Staying on Top of the Curve: A Cascade Model of Term Structure Dynamics

Abstract

This paper specifies term structure dynamics by a recursive cascade of heterogeneously persistent factors. The cascade naturally orders economic shocks by their adjustment speeds, and generates smooth interest-rate curves in closed form. For a class of specifications, the number of parameters is invariant to the size of the state space, and the term structure converges to a stochastic limit as the state dimension goes to infinity. High-dimensional specifications fit observed term structure almost perfectly, match the observed low correlation between movements in different maturities, and produce stable interest-rate forecasts that outperform lower-dimensional specifications.

A dimension‐invariant cascade model for VIX futures

“…To address the above issues, we propose a new model of volatility by allowing for a cascading structure of volatility components, motivated by the interest rate model of Calvet, Fisher, and Wu (). The cascading volatility model essentially has one governing factor with multiple layers or commonly referenced as factors.…”

“…The choice of six factors, as opposed to more, is made to achieve a balance between flexibility and computational burden. Calvet et al () investigate both the in‐sample fitting and the out‐of‐sample predictive power of more factors in the modeling of the interest rate term structure, in which they used a maximal 15‐factor model to fit the 15 maturity strips of LIBOR and swap rates. However, the square root function in our VIX futures pricing formula (see Equation ) makes its computation significantly more challenging than that of their interest rate pricing formula.…”

“…1 Calvet et al (2018) select 15 factors for 15 daily interest rates. 2 We also estimated a three-factor model that performed adequately but not as well as the six-factor model both in-sample and out-of-sample.…”

Comparing null models for testing multifractality in time series

“…Many methods are proposed to empirically uncover the multifractality, such as the partition function approach [2], the structure function approach [3], the wavelet transform approach [4][5][6], the detrended fluctuation approaches [7][8][9], multifractal natural time analysis [10] and so on. By employing the above-mentioned methods, it is found that many financial time series (returns, volatilities, bid-ask spreads, to list a few) from different markets around the world exhibit significant multifractal characteristics [11][12][13][14][15][16][17][18][19][20], which not only inspires people to construct models (multifractal random walk (MRW) [21,22], Markov-switching multifractal (MSM) models [23,24], and (a) E-mail: zqjiang@ecust.edu.cn so on) to replicate such important stylized facts, but also motive researchers to find the sources of multifractality.…”

“…The renewed value is drawn from a binomial distribution [m 0 , 1 − m 0 ] with equal probability. In MSM, {σ 2 , b, γk, m 0 } are the parameters to be estimated and can be estimated by maximum likelihood estimation [24] and generalized method of moments [38].k corresponds to the volatility frequency and is given while doing the estimation. For simplicity, we set the initial value M k,0 as m 0 .…”