Do Bonds Span Volatility Risk in the U.S. Treasury Market? A Specification test for Affine Term Structure Models

We investigate whether bonds span the volatility risk in the U.S. Treasury market, as predicted by most 'affine' term structure models. To this end, we construct powerful and model-free empirical measures of the quadratic yield variation for a cross-section of fixed-maturity zero-coupon bonds ("realized yield volatility") through the use of high-frequency data. We find that the yield curve fails to span yield volatility, as the systematic volatility factors are largely unrelated to the cross-section of yields. We conclude that a broad class of affine diffusive, Gaussian-quadratic and affine jump-diffusive models is incapable of accommodating the observed yield volatility dynamics. An important implication is that the bond markets per se are incomplete and yield volatility risk cannot be hedged by taking positions solely in the Treasury bond market. We also advocate using the empirical realized yield volatility measures more broadly as a basis for specification testing and (parametric) model selection within the term structure literature.

Realized volatility

Realized volatility is a nonparametric ex-post estimate of the return variation. The most obvious realized volatility measure is the sum of finely-sampled squared return realizations over a fixed time interval. In a frictionless market the estimate achieves consistency for the underlying quadratic return variation when returns are sampled at increasingly higher frequency. We begin with an account of how and why the procedure works in a simplified setting and then extend the discussion to a more general framework. Along the way we clarify how the realized volatility and quadratic return variation relate to the more commonly applied concept of conditional return variance. We then review a set of related and useful notions of return variation along with practical measurement issues (e.g., discretization error and microstructure noise) before briefly touching on the existing empirical applications.Stochastic analysis

Chiuse poetiche e senso della fine. Spunti per una tipologia

Ricordata la sfuggente polisemia del concetto di fine, lo studio (che privilegia l'analisi delle strutture formali, con rilievi di stilistica e metrica) tratta due questioni di carattere generale: quando un testo possa dirsi compiuto e cosa rafforzi una chiusa. Dapprima viene fissata, anche attraverso un'analisi contrastiva, la differenza tra compiutezza e scarto conclusivo, tra effetti di saturazione ed effetti più propriamente clausolari; quindi vengono definite, cercando di valutarne la portata, alcune tra le principali tecniche di intensificazione della chiusa poetica; tecniche sostanzialmente riconducibili a tre ordini di fenomeni: 1) chiuse intensificate da sottolineature tematiche e suggestioni iconiche; 2) chiuse scandite attraverso figure di ricorrenza e variazione; 3) chiuse rilevate da una strategica distribuzione delle informazioni, attraverso dinamiche di attesa e sorpresa, di tensione e soluzione. La varia casistica è illustrata con esempi tratti principalmente, ma non solo, dalla letteratura italiana (e in particolare dalla poesia del Novecento), senza però circoscrivere preliminarmente un corpus omogeneo, coll'intento di mettere in luce come meccanismi conclusivi analoghi ritornino in testi diversissimi per genere ed epoca.Reviewing the ever-fugitive concept of fine, the study (which prioritises the analysis of formal structures, with particular emphasis being given to stylistics and metrics) deals with two questions of a general character: when can a text can be said to be complete, and what elements reinforce a closure? First, also through contrastive analysis, the article sets out the difference between completion and discarded conclusion, between effects of saturation and effects that more properly form part of closure. Thus the author, in an effort to evaluate the scope of this, defines some of the main techniques of the intensification of poetic closure, techniques that are substantially aimed at analysing three types of phenomenon: 1) closures that intensify thematic emphasis and iconic suggestion; 2) closures articulated through figures of recurrence and variation; 3) closures that highlight a strategic distribution of information, through the dynamics of expectation and surprise, of tension and solution. The various types are illustrated with examples taken largely, though not exclusively, from Italian literature (and, in particular, the poetry of the Novecento), without, however, circumscribing an essentially homogenous corpus. The intention is to shed light on the ways in which analogous mechanisms of conclusion recur in the most diverse of texts, throughout different genres and periods

Stochastic volatility

Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.Stochastic analysis

Can Standard Preferences Explain the Prices of out of the Money S&P 500 Put Options

Prior to the stock market crash of 1987, Black-Scholes implied volatilities of S&P 500 index options were relatively constant across moneyness. Since the crash, however, deep out-of-the-money S&P 500 put options have become %u2018expensive%u2019 relative to the Black-Scholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has %u2018standard preferences%u2019 and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the %u2018volatility smirk%u2019 can be rationalized if the agent is endowed with Epstein-Zin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both at-the-money and deep out-of-the-money puts, and the level of the risk-free rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in the volatility smirk that has maintained since the 1987 market crash. To this end, we extend the model to a Bayesian setting in which the agent updates her beliefs about the average jump size in the event of a jump. Note that such beliefs only update at crash dates, and hence can explain why the volatility smirk has not diminished over the last eighteen years. We find that the model can capture the shape of the implied volatility curve both pre- and post-crash while maintaining reasonable estimates for expected returns, price-dividend ratios, and risk-free rates.

Portfolio choice over the life-cycle when the stock and labor markets are cointegrated

We study portfolio choice when labor income and dividends are cointegrated. Economically plausible calibrations suggest young investors should take substantial short positions in the stock market. Because of cointegration the young agent's human capital effectively becomes.Portfolio management ; Stock market ; Labor market

Local well-posedness of nonlocal Burgers equations

International audienceThis paper is concerned with nonlocal generalizations of the inviscid Burgers equation arising as amplitude equations for weakly nonlinear surface waves. Under homogeneity and stability assumptions on the involved kernel it is shown that the Cauchy problem is locally well-posed in $H^2(\R)$, and a blow-up criterion is derived. The proof is based on a priori estimates without loss of derivatives, and on a regularization of both the equation and the initial data