Morphology of government yield curves in less liquid markets


This is an empirical and quantitative project in finance, with the main objective to understand what expectations of the future interest rates’ evolution are confined in the government yield curves of less liquid markets (henceforth: LLMs) and to explore methods to improve their forecasting power.

We will offer novel insights on how the risk-free interest rates term structure can be obtained for government bonds and quantitative solutions to the following issues: (i) generally shorter recorded history of LLMs compared to liquid markets, (ii) extreme sensitivity of risk premium inference due to the issues with estimation of the  short end of the yield curve, (iii) insufficient diversity of maturities of bonds, (iv) insufficiently precise quotes for many of the ‘off-the-run’ maturities. The true innovation of our proposed research rests upon proposing a comprehensive set of solutions to all these issues in an internally coherent, model-consistent way. Ultimately, we provide insights about the information confined in yield curves in LLMs and about the expectations to be extracted for policy purposes from the yield curve. A tangible outcome of our work, in addition to two scientific articles will consist of providing canonical parameters of the yield curves and the risk premia estimates.  In this study we will verify the following main hypotheses that in LLMs:

Hypothesis 1: Pure Expectations Hypothesis does not hold universally.

Hypothesis 2: There exists a class of weighting schemes which improves fit relative to conventionally used methods.

Hypothesis 3: Unlike in the case of liquid markets, professional forecasters expectations do not help to increase the informational content of the yield curves in the case of LLMs.

Hypothesis 4: Spanning hypothesis holds in LLMs.  

In order to verify our hypotheses, we intend to conduct detailed studies that involve more micro-structural data of a certain market on bonds characteristics, turnover (monthly and daily, where available), outstanding amounts, bid-ask spreads, number of transactions traded daily, bid and ask yields obtained both from publicly available sources as well as usually provided on commercial basis. We intend to come up with a methodology that generates meaningful estimations of risk premia for less liquid markets, in doing so, following closely robustness checks done for US, UK and Euro Area government bonds markets. We intend to use the publicly available data to the maximum and draw from privately broadcasted data only for comparison reasons to avoid any derived data claims from commercial providers once the resultant datasets of yield curve decompositions will be published.



Źródło finansowania | FinancingNarodowe Centrum Nauki, PRELUDIUM 19

Projekt realizowany | Timeline: 12/2020 -- 12/2023

Kierownik | Principal Investigator: Marcin Dec

Budżet łączny | Total budget: 114 572 zł

  • wynagrodzenia dla podstawowych wykonawców | compensation to researchers: 54 000 zł
  • komputery i oprogramowanie | hardware and software: 10 056 zł
  • konferencje i inne wyjazdy | conference travels: 12 300 zł
  • książki i opłaty publikacyjne | books and publication fees: 19 121 zł
  • koszty pośrednie dla FAME | overheads for FAME: 19 095 zł

The general objective of this project is to study risk term structure of government bonds in less liquid markets and characterise expectations confined in current yield curves. Parsimonious yield curve fitting is predominantly a nonlinear constrained optimisation problem and therefore it is important that the objective function’s numerical construction is as computationally light as possible, hence we will turn to matrices of bonds cashflows and corresponding vectors year fractions. Especially important here are the techniques involved in finding heuristically the objective function’s minimum - with set of different starting parameters to reflect variability in possible yield curve shapes. Based on, previously fitted by us, the historical yield curves we will extract market expectations of the future interest rates via calculation of implied forward rate structure. We will use all of the data on realized and implied rates to conduct tests of different versions of expectations hypotheses. We aim in this project to uncover the risk adjusted expectations about future interest rates paths that are implied by yield curves in which we will follow the three stepped regressions in line with Adrian, Crump and Moench 2013 and test different number of factors in our model to extract market prices of risk. ACM in its core is based on relatively simple and well-established tools of principal component analysis (PCA) and a vector autoregressive model of order 1 (VAR) we will obviously use in our calculations. We will use Wald or Anderson test statistics to infer on the optimal number of stochastic latent factors to be taken in our final model as well to evaluate statistical significance of particular coefficients estimates interpreted as the prices of risk. On the top of these experiments we will also implement a bias correction of some sort in order to check its relevance for a particular less liquid market of choice.

  • We are working hard for you and develop YIELD's project results dissemination page here.

    In the meantime, please enjoy a MATLAB film on the history of Polish government bond market.

Opublikowane | Published

  • From point through density valuation to individual risk assessment in the discounted cash flows method | International Journal of Finance and Economics

    We review the developments and practice of the discounted cash-flow method in finance with an intermediate goal of presenting parsimonious methods of generating density  valuation rather than point forecasts. Our ultimate aim is to select, propose and  discuss some density-based risk measures that may be used by appraisers and investment analysts when conducting DCF valuation for broad group of heterogeneous (by risk appetite) final users or investors. Such a toolbox may be applied directly by the latter group without necessity to rely on aggregated point valuations and recommendations.

    Sample Matlab code to replicate the result of the two examples from this article is here.

  • Markovian and multi-curve friendly parametrisation of a HJM model used in valuation adjustment of interest rate derivatives | Bank i Kredyt

    We consider feasible Heath-Jarrow-Morton framework specifications that are easily implementable in XVA engines when pricing linear and non-linear interest rate derivatives in a multi-curve environment. Our particular focus is on relatively less liquid markets (Polish PLN) and the calibration problems arising from that fact. We first develop the necessary tool-kit for multi- -curve construction and XVA integration and then show and discuss various specifications of the HJM model with regard to their practical usage. We demonstrate the importance of the Cheyette subclass and derive the dynamics of instantaneous forward rates in generic forms of different models. We performed calibrations of several one-factor models of that form and found that even with a relatively simple specification, i.e. Hull-White with two summands, we may achieve satisfactory results in terms of the quality of the calibration and calculation time.


W toku | Work in progress

  • Parsimonious yield curve modeling in less liquid markets

    Less liquid markets for government bonds (LLMs) are characterized by many well recognized challenges which reduce the reliability of the classic Nelson-Siegel-Svensson (NSS) parsimonious approach. We document key stylized facts about government bond markets concerning liquidity, diversity of maturities available, bid-ask spread in price quotes, as well as price distortion in the very short end of the curve due to switch auctions. Based on these facts, we augment the NSS approach with model- and data-driven endogenous system of weights which permits reliable estimation of yield curves in LLMs. We apply our approach to the data for one of the largest European emerging markets: Poland. Through a battery of sensitivity analyses we show that there exists a class of weights that systematically gives better results than the classic NSS approach. The best fit weights have at least the same weight for the short end of the curve as a sum for all other tenors of bonds. It proves that inferring from the liquidity in particular maturities raises the information content and quality of yield curve estimation, which links our results to the expectation hypotheses. Unlike findings for most mature markets (e.g. US), for Poland there is a limited domain where pure expectations hypothesis (PEH) cannot be ruled out. Moreover, expectations hypothesis (EH) holds in Poland for almost all horizons. The existence of term premia structure explains the differences between compounded rates of returns from shorter investments and longer term zero-coupon yields of corresponding maturity.