SINGLE-FACTOR DURATION MODELS: CANADIAN TESTS

Single-factor duration models of bond returns are derived from an underlying stochastic process of the term structure of interest rates. It is shown that beta in these models is a function of the parameters of the stochastic process and of implied measures of duration. Using unsmoothed Canadian monthly prices on default-free government bonds, the single-factor duration model is found to perform well from 1963 to 1986, but the hypothesis of stationarity of the duration-based bond returns model for the period cannot be accepted. Some of the underlying stochastic processes imply stationary models and some of them imply nonstationary bond return models. The models of this paper open the door to a variety of linear bond return models having a strong theoretical support based on a theory of the stochastic motion of the term structure.     

Stochastic durations,the convexity effect,and the impact of interest rate changes

This article shows that the equilibrium models of bond pricing do not preclude arbitrage opportunities caused by convexity. Consequently, stochastic durations derived from these models are limited in their ability to act as interest rate risk measures. The research of the present article makes use of an intertemporal utility maximization framework to determine the conditions under which duration is an adequate interest rate risk measure. Additionally, we show that zero coupon bonds satisfy those equilibrium conditions, whereas coupon bonds or bond portfolios do not as a result of the convexity effect. The results are supported by empirical evidence, which confirms the influence of convexity on the deviation of coupon bond returns from equilibrium.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stochastic risk premiums,stochastic skewness in currency options,and stochastic discount factors in international economies

We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using time-series returns and option prices on three currency pairs that form a triangular relation. Estimation shows that the average risk premium in Japan is larger than that in the US or the UK, the global risk premium is more persistent and volatile than the country-specific risk premiums, and investors respond differently to different shocks. We also identify high-frequency jumps in each economy but find that only downside jumps are priced. Finally, our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals.     

Structural models of credit risk are useful: Evidence from hedge ratios on corporate bonds

Structural models of credit risk provide poor predictions of bond prices. We show that, despite this, they provide quite accurate predictions of the sensitivity of corporate bond returns to changes in the value of equity (hedge ratios). This is important since it suggests that the poor performance of structural models may have more to do with the influence of non-credit factors rather than their failure to capture the credit exposure of corporate debt. The main result of this paper is that even the simplest of the structural models [Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29, 449–470] produces hedge ratios that are not rejected in time-series tests. However, we find that the Merton model (with or without stochastic interest rates) does not capture the interest rate sensitivity of corporate debt, which is substantially lower than would be expected from conventional duration measures. The paper also shows that corporate bond prices are related to a number of market-wide factors such as the Fama-French SMB (small minus big) factor in a way that is not predicted by structural models.     

Model-free hedge ratios and scale-invariant models

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price–volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.     

Pure jump Lévy processes for asset price modelling

The goal of the paper is to show that some types of Lévy processes such as the hyperbolic motion and the CGMY are particularly suitable for asset price modelling and option pricing. We wish to review some fundamental mathematic properties of Lévy distributions, such as the one of infinite divisibility, and how they translate observed features of asset price returns. We explain how these processes are related to Brownian motion, the central process in finance, through stochastic time changes which can in turn be interpreted as a measure of the economic activity. Lastly, we focus on two particular classes of pure jump Lévy processes, the generalized hyperbolic model and the CGMY models, and report on the goodness of fit obtained both on stock prices and option prices.     

Portfolio Selection in Stochastic Environments

In this article, I explicitly solve dynamic portfolio choiceproblems, up to the solution of an ordinary differential equation(ODE), when the asset returns are quadratic and the agent hasa constant relative risk aversion (CRRA) coefficient. My solutionincludes as special cases many existing explicit solutions ofdynamic portfolio choice problems. I also present three applicationsthat are not in the literature. Application 1 is the bond portfolioselection problem when bond returns are described by "quadraticterm structure models." Application 2 is the stock portfolioselection problem when stock return volatility is stochasticas in Heston model. Application 3 is a bond and stock portfolioselection problem when the interest rate is stochastic and stockreturns display stochastic volatility. (JEL G11)     

An examination of alternative CAPM-based models in UK stock returns

We evaluate the performance of unconditional and conditional versions of seven stochastic discount factor models in UK stock returns between January 1975 and December 2001. We find that the conditional four-moment capital asset pricing model (CAPM) has the best performance among the models we consider in terms of the lowest [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 591–607] distance measure and explaining the time-series predictability of industry portfolio excess returns. Conditional models also do a better job than unconditional models. However we find that the superior performance of the conditional four-moment CAPM, and conditional models in general, arises in part due to overfitting the data.     

Stock and bond returns with Moody Investors

We present a tractable, linear model for the simultaneous pricing of stock and bond returns that incorporates stochastic risk aversion. In this model, analytic solutions for endogenous stock and bond prices and returns are readily calculated. After estimating the parameters of the model by the general method of moments, we investigate a series of classic puzzles of the empirical asset pricing literature. In particular, our model is shown to jointly accommodate the mean and volatility of equity and long term bond risk premia as well as salient features of the nominal short rate, the dividend yield, and the term spread. Also, the model matches the evidence for predictability of excess stock and bond returns. However, the stock–bond return correlation implied by the model is somewhat higher than that in the data.     

BOND PORTFOLIO IMMUNIZATION: TESTS OF MATURITY, ONE- AND TWO-FACTOR DURATION MATCHING STRATEGIES

This paper provides additional evidence on the usefulness of duration as a strategy tool by developing a two-factor duration model and by using a reasonably reliable database to compare empirically the relative performance of maturity, one-factor duration, and two-factor duration matching strategies in immunizing portfolios of default-free and option-free bonds against interest rate risk. The results suggest that, on average, duration models, even for arbitrarily assumed simple stochastic processes, are more accurate than maturity models and that increased accuracy may be achieved by increasing the length of the planning period and the number of factors in the model.     

U.S. stock market crash risk, 1926–2010

This paper examines how well alternate time-changed Lévy processes capture stochastic volatility and the substantial outliers observed in U.S. stock market returns over the past 85 years. The autocorrelation of daily stock market returns varies substantially over time, necessitating an additional state variable when analyzing historical data. I estimate various one- and two-factor stochastic volatility/Lévy models with time-varying autocorrelation via extensions of the Bates (2006) methodology that provide filtered daily estimates of volatility and autocorrelation. The paper explores option pricing implications, including for the Volatility Index (VIX) during the recent financial crisis.     

The independence axiom and asset returns

This paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal asset-pricing framework. The resulting models are amenable to empirical analysis using market data and standard Euler equation methods. We are thereby able to provide the first nonlaboratory-based evidence regarding the usefulness of several new theories of risk preference for addressing standard problems in dynamic economics. Using both stock and bond returns data, we find that a model incorporating risk preferences that exhibit first-order risk aversion accounts for significantly more of the mean and autocorrelation properties of the data than models that exhibit only second-order risk aversion. Unlike the latter class of models which require parameter estimates that are outside of the admissible parameter space, e.g., negative rates of time preference, the model with first-order risk aversion generates point estimates that are economically meaningful. We also examine the relationship between first-order risk aversion and models that employ exogenous stochastic switching processes for consumption growth.     

Keep on smiling? The pricing of Quanto options when all covariances are stochastic

The paper introduces a model for the joint dynamics of asset prices which can capture both a stochastic correlation between stock returns as well as between stock returns and volatilities (stochastic leverage). By relying on two factors for stochastic volatility, the model allows for stochastic leverage and is thus able to explain time-varying slopes of the smiles. The use of Wishart processes for the covariance matrix of returns enables the model to also capture stochastic correlations between the assets. Our model offers an integrated pricing approach for both Quanto and plain-vanilla options on the stock as well as the foreign exchange rate. We derive semi-closed form solutions for option prices and analyze the impact of state variables. Quanto options offer a significant exposure to the stochastic covariance between stock prices and exchange rates. In contrast to standard models, the smile of stock options, the smile of currency options, and the price differences between Quanto options and plain-vanilla options can change independently of each other.     

Jump-diffusion volatility models for variance swaps: An empirical performance analysis

This paper studies a class of tractable jump-diffusion models, including stochastic volatility models with various specifications of jump intensity for stock returns and variance processes. We employ the Markov chain Monte Carlo (MCMC) method to implement model estimation, and investigate the performance of all models in capturing the term structure of variance swap rates and fitting the dynamics of stock returns. It is evident that the stochastic volatility models, equipped with self-exciting jumps in the spot variance and linearly-dependent jumps in the central-tendency variance, can produce consistent model estimates, aptly explain the stylized facts in variance swaps, and boost pricing performance. Moreover, our empirical results show that large self-exciting jumps in the spot variance, as an independent risk source, facilitate term structure modeling for variance swaps, whilst the central-tendency variance may jump with small sizes, but signaling substantial regime changes in the long run. Both types of jumps occur infrequently, and are more related to market turmoils over the period from 2008 to 2021.     

Box-Cox stochastic volatility models with heavy-tails and correlated errors

This paper presents a Markov chain Monte Carlo (MCMC) algorithm to estimate parameters and latent stochastic processes in the asymmetric stochastic volatility (SV) model, in which the Box-Cox transformation of the squared volatility follows an autoregressive Gaussian distribution and the marginal density of asset returns has heavy-tails. We employed the Bayes factor and the Bayesian information criterion (BIC) to examine whether the Box-Cox transformation of squared volatility is favored against the log-transformation. When applying the heavy-tailed asymmetric Box-Cox transformed SV model, three competing SV models and the t-GARCH(1,1) model to continuously compounded daily returns of the Australian stock index, we find that the Box-Cox transformation of squared volatility is strongly favored by Bayes factors and BIC against the log-transformation. While both criteria strongly favor the t-GARCH(1,1) model against the heavy-tailed asymmetric Box-Cox transformed SV model and the other three competing SV models, we find that SV models fit the data better than the t-GARCH(1,1) model based on a measure of closeness between the distribution of the fitted residuals and the distribution of the model disturbance. When our model and its competing models are applied to daily returns of another five stock indices, we find that in terms of SV models, the Box-Cox transformation of squared volatility is strongly favored against the log-transformation for the five data sets.     

Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility

Most term structure models assume bond markets are complete, that is, that all fixed income derivatives can be perfectly replicated using solely bonds. How ever, we find that, in practice, swap rates have limited explanatory power for returns on at–the–money straddles—portfolios mainly exposed to volatility risk. We term this empirical feature "unspanned stochastic volatility" (USV). While USV can be captured within an HJM framework, we demonstrate that bivariate models cannot exhibit USV. We determine necessary and sufficient conditions for trivariate Markov affine systems to exhibit USV. For such USV models, bonds alone may not be sufficient to identify all parameters. Rather, derivatives are needed.     

Una medida de eficiencia de mercado. Un enfoque de teoría de la información

In this paper, based on the concept of Shannon entropy, we propose a measure of market efficiency by using the empirical density function of returns. Under certain conditions of ergodicity and stationarity, it is shown that the sample entropy converges to the entropy of the dominant state. It is also shown that the proposed measure is consistent with some of the axioms from Artzner et al. (1999) of a coherent risk measure. Bounds on the behavior of entropy as a measure of efficiency on the basis of extreme cases are also established; going from deterministic processes to pure white noise stochastic processes. Finally, for illustrative purposes, we carry out several applications of the proposed efficiency measure of capital to different markets: DJIA, S&P500, FTSE100 and IPC.     

The time-varying asymmetry of exchange rate returns: A stochastic volatility – stochastic skewness model

While the time-varying volatility of financial returns has been extensively modelled, most existing stochastic volatility models either assume a constant degree of return shock asymmetry or impose symmetric model innovations. However, accounting for time-varying asymmetry as a measure of crash risk is important for both investors and policy makers. This paper extends a standard stochastic volatility model to allow for time-varying skewness of the return innovations. We estimate the model by extensions of traditional Markov Chain Monte Carlo (MCMC) methods for stochastic volatility models. When applying this model to the returns of four major exchange rates, skewness is found to vary substantially over time. In addition, stochastic skewness can help to improve forecasts of risk measures. Finally, the results support a potential link between carry trading and crash risk.     

Fundamental Economic Variables,Expected Returns,and Bond Fund Performance

In this article, we develop relative pricing (APT) models that are successful in explaining expected returns in the bond market. We utilize indexes as well as unanticipated changes in economic variables as factors driving security returns. An innovation in this article is the measurement of the economic factors as changes in forecasts. The return indexes are the most important variables in explaining the time series of returns. However, the addition of the economic variables leads to a large improvement in the explanation of the cross-section of expected returns. We utilize our relative pricing models to examine the performance of bond funds.