US Treasury Yield Research Articles

Canonical Least-Squares Monte Carlo: Empirical Evidences from S&P 100 Index and IBM Puts

This paper tests empirically the recently proposed canonical least-squares Monte-Carlo (CLM) method for pricing American options. Market data used are daily last prices for the American style S&P 100 Index puts (OEX puts) and IBM puts from 30 July 2008 to 30 January 2009, the period of which covers the US financial crisis of 2008. Unlike what have been done in many other similar empirical studies, rates interpolated from the US Treasury yield curve are used, and dividends, a continuous constant yield for the S&P 100 Index and a fixed cash amount for the IBM common stock, are taken into consideration. Compared with the benchmark prices from finite difference using historic volatilities, CLM outperforms in almost all twelve categories of moneyness and maturity for both OEX and IBM puts, and is shown to be a viable alternative for pricing American style options.

The role of no-arbitrage on forecasting: Lessons from a parametric term structure model

Parametric term structure models have been successfully applied to numerous problems in fixed income markets, including pricing, hedging, managing risk, as well as to the study of monetary policy implications. In turn, dynamic term structure models, equipped with stronger economic structure, have been mainly adopted to price derivatives and explain empirical stylized facts. In this paper, we combine flavors of those two classes of models to test whether no-arbitrage affects forecasting. We construct cross-sectional (allowing arbitrages) and arbitrage-free versions of a parametric polynomial model to analyze how well they predict out-of-sample interest rates. Based on US Treasury yield data, we find that no-arbitrage restrictions significantly improve forecasts. Arbitrage-free versions achieve overall smaller biases and root mean square errors for most maturities and forecasting horizons. Furthermore, a decomposition of forecasts into forward-rates and holding return premia indicates that the superior performance of no-arbitrage versions is due to a better identification of bond risk premium.

Input modelling for financial simulations using the bootstrap

Inputs are the fuel that powers simulations. If one is designing a new system or product, inputs are scenarios representing the conditions with which the new system must cope. The need for large numbers of realistic scenarios applies to every domain in which simulation is used as part of the system design process. To be useful, scenarios should mimic the underlying data generating process by reflecting the auto- and cross-correlations of the historical data. We describe a new scenario generation procedure based on the nearest-neighbour bootstrap. We also propose a new performance evaluation criterion for multivariate time-series scenario generators based on the distribution of a composite correlation discrepancy measure. We illustrate the new method and measure by generating simulated scenarios for the US Treasury yield curve.

Over-confidence and the Probability Assessment Ability of Retail Investors

This study directly tests of the ability of retail investors to assess the probability of pay-offs to various financial assets over short term (7 days) and medium term (3 month) periods. Psychology studies have demonstrated that decision makers are typically over-confident in their ability to assess uncertainty (Lichtenstein, Fischhoff and Phillips 1982, Yates 1990). Daniel, Hirschleifer and Subrahmanyam 1998, Odean 1998, Scheinkman and Xiong 2003, and others, have studied the effect of investor over-confidence on financial market equilbria. However, it is questionable whether the results of the pyschology studies are relevant to decision making by investors in financial markets. The psychology studies show that the level of over-confidence exhibited by decision makers is highly dependent on the context of the assessment of uncertainty. The level of over-confidence varies with: the difficulty of the assessment; the rarity of the event in question; and the level of training of the assessors. Moreover, the psychology studies of over-confidence have not studied the assessment of uncertainty of financial asset pay-offs. Instead, they have focused on weather forecasting (Murphy and Winkler 1977 ), medical prognosis (Murphy and Poses 1993) and other contexts. We collect from 309 participants (mostly MBA students) their subjective assessments of the probabilities that particular assets will increase in price over a defined period. Each Monday, before markets open, participants assess the probabilities of 3 events that could occur over the next week (the SP the 10 year US Treasury yield rises; the Brent price of crude oil rises) and 3 events that could occur over the next 3 months (a specified industry and 2 individual stocks would outperform the S&P500 over 3 months). A total of 15,576 probability assessments are collected over 26 weeks. The participants exhibit a high level of over-confidence in their ability to assess the probabilities of directional changes in asset prices. However, in contrast to assumptions in the finance literature, the over-confidence is not more severe in males than females. Participants who have worked in the investment management industry exhibit less over-confidence. Over 80 percent of the participants own stocks directly. Our sample of retail investors do not provide probability assessments that have more refinement than assessments based on the long-run average of weekly changes. Thereby providing further support for the efficient market hypothesis.

Markov Representation of the Heath-Jarrow-Morton Model

This paper provides a derivation of an arbitrage free approximation to any HJM model as a continuous time Markov model with a finite number of state variables. Arbitrage freedom is maintained exactly at the cost of approximating any particular term structure of volatility. Using a large enough set of state variables, any ``reasonable'' term structure of volatility can be approximated to any desired level of accuracy in a systematic fashion. The state variables fall into two sets. One set specifies the values of a finite number of forward rates of different maturities. The other set determines how to ``interpolate'' to other maturities; their values depend on the integrated covariances of the variables in the first set. A restriction of the model to volatility term structures dependent only on time and relative maturity is derived: a general volatility structure with this property is approximated as a sum of exponentials in the relative maturity, weighted by arbitrary functions of the time and the current term structure. A three factor, 19 state version of this model is fitted to 12 years of weekly US Treasury yield curve data. The results indicate that it is possible to achieve an accurate representation of the empirical term structure factors with only two or three exponential terms per factor. NOTE: This paper is available in TeX (with macros) or postscript form.

The maturity structure of term premia with time-varying expected returns

This paper analyzes the maturity structure of term premia using McCulloch’s US Treasury yield curve data from 1953–91, allowing expected returns to vary across time. One, 3, 6, and 12 month holding period returns on maturities up to 5 years are projected on 3 ex ante variables to compute time-varying expected returns, and simulations are employed to generate distributions of conditionally expected return premia. The likelihood of expected returns monotonically increasing in maturity (as implied by the liquidity preference hypothesis) is relatively high when the yield curve is steep and interest rates are high, and with longer holding periods, but low in other cases. The hypothesis that intermediate maturity bonds have the highest expected returns (a “hump-shaped” maturity-return pattern) around the onset of recessions does not receive much support.