Multifactorial Heath-Jarrow-Morton model using principal component analysis

Higher moments interaction between the US treasury yields, energy assets, and green cryptos: Dynamic analysis with portfolio implications

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

This paper presents an analysis of models for Japanese short-term inter- est rate. The models are constructed based on mean reverting model using Bayesian method to capture the dynamics of short-term interest rate. The parameters of our models are estimated by marginal likelihood and posterior expectation and we shall make model selection using the information criterion EIC(extended information cri- terion). An application of the models will be implemented using weekly Japanese average interest rates on certificates of deposit (new issues) less than 30 days in the period from January 2001 to December 2008. 1 Introduction Correct modeling of the short-term interest rate is essential in finace, as it is this rate that is fundamental to the pricing of securities and important for risk man- agement. In the study of the short-term interest rate dynamics, various models have been suggested. There are examples of these models, such as Vasicek model by Vasicek(1977), CIR model by Cox, Ingersoll and Ross(1985) and so on. An empirical comparison of these models was made by Chan, Karolyi, Longstaff and Sanders(1992). In the paper, the param- eters are estimated by generalized method of moments(GMM) and they implemented the hypothesis testing methods developed by Newey and West for evaluation of the models. In the parameter estimation of mean reverting model using GMM, it is known that the results are easy to be influenced by an initial values, and it becomes often unstable. Recently, Ahangarani(2005) employed maximum likelihood method for parameter esti- mation and log likelihood ratio test for model selection, and Kawada(2007) implemented GMM and made model selection using the information criterion EIC(extended information criterion) for various short-term interest rate models. Another articles of the interest rate model, using Bayesian framework, Jones(2003) published study about nonlinear drift of the interest rate model in detail, and Gray(2005) studied continuous time short rate models and the parameters estimated by Markov chain Monte Carlo(MCMC) method. Sanford and Martin(2006) made estimation using MCMC algorithm and model selection is made by Bayes factors for each model calculated using Savage-Dickey density ratio. In addition, a recent study by Hong and Lin(2006) examined a variety of short-term interest rate mod- els including the single-factor diffusion models, GARCH models, Markov regime-switching models and jump-diffusion models for Chinese rates. However, more useful models which capture the dynamics of the short-term interest rate are needed. In this paper, we suggest two hierarchical Bayes models based on mean reverting model. The parameters of the models are treated as random variables so that we have to consider appropriate prior distributions for them. By regarding parameters as random variables, we can consider that model construction and estimation involve necessarily some uncertainty and utilize the prior information of interest rate. In the first hierarchical Bayes model, we assume that volatility is constant, and in the second one, it depends on the

In the financial world, the thing that is interesting for investors today is to predict a reasonable Asian Call Option price that does not cause the seller or buyer of the option to experience losses. The constant interest assumption is more often used by previous research as an assumption in predicting the price of Asian Call Options. This is not in line with the fact that interest rate movements are not constant. The use of incorrect assumptions will affect the accuracy of prediction results. In overcoming this problem, this study aims to predict the price of Asian Call Options with non-constant interest rates using Monte Carlo simulation. The non-constant interest rate model used is Cox-Ingersoll-Ross (CIR) because this model produces positive interest rates. This study begins with a screening of Normally distributed interest rate data. The data is used to determine the parameters of the CIR interest rate model. Next, an Asian Call Option price simulation with non-constant interest rates was carried out and ended by analyzing a graph of the Asian Call Option price simulation results with non-constant interest rates. The simulated price result of the Asian Call Option with non-constant interest rates converged at the value of $170.82. Based on the price chart of Asian Call Options with different strike prices, the larger the strike price causes, the larger the Asian Call Option price, which corresponds to the price characteristics of the Asian Call Option. In addition, by extending the maturity period, the price of Asian Call Options with non-constant interest rates is greater according to the price characteristics of Asian Call Options.

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis.

The impact of crisis periods and monetary decisions of the Fed and the ECB on the sovereign yield curve network

This paper develops and estimates an interest rate model with investor attitude factors, which are extracted by a text mining method. First, we consider two contrastive attitudes (optimistic versus conservative) towards uncertainties about Brownian motions driving economy, develop an interest rate model, and obtain an empirical framework of the economy consisting of permanent and transitory factors. Second, we apply the framework to a bond market under extremely low interest rate environment in recent years, and show that our three-factor model with level, steepening and flattening factors based on different investor attitudes is capable of explaining the yield curve in the Japanese government bond (JGB) markets. Third, text mining of a large text base of daily financial news reports enables us to distinguish between steepening and flattening factors, and from these textual data we can identify events and economic conditions that are associated with the steepening and flattening factors. We then estimate the yield curve and three factors with frequencies of relevant word groups chosen from textual data in addition to observed interest rates. Finally, we show that the estimated three factors, extracted only from the bond market data, are able to explain the movement in stock markets, in particular Nikkei 225 index.

EMPIRICAL STUDIES ON INTEREST RATE DERIVATIVES by Xudong Sun Dr. Hongtao Yang, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas, USA Interest rate models are the building blocks of nancial market and the interest rate derivatives market is the largest derivatives market in the world. In this dissertation, we shall focus on numerical pricing of interest rate derivatives, estimating model parameters by Kalman lter, and studying various models empirically. We shall propose a frontxing nite element method to price the American put option under the quadratic term structure framework and compare it with a trinomial tree method and common nite element method. Numerical test results show the superiority of our frontxing nite element method in the aspects of computing the option and free boundary simultaneously with high accuracy. We shall also employ the Kalman lter and its variant techniques to estimate parameters of the a ne term structure models as well as quadratic term structure models. Various comparisons of di erent Kalman lter performance and both the in-sample t and out-sample t for Monte Carlo simulations as well as real treasury yield data are presented. In addition, we shall propose a general one-factor interest rate model and apply a homotopy perturbation method to valuate bond prices. One of the attractive qualities of the approximated solution of homotopy perturbation method is its fast speed of achieving the same accuracy compared to the tree method.

The article examines the application of the Principal Component Analysis (PCA) and machine learning method, the Long Short-Term Memory (LSTM), in the prediction of the yield curve for Poland. The PCA was applied to decompose the yield curve, forecast its components using the LSTM, and obtain the yield curve predictions upon recomposition. The results from the PCA-LSTM model were compared to predictions generated directly by the LSTM model, simple autoregression and random walk, which serves as a benchmark. Overall, LSTM predictions are the most accurate with PCA-LSTM being a close second, nonetheless PCA-LSTM is more accurate in short-term forecasting of interest rates at long maturities. Both methods outperform the benchmark, while autoregression usually underperforms. For these reasons, the PCA-LSTM as well as the LSTM can be useful in interest rate management or building trading strategies. The PCA-LSTM has the advantage that it can focus on particular components of the yield curve, such as variability of the yield curve’s level or steepness.

Out-of-Sample Performance of Spot Interest Rate Models

Dynamics of Market Anomalies and Measurement Errors of Risk-Free Interest Rates

Dynamics of Market Anomalies and Measurement Errors of Risk-Free Interest Rates

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

Spillover and risk transmission between the term structure of the US interest rates and Islamic equities

The Term Structure of Interest Rates in a DSGE Model