and NYE $({\hat{L}}_{j}^{m e a n}),$ according to the regression for j-th year. Thus,

L_{j}^{m e a n} = {\hat{L}}_{j}^{m e a n} + Δ_{j} = {\hat{L}}_{j}^{m e a n} + {\hat{Δ}}_{j} + (Δ_{j} - {\hat{Δ}}_{j}) .

If as estimate of $L_{j}^{m e a n}$ we take ${\hat{L}}_{j}^{m e a n} + {\hat{Δ}}_{j},$ then its absolute error is equal to ${\hat{Δ}}_{j} - Δ_{j} .$

The latter difference according to our calculations for years 2015, 2016, 2017, 2018, 2019 was always less by absolute value than $| {\hat{Δ}}_{j} | .$

Conclusion

We have found a short-term pattern in LIBOR dynamics. Namely, the 2-month LIBOR experiences a jump after Xmas. The sign and size of the jump depends on data trend on 21 days before Xmas. The results are obtained in the form of the jump per se and as mean predicted value of LIBOR between Xmas and NYE. A swap market player may try to use this information to predict behaviour of LIBOR to do a better game on his part. For Xmas of 2020, on a date of Dec 24, one can compute a and b according to (1) on 21 calendar days and use the formula (3) to predict the jump after Xmas.

In the pre-print¹³ of this paper, one can find our predictions for the jump after Xmas of 2019 and see that later data from the event confirmed it.

Data availability

Source data

All data used in this paper can be found at IBORate (http://iborate.com/usd-libor/)¹.

Extended data

The code used to develop the model is available at: https://github.com/keshmish/Chistmas-Jump-in-LIBOR/.

Archived code at time of publication: https://doi.org/10.5281/zenodo.3977133¹².

License: MIT License.

Acknowledgements

We would like to show our gratitude to the Institute for Mathematics and its Applications (https://ima.umn.edu/node), U. of Minnesota for organizing Math-to-Industry Boot Camp IV, where Fadil Santosa and Daniel Spirn suggested to search for some patterns in LIBOR behaviour around national holidays. We thank Davood Damircheli, Anthony Nguyen and Samantha Pinella for discussions and participation in the first attempts to detect the pattern.

Faculty Opinions recommended

References

1. IBORate: LIBOR database. Cited 15 Jan 2020. http://iborate.com/usd-libor/
2. Jamshidian F: LIBOR and swap market models and measures. Financ Stoch. 1997; 1: 293–330. Publisher Full Text
3. Schoenmakers J: Robust Libor Modelling and Pricing of Derivative Products. Chapman and Hall/CRC, New York, 2005. Reference Source
4. Moreni N, Pallavicini A: Parsimonious HJM modelling for multiple yield-curve dynamics. Quant Finance. Routledge, 2014; 14(2): 199–210. Publisher Full Text
5. Hinch M, McCord M, McGreal S: LIBOR and interest rate spread: sensitivities of the Australian housing market. Pac Rim Prop Res J. Routledge, 2019; 25(1): 73–99. Publisher Full Text
6. Heltman J: Libor is going dark in 2021, and some banks aren’t ready. American Banker, 2018; Cited 15 Jan 2020. Reference Source
7. Farrar D: You might have heard that LIBOR is going away.... Consumer Financial Protection Bureau. 2019; Cited 15 Jan 2020. Reference Source
8. The LIBOR Transition. Congressional Research Service. 2022; Cited 3 July 2023. Reference Source
9. Rhame L, Reback T, Korz A: LIBOR reform: From theoretical to tactical. FS Investments. 2020; Cited 3 July 2023. Reference Source
10. Guggenheim B, Schrimpf A: At the crossroads in the transition away from LIBOR: from overnight to term rates. BIS Working Papers. Cited 3 July 2023. Reference Source
11. Mubarik F: Benchmarking Islamic Finance: Goodbye to the LIBOR. Taylor&Francis Group. Cited 3 July 2023. Reference Source
12. Mikheev V: Code in R for Xmass Jump in Libor. http://www.doi.org/10.5281/zenodo.3977133
13. Mikheev V, Miheev SE: Christmas Jump in LIBOR. Arxiv. 2019. Reference Source

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Version 2

VERSION 2 PUBLISHED 09 Oct 2020

Author details Author details

¹ Mathematics, Kansas State University, Manhattan, KS, 66502, USA
² Applied Mathematics and Control Processes, St. Petersburg State University, St. Petersburg, 198504, Russian Federation

Serge E. Miheev
Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Supervision, Validation, Writing – Original Draft Preparation

Competing interests

No competing interests were disclosed.

Grant information

The author(s) declared that no grants were involved in supporting this work.

Article Versions (2)

version 2

Revised

Published: 27 Jul 2023, 9:1221

https://doi.org/10.12688/f1000research.26024.2

version 1

Published: 09 Oct 2020, 9:1221

https://doi.org/10.12688/f1000research.26024.1

© 2023 Mikheev V and Miheev SE. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mikheev V and Miheev SE. Repeating Christmas jump in LIBOR [version 2; peer review: 2 approved]. F1000Research 2023, 9:1221 (https://doi.org/10.12688/f1000research.26024.2)

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Reviewer Report 04 Aug 2023

FAUZIA MUBARIK, Department of Management Science, National University of Modern Languages, Islamabad, Pakistan

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https://doi.org/10.5256/f1000research.152396.r191301

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Reviewer Report 30 May 2022

FAUZIA MUBARIK, Department of Management Science, National University of Modern Languages, Islamabad, Pakistan

Approved with Reservations

https://doi.org/10.5256/f1000research.28719.r127765

The article has a good readability and qualifies to be approved with reservations. This article has an interesting way forward to identify and recognize the most recent developments in the Alternative Reference Rates (ARR); Secured Overnight Financing Rate (SOFR) of United States, Sterling Overnight Index Average (SONIA) of England, Euro Short-Term Rate (ESTR) of European Union, Swiss Average Rate Overnight (SARON) of Switzerland and Tokyo Overnight Average Rate (TONAR) of Japan introduced in the global financial market as the successors to LIBOR.

The article can be published after incorporating the following suggestions/recommendations;

The in-text citations are missing.
The results can be strengthened through empirical support. 2021 and 2020 were big years for LIBOR research, please cite some of this research – or conduct more of your own – to strengthen your results. See this Congressional Report, this from KKR Investments, and this from the Bank for International Settlements, for example.
The researcher may explain whether any windows are created to study the jumps.
Is it a two step study, first of 21 days and 6 days; second of 15 days and 3 days?
Is the prediction in the jump studied through mean of the regression method?

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Financial Economics, Islamic Finance

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Author Response 28 Apr 2023

Vikenty Mikheev, Mathematics, Kansas State University, Manhattan, 66502, USA

28 Apr 2023

Author Response

1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR ... Continue reading 1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR transition, which is a little unrelated to our topic. Unfortunately, adding data after 2020 is hard since the LIBOR got mostly shut down in 2021. There above, you mentioned similar to LIBOR data where the proposed here method could be tried on. This is a very useful hint. Thanks!

3. We hope that the section "Why 15 week days before and 3 week days after Xmas?" explains this very reasonable question.

4,5. "Two-step" in our research stays for two-step regression. First, we find (by a regression) the parameters of a function for each year from 1997 to 2019. Second, we do another regression, this time on those found parameters to predict the next year.
1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR transition, which is a little unrelated to our topic. Unfortunately, adding data after 2020 is hard since the LIBOR got mostly shut down in 2021. There above, you mentioned similar to LIBOR data where the proposed here method could be tried on. This is a very useful hint. Thanks!

3. We hope that the section "Why 15 week days before and 3 week days after Xmas?" explains this very reasonable question.

4,5. "Two-step" in our research stays for two-step regression. First, we find (by a regression) the parameters of a function for each year from 1997 to 2019. Second, we do another regression, this time on those found parameters to predict the next year.
Competing Interests: No competing interests were disclosed. Close
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Author Response 28 Apr 2023

Vikenty Mikheev, Mathematics, Kansas State University, Manhattan, 66502, USA

28 Apr 2023

Author Response

1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR ... Continue reading 1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR transition, which is a little unrelated to our topic. Unfortunately, adding data after 2020 is hard since the LIBOR got mostly shut down in 2021. There above, you mentioned similar to LIBOR data where the proposed here method could be tried on. This is a very useful hint. Thanks!

3. We hope that the section "Why 15 week days before and 3 week days after Xmas?" explains this very reasonable question.

4,5. "Two-step" in our research stays for two-step regression. First, we find (by a regression) the parameters of a function for each year from 1997 to 2019. Second, we do another regression, this time on those found parameters to predict the next year.
1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR transition, which is a little unrelated to our topic. Unfortunately, adding data after 2020 is hard since the LIBOR got mostly shut down in 2021. There above, you mentioned similar to LIBOR data where the proposed here method could be tried on. This is a very useful hint. Thanks!

3. We hope that the section "Why 15 week days before and 3 week days after Xmas?" explains this very reasonable question.

4,5. "Two-step" in our research stays for two-step regression. First, we find (by a regression) the parameters of a function for each year from 1997 to 2019. Second, we do another regression, this time on those found parameters to predict the next year.
Competing Interests: No competing interests were disclosed. Close
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Reviewer Report 02 Mar 2022

Victor Malyutin, Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus

Approved

https://doi.org/10.5256/f1000research.28719.r123668

The behavior of LIBOR after Christmas from December 26 to December 31 is studied in the paper. The Authors use linear regression to find the regression coefficients for data before Xmas and jump after Xmas for each selected year. To get the jump prediction formula the linear-quadratic regression on two-dimensional nodes is used. The prediction of the jump can be used to predict the mean LIBOR after Xmas and before NYE. Presented results demonstrate that predicted results approximate real values well.

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Mathematical statistics

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

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Victor Malyutin, Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus
FAUZIA MUBARIK, National University of Modern Languages, Islamabad, Pakistan

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Approved With Reservations

The in-text citations are missing.
The results can be strengthened through empirical support. 2021 and 2020 were big years for LIBOR research, please cite some of this research – or conduct more of your own – to strengthen your results. See this Congressional Report, this from KKR Investments, and this from the Bank for International Settlements, for example.
The researcher may explain whether any windows are created to study the jumps.
Is it a two step study, first of 21 days and 6 days; second of 15 days and 3 days?
Is the prediction in the jump studied through mean of the regression method?

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Financial Economics, Islamic Finance

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Responses (1)

Author Response

28 Apr 2023

Vikenty Mikheev, Mathematics, Kansas State University, Manhattan, 66502, USA

1. If you could specify where exactly those missing citations were supposed to be, it would help us a lot.

2. The articles you mentioned are talking about LIBOR transition, which is a little unrelated to our topic. Unfortunately, adding data after 2020 is hard since the LIBOR got mostly shut down in 2021. There above, you mentioned similar to LIBOR data where the proposed here method could be tried on. This is a very useful hint. Thanks!

3. We hope that the section "Why 15 week days before and 3 week days after Xmas?" explains this very reasonable question.

4,5. "Two-step" in our research stays for two-step regression. First, we find (by a regression) the parameters of a function for each year from 1997 to 2019. Second, we do another regression, this time on those found parameters to predict the next year.

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Competing Interests

No competing interests were disclosed.

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Reviewer Report

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02 Mar 2022 | for Version 1

Victor Malyutin, Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk, Belarus

13 Views Cite this report Responses(0)

Approved

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Mathematical statistics

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

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Alongside their report, reviewers assign a status to the article:

Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions

[1] 1. IBORate: LIBOR database. Cited 15 Jan 2020. http://iborate.com/usd-libor/

[2] 2. Jamshidian F: LIBOR and swap market models and measures. Financ Stoch. 1997; 1: 293–330. Publisher Full Text

[3] 3. Schoenmakers J: Robust Libor Modelling and Pricing of Derivative Products. Chapman and Hall/CRC, New York, 2005. Reference Source

[4] 4. Moreni N, Pallavicini A: Parsimonious HJM modelling for multiple yield-curve dynamics. Quant Finance. Routledge, 2014; 14(2): 199–210. Publisher Full Text

[5] 5. Hinch M, McCord M, McGreal S: LIBOR and interest rate spread: sensitivities of the Australian housing market. Pac Rim Prop Res J. Routledge, 2019; 25(1): 73–99. Publisher Full Text

[6] 6. Heltman J: Libor is going dark in 2021, and some banks aren’t ready. American Banker, 2018; Cited 15 Jan 2020. Reference Source

[7] 7. Farrar D: You might have heard that LIBOR is going away.... Consumer Financial Protection Bureau. 2019; Cited 15 Jan 2020. Reference Source

[8] 8. The LIBOR Transition. Congressional Research Service. 2022; Cited 3 July 2023. Reference Source

[9] 9. Rhame L, Reback T, Korz A: LIBOR reform: From theoretical to tactical. FS Investments. 2020; Cited 3 July 2023. Reference Source

[10] 10. Guggenheim B, Schrimpf A: At the crossroads in the transition away from LIBOR: from overnight to term rates. BIS Working Papers. Cited 3 July 2023. Reference Source

[11] 11. Mubarik F: Benchmarking Islamic Finance: Goodbye to the LIBOR. Taylor&Francis Group. Cited 3 July 2023. Reference Source

[12] 12. Mikheev V: Code in R for Xmass Jump in Libor. http://www.doi.org/10.5281/zenodo.3977133

[13] 13. Mikheev V, Miheev SE: Christmas Jump in LIBOR. Arxiv. 2019. Reference Source

Repeating Christmas jump in LIBOR

Abstract

Keywords

Revised Amendments from Version 1

Introduction

Figure 1. Data of 2-month LIBOR from 1987 to 2019.

Figure 2. 2-month LIBOR values 21 days before Xmas and 6 days after from 2004–2019 years combined.

Figure 3. Data from 2012 year around Xmas.

Figure 4. Data from 2004 year around Xmas.

Methods

Definition and models

Figure 5. Approximation on data of 2012 year.

Figure 6. Approximation on data of 2004 year.

Why 15 week days before and 3 week days after Xmas?

Results

Table 1. Model Δ ≈ β0 + β1a + β2b + β3ab and its predictions with p-values p for 2019 year.

Conclusion

Data availability

Source data

Extended data

Acknowledgements

References

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Table 1. Model Δ ≈ β₀ + β₁a + β₂b + β₃ab and its predictions with p-values p for 2019 year.