Interest Rate Term Structure Model Research Articles

The Practicality of Vasicek Model in China’s Financial Market

In the changing financial market, the price of financial products fluctuates continuously over time. The study of the static term structure of the interest rate on the market can no longer satisfy the actual needs, and the dynamic model is imperative. Compared with the static term structure, the dynamic model introduces a stochastic differential term on the basis of the static term structure model of interest rate. This paper shows some relevant models including Vasicek Model, Single-Factor Dynamic Model, Multi-Factor Dynamic Model, and Kalman Filter method. To conclude, in the multi-factor dynamic interest rate term structure model, Kalman Filter has many benefits. However, it still has actual limitations. The multi-factor Vasicek model still needs some analysis to find the error and do the correction. In the research of bond pricing, risk management, and other aspects, the multi-factor model should be the main direction.

Pricing analysis of Dong Wu Su Yuan Industry based on the pricing model of public REITs

Given that infrastructure public REITs in China are still in the early stage of development, this paper firstly reviews their current status from relevant sources and briefly describes their definitions, development status and main characteristics. The option-adjusted spread method based on Monte Carlo simulation is chosen as the pricing model. The term adjusted spread method needs to consider the interest rate term structure, so the CIR model is used as the interest rate term structure model for interest rate forecasting, and the three CIR parameter values obtained by fitting are brought into the CIR model using Monte Carlo method simulation to obtain 1000 forward interest rate paths, and the spot interest rate is obtained according to the forward interest rate curve path, and the spot interest rate is used to combine with the option adjusted spread OAS to discount the 1000 present values. The average value of the 1000 present values is the pricing result. Comparing the pricing result with the market value, it is found that the two are basically equal. This shows that the option-adjusted spread method based on Monte Carlo simulation can evaluate the value of public REITs more scientifically and reasonably.

Using Particle Swarm Optimization Algorithm to Calibrate the Term Structure Model

One of the advantages of stochastic differential equations (SDE) is that they can follow a variety of different trends so that they can establish complex dynamic systems in the economic and financial fields. Although some estimation methods have been proposed to identify the unknown parameters in virtue of the results in the SDE model to speed up the process, these solutions only focus on using explicit approach to solve SDEs, and therefore they are not reliable to deal with data source merged being large and varied. Thus, this study makes progress in creating a new implicit way to fill in the gaps of accurately calibrating the unknown parameters in the SDE model. Essentially, the primary goal of the article is to generate rigid SDE simulation. Meanwhile, the particle swarm optimization method serves a purpose to search and simultaneously obtain the optimal estimation of the model unknown parameters in the complicated experiment of parameter space in an effective way. Finally, in an interest rate term structure model, it is verified that the method effectively deals with parameter estimation in the SDE model.

Short Rate Dynamics: A Fed Funds and SOFR perspective

The Secured Overnight Funding Rate (SOFR) is becoming the main Risk–Free Rate benchmark in US dollars, thus interest rate term structure models need to be updated to reflect the key features exhibited by the dynamics of SOFR and the forward rates implied by SOFR futures. Historically, interest rate term structure modelling has been based on rates of substantially longer time to maturity than overnight, but with SOFR the overnight rate now is the primary market observable. This means that the empirical idiosyncrasies of the overnight rate cannot be ignored when constructing interest rate models in a SOFR–based world. As a rate reflecting transactions in the Treasury overnight repurchase market, the dynamics of SOFR are closely linked to the dynamics Effective Federal Funds Rate (EFFR), which is the interest rate most directly impacted by US monetary policy target rate decisions. Therefore, these rates feature jumps at known times (Federal Open Market Committee meeting dates), and market expectations of these jumps are reflected in prices for futures written on these rates. On the other hand, forward rates implied by Fed Funds and SOFR futures continue to evolve diffusively. The model presented in this paper reflects the key empirical features of SOFR dynamics and is calibrated to futures prices. In particular, the model reconciles diffusive forward rate dynamics with piecewise constant paths of the target short rate.

Term structure of interest rates: Modelling the risk premium using a two horizons framework

• We propose a portfolio choice model of interest rate term structure with a preference parameter for alternative horizons. • The riskless asset is the one whose duration coincides with the investor’s horizon; any other duration implies a risk exposure. • The investor compares at the 3 and 6-month horizons the market risk premia to those they require to take risky positions. • US 3 and 6-month T-Bill rates stand for short and long rates while the expected short rate is provided by survey data. • The preference parameter significantly varies over time and the market favors the short horizon by two-thirds on average. We propose a two-horizon interest rate term structure model where the maturity of the riskless rate is the one of the debt security whose duration equals investor's desired horizon. Our framework thus relaxes the usual assumptions of the literature that the riskless rate is unchangingly the short period rate. A representative investor compares at each of the 3- and the 6-month horizons the risk premium offered by the market and the one they require to take a risky position, the latter premium being determined by the portfolio choice theory. Due to market frictions, the deviation between the offered and required risk premium evolves according to a mean-reverting process. Using 3-month ahead survey-based expectations of the US 3-month Treasury Bill rate, we employ Kalman filtering to estimate the market risk premium where the preference parameter of investors for alternative horizons is time-varying. We find that the market comprises both a group of agents with 3-month preferred horizon and a group of agents with 6-month preferred horizon with a weigh of two-thirds for the first group.

Deep Option Pricing - Term Structure Models

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options within the setting of interest rate term structure models. This aims to accelerate existing numerical methods which is important for applications like historical VaR or exposure calculation being used in financial institutions. With ANNs being a universal function approximation method, this method trains an ANN on synthetically generated data including term structures of yield and volatility. Then, within an VaR or exposure calculation instead of applying costly numerical methods for the financial model, the engine runs the trained ANN. This is faster and more efficient and allows (a) considering term structures of yields, (b) term structures of volatilities and (c) trade interpolation. We outline the generation of the training data, the neural net selection and propose further methods for optimization. In particular we consider a control variate method and the application of no-arbitrage conditions and regularization to the cost function used for learning and calibration. Finally, we test our approach on the Hull-White model with time-dependent term structure for volatility and the the Trolle-Schwartz model. The latter adds an un-spanned stochastic volatility to the rates dynamic. The numerical results show that the ANN solution, especially the one with the control variate, is accurate and reduces the computing time significantly.

Real-World Forward Rate Dynamics With Affine Realizations

We investigate the existence of affine realizations for Lévy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven by Wiener processes, all results obtained under the risk-neutral approach concerning the existence of affine realizations are transferred to the general case. A similar result holds true for models driven by compound Poisson processes with finite jump size distributions. However, in the presence of jumps with infinite activity we obtain severe restrictions on the structure of the market price of risk; typically, it must even be constant.

The use of Bayes factors to compare interest rate term structure models

Studies of the term structure of interest rates try to explain the relationship between the yield to maturity on zero-coupon bonds and their time to maturity. Over the years, many theoretical models have been developed to explain the stylized facts of U.S. Treasury yields; however, model comparison, parameter estimation and hypothesis testing remain thorny issues. The purpose of this paper is to show that Bayesian methods and Markov Chain Monte Carlo (MCMC) methods, in particular, may help resolve a number of these problems, especially those related to model comparison. We use MCMC to compare the seminal models of Vasicek and Cox, Ingersoll and Ross (CIR). The most surprising result of our analysis is that one of these two models is almost 50 000 times more likely than the other. In contrast, results in the previous literature have been much more ambiguous because they are based on a variety of goodness-of-fit measures. A Monte Carlo study shows that these results are not spurious: the MCMC method is able to select the correct data generation model, whereas goodness-of-fit measures are virtually indistinguishable regardless of whether the data were generated from Vasicek or CIR.

Upper and lower bounds for convex value functions of derivative contracts

The aim of this paper is to compute upper and lower bounds for convex value functions of derivative contracts. Laprise et al. (2006) compute bounds for American-style vanilla options by selected portfolios of call options. We provide an alternative interpretation of their numerical procedure as a stochastic dynamic program for which the Bellman value function is approximated by selected piecewise linear interpolations at each decision date. The stochastic dynamic program does not (directly) depend on portfolios of call options, but rather on a key ingredient: some transition parameters of the underlying asset. More in line with the literature on dynamic programming, our procedure is contract free and is well designed to accommodate all one-dimensional convex value functions of derivative contracts. In support of this, we revisit the numerical investigation of Laprise et al. (2006) and enlarge their findings to include options embedded in bonds under affine term-structure models of interest rates.

Analyzing interest rate risk: Stochastic volatility in the term structure of government bond yields

We propose a Nelson–Siegel type interest rate term structure model where the underlying yield factors follow autoregressive processes with stochastic volatility. The factor volatilities parsimoniously capture risk inherent to the term structure and are associated with the time-varying uncertainty of the yield curve’s level, slope and curvature. Estimating the model based on US government bond yields applying Markov chain Monte Carlo techniques we find that the factor volatilities follow highly persistent processes. We show that yield factors and factor volatilities are closely related to macroeconomic state variables as well as the conditional variances thereof.

Valuation of Guaranteed Annuity Options in Affine Term Structure Models

We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include stochastic duration approach, Edgeworth expansion and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.

Affine Realizations for Levy Driven Interest Rate Models with Real-World Forward Rate Dynamics

We investigate the existence of affine realizations for interest rate term structure models driven by Levy processes. Using as numeraire the growth optimal portfolio, we model the interest rate term structure under the real-world probability measure, and hence, we do not need the existence of an equivalent risk-neutral probability measure. Furthermore, we include finite dimensional external factors, thus admitting a stochastic volatility structure.

Introducing the Citi LMM Term Structure Model for Mortgages

Valuation of mortgage-backed securities pairs a prepayment model with a term-structure model of interest rates. While the prepayment model is crucial, the choice of the term-structure model matters as well. The article presents Citigroup’s Libor Market Model for MBS valuation and compares it to the short-rate term-structure model currently in production. The new LMM term-structure model improves control over the volatility and correlations structure of forward LIBORs. This leads to more realistic correlations of swap rates. The new model achieves a more accurate calibration to the entire volatility surface. The authors discuss consequences for serial correlation of swap rates and mortgage option volatility. The Mortgage Option-Adjusted Term Structure (MOATS) model, Citi’s approach to arbitrage-free mortgage rate modeling, has been re-implemented to work with LMM, retaining all desirable properties. The LMM produces wider OASs and longer durations than in the current model; the partial durations and vegas are comparable.

Real-world jump-diffusion term structure models

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event-driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and, for specific volatility structures, finite-dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate in a non-Markovian setting, a class of tractable affine term structures is derived where an equivalent risk-neutral probability measure may not exist.

Choice of Interest Rate Term Structure Models for Assets and Liability Management

This paper compares the pricing and hedging performance of the LMM model against twospot-rate models, namely Hull-White and Black-Karasinski, and the more recent SwapMarket Model from an Asset-Liability-Management (ALM) perspective. In contrast toprevious studies in the literature, our emphasis here is on ALM and we use hedgingperformance on Bermudan swaptions to proxy risk management outcome of long-termmortgage loans. Our tests involve calibrating the four interest rate models to Europeanswaption prices for EURO and USD over the period February 2005 to September 2007. Thecalibrated models are then used to price and hedge a constant 11-year Bermudan swaptionportfolio using a series of interest rate swaps and a 1-year holding-revision period. Ourempirical results show that, the calibrated parameters of all four models are stable and theirpricing errors are small and comparable. No single model dominates in the pricing exercise.The hedging performance of all four models is similar for the Euro market. For the USDmarket, the short rate models perform marginally better than SMM and LMM. The HWmodel is marginally better than BK model in terms of model parameter stability and smallerpricing and hedging errors.

Yield curve factors, term structure volatility, and bond risk premia

We introduce a Nelson-Siegel type interest rate term structure model with the underlying yield factors following autoregressive processes revealing time-varying stochastic volatility. The factor volatilities capture risk inherent to the term struc- ture and are associated with the time-varying uncertainty of the yield curve’s level, slope and curvature. Estimating the model based on U.S. government bond yields applying Markov chain Monte Carlo techniques we find that the yield factors and factor volatilities follow highly persistent processes. Using the extracted factors to explain one-year-ahead bond excess returns we observe that the slope and cur- vature yield factors contain the same explanatory power as the return-forecasting factor recently proposed by Cochrane and Piazzesi (2005). Moreover, we identify slope and curvature risk as important additional determinants of future excess returns. Finally, we illustrate that the yield and volatility factors are closely con- nected to variables reflecting macroeconomic activity, inflation, monetary policy and employment growth. It is shown that the extracted yield curve components have long-term prediction power for macroeconomic fundamentals.

Yield Curve Factors, Factor Volatilities, and the Predictability of Bond Excess Returns

We introduce a Nelson-Siegel type interest rate term structure model with the underlying yield factors following autoregressive processes revealing time-varying stochastic volatility. The factor volatilities capture risk inherent to the term structure and are associated with the time-varying uncertainty of the yield curve's level, slope and curvature. Estimating the model based on U.S. government bond yields applying Markov chain Monte Carlo techniques we find that the yield factors and factor volatilities follow highly persistent processes. Using the extracted factors to explain one-year-ahead bond excess returns we observe that the slope and curvature yield factors contain the same explanatory power as the return-forecasting factor recently proposed by Cochrane and Piazzesi (2005). Moreover, we identify slope and curvature risk as important additional determinants of future excess returns. Finally, we illustrate that the yield and volatility factors are closely connected to variables reflecting macroeconomic activity, inflation, monetary policy and employment growth. It is shown that the extracted yield curve components have long-term prediction power for macroeconomic fundamentals.

Choice of Interest Rate Term Structure Model for Assets and Liability Management

Choice of Interest Rate Term Structure Model for Assets and Liability Management

VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS

We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.

Some results on strong solutions of SDEs with applications to interest rate models

In this work, we investigate SDEs whose coefficients may depend on the entire past of the solution process. We introduce different Lipschitz-type conditions on the coefficients. It turns out that for existence and uniqueness of a strong solution it suffices to have Lipschitz continuity in mean, in a sense to be made precise. We then investigate when it suffices to have local Lipschitz conditions. Furthermore we consider the case of drift coefficients which are locally Lipschitz in mean. Finally we show how these results can be applied to prove existence and uniqueness of solutions in interest rate term structure models.