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## Rare Disasters and Asset Markets in the Twentieth Century

Barro, Robert
Fonte: MIT Press Publicador: MIT Press
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The potential for rare economic disasters explains a lot of asset-pricing puzzles. I calibrate disaster probabilities from the twentieth century global history, especially the sharp contractions associated with World War I, the Great Depression, and World War II. The puzzles that can be explained include the high equity premium, low risk-free rate, and volatile stock returns. Another mystery that may be resolved is why expected real interest rates were low in the United States during major wars, such as World War II. The model, an extension of work by Rietz, maintains the tractable framework of a representative agent, time-additive and isoelastic preferences, and complete markets. The results hold with i.i.d. shocks to productivity growth in a Lucas-tree type economy and also with the inclusion of capital formation.; Economics

## Idiosyncratic volatility, aggregate volatility risk, and the cross-section of returns

Barinov, Alexander (1981 - ); Schwert, G. William (1950 - )
Fonte: University of Rochester Publicador: University of Rochester
Tipo: Tese de Doutorado Formato: Number of Pages:ix, 145 leaves
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Thesis (Ph. D.)--University of Rochester. William E. Simon Graduate School of Business Administration, 2008.; The first chapter presents a simple real options model that explains why in cross-section high idiosyncratic volatility implies low future returns and why the value effect is stronger for high volatility firms. In the model, high idiosyncratic volatility makes growth options a hedge against aggregate volatility risk. Growth options become less sensitive to the underlying asset value as idiosyncratic volatility goes up. It cuts their betas and saves them from losses in volatile times that are usually recessions. Growth options value also positively depends on volatility. It makes them a natural hedge against volatility increases. In empirical tests, the aggregate volatility risk factor explains the idiosyncratic volatility discount and why it is stronger for growth firms. The aggregate volatility risk factor also partly explains the stronger value effect for high volatility firms. I also find that high volatility and growth firms have much lower betas in recessions than in booms. In the second chapter I show that the aggregate volatility risk factor (the BVIX factor) explains the well-known underperformance of small growth firms. The BVIX factor also reduces the underperformance of IPOs and SEOs by 45% and makes it statistically insignificant. The BVIX factor is unrelated to the investment factor proposed by Lyandres...

## Stochastic Volatility.

Ghysels, E.; Harvey, A.; Renault, E.
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 3941208 bytes; application/pdf
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This paper prepared for the Handbook of Statistics (Vol.14: Statistical Methods in Finance), surveys the subject of stochastic volatility. the following subjects are covered: volatility in financial markets (instantaneous volatility of asset returns, implied volatilities in option prices and related stylized facts), statistical modelling in discrete and continuous time and, finally, statistical inference (methods of moments, quasi-maximum likelihood, likelihood-based and bayesian methods and indirect inference).

## VaR and expected shortfall: A non-normal regime switching framework

Elliott, R.; Miao, H.
Fonte: IOP Publishing Ltd. Publicador: IOP Publishing Ltd.
Tipo: Artigo de Revista Científica
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We have developed a regime switching framework to compute the Value at Risk and Expected Shortfall measures. Although Value at Risk as a risk measure has been criticized by some researchers for lack of subadditivity, it is still a central tool in banking regulations and internal risk management in the finance industry. In contrast, Expected Shortfall is coherent and convex, so it is a better measure of risk than Value at Risk. Expected Shortfall is widely used in the insurance industry and has the potential to replace Value at Risk as a standard risk measure in the near future. We have proposed regime switching models to measure value at risk and expected shortfall for a single financial asset as well as financial portfolios. Our models capture the volatility clustering phenomenon and variance-independent variation in the higher moments by assuming the returns follow Student-t distributions.; Robert J. Elliott and Hong Miao

## Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

Kasa, Kenneth; Walker, Todd B.; Whiteman, Charles H.
Tipo: Trabalho em Andamento Formato: 296970 bytes; application/pdf
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This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions.

## On the economic link between asset prices and real activity

Peña Sánchez de Rivera, Juan Ignacio; Rodríguez, Rosa
Tipo: Trabalho em Andamento Formato: application/pdf
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This paper presents a model linking two financial markets (stocks and bonds) with the real business cycle, in the framework of the Consumption Capital Asset Pricing Model with Generalized Isoelastic Preferences. Besides interest rate term spread, the model includes a new variable to forecast economic activity: stock market term spread, which constitutes the slope of expected stock market returns. The empirical evidence documented in this paper suggests systematic relationships between the state of the business cycle and the shapes of two yield curves (interest rates and expected stock returns). Results are robust to changes in measures of economic growth, stock prices, interest rates and expectation-generating mechanisms.

## On the economic link between asset prices and real activity

Peña Sánchez de Rivera, Juan Ignacio; Rodríguez López, Rosa
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article Formato: application/pdf
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This paper presents a model linking two financial markets (stocks and bonds) with real business cycle, in the framework of the Consumption Capital Asset Pricing Model with Generalized Isoelastic Preferences. Besides interest rate term spread, the model includes a new variable to forecast economic activity: stock market term spread. This is the slope of expected stock market returns. The empirical evidence documented in this paper suggests systematic relationships between business cycle’s state and the shapes of two yield curves (interest rates and expected stock returns). Results are robust to changes in measures of economic growth, stock prices, interest rates and expectations generating mechanisms.; The authors are from Universidad Carlos III de Madrid. Partial financial support was provided by DGICYT grants PB98-0030, BEC2002-0279 and SEC2003-06457. Seminar participants at various universities and conferences provided useful comments. The authors thank the anonymous referee who provided astute comments that considerably improved the study. The usual disclaimer applies. (Paper received March 2005, revised version accepted August 2006. Online publication December 2006)

## New simulation schemes for the Heston model

Bégin, Jean-François
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
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Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion...

## Asset Prices and Exchange Rates

Pavlova, Anna; Rigobon, Roberto
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Tipo: Trabalho em Andamento Formato: 712125 bytes; application/pdf
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This paper develops a simple two-country, two-good model, in which the real exchange rate, stock and bond prices are jointly determined. The model predicts that stock market prices are correlated internationally even though their dividend processes are independent, providing a theoretical argument in favor of financial contagion. The foreign exchange market serves as a propagation channel from one stock market to the other. The model identifies interconnections between stock, bond and foreign exchange markets and characterizes their joint dynamics as a three-factor model. Contemporaneous responses of each market to changes in the factors are shown to have unambiguous signs. These implications enjoy strong empirical support. Estimation of various versions of the model reveals that most of the signs predicted by the model indeed obtain in the data, and the point estimates are in line with the implications of our theory. Furthermore...

## Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty

Chen, Wei
Tipo: Artigo de Revista Científica
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G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments in the sense of sub-linearity with Hurst index $H\in (0,1)$. This process has stationary increments, self-similarity, and long rang dependence properties in the sense of sub-linearity. These properties make the fractional G-Brownian motion a suitable driven process in mathematical finance. We construct wavelet decomposition of the fGBm by wavelet with compactly support. We develop fractional G-white noise theory, define G-It\^o-Wick stochastic integral, establish the fractional G-It\^o formula and the fractional G-Clark-Ocone formula, and derive the G-Girsanov's Theorem. For application the G-white noise theory, we consider the financial market modelled by G-Wick-It\^o type of SDE driven by fGBm. The financial asset price modelled by fGBm has volatility uncertainty, using G-Girsanov's Theorem and G-Clark-Ocone Theorem, we derive that sublinear expectation of the discounted European contingent claim is the bid-ask price of the claim.

## Non-Equivalent Beliefs and Subjective Equilibrium Bubbles

Tipo: Artigo de Revista Científica
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This paper develops a dynamic equilibrium model where agents exhibit a strong form of belief heterogeneity: they disagree about zero probability events. It is shown that, somewhat surprisingly, equilibrium exists in this setting, and that the disagreement about nullsets naturally leads to equilibrium asset pricing bubbles. The bubbles are subjective in the sense that they are perceived by some but not necessarily all agents. In contrast to existing models, bubbles arise with no restrictions on trade beyond a standard solvency constraint.; Comment: 30 pages

## No-arbitrage pricing under cross-ownership

Fischer, Tom
Tipo: Artigo de Revista Científica
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We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no-arbitrage. An existence result and a uniqueness result are proven. Examples and an algorithm for the simultaneous calculation of all no-arbitrage prices are provided. A result on capital structure irrelevance for groups of firms regarding externally held claims is discussed, as well as financial leverage and systemic risk caused by cross-ownership.; Comment: Excerpts and ideas from this paper have been presented at the Scientific Conference of the German Association for Actuarial and Financial Mathematics (DGVFM), Bremen, April 30, 2010. Some methods and systems derived from this work have been subject to a provisional (successful) patent filing

## Error analysis in Fourier methods for option pricing

Crocce, Fabián; Häppölä, Juho; Kiessling, Jonas; Tempone, Raúl
Tipo: Artigo de Revista Científica
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We provide a bound for the error committed when using a Fourier method to price European options when the underlying follows an exponential \levy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation that can be solved analytically in terms of the characteristic exponent of the \levy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a novel bound for the error and use this bound to set the parameters for the numerical method. We analyse the properties of the bound for a dissipative and pure-jump example. The bound presented is independent of the asymptotic behaviour of option prices at extreme asset prices. The error bound can be decomposed into a product of terms resulting from the dynamics and the option payoff, respectively. The analysis is supplemented by numerical examples that demonstrate results comparable to and superior to the existing literature.; Comment: 21 pages, 3 figures, 1 table

## Robust pricing and hedging of double no-touch options

Cox, Alexander M. G.; Obloj, Jan
Tipo: Artigo de Revista Científica
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Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of super- and sub-hedging strategies to establish the bounds, and the use of Skorokhod embedding techniques to show the bounds are the best possible. In addition to establishing rigorous bounds, we consider carefully what is meant by arbitrage in settings where there is no {\it a priori} known probability measure. We discuss two natural extensions of the notion of arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are needed to establish equivalence between the lack of arbitrage and the existence of a market model.; Comment: 32 pages, 5 figures

## Moment Explosions and Long-Term Behavior of Affine Stochastic Volatility Models

Keller-Ressel, Martin
Tipo: Artigo de Revista Científica
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We consider a class of asset pricing models, where the risk-neutral joint process of log-price and its stochastic variance is an affine process in the sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results on the long-term behavior of the model, including an expression for the invariant distribution of the stochastic variance process. We study moment explosions of the price process, and provide explicit expressions for the time at which a moment of given order becomes infinite. We discuss applications of these results, in particular to the asymptotics of the implied volatility smile, and conclude with some calculations for the Heston model, a model of Bates and the Barndorff-Nielsen-Shephard model.; Comment: minor revision

## Option Pricing and Hedging with Small Transaction Costs

Kallsen, Jan; Muhle-Karbe, Johannes
Tipo: Artigo de Revista Científica
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An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless optimizer. By applying these results in the presence of a random endowment, we obtain asymptotic formulas for utility indifference prices and hedging strategies in the presence of small transaction costs.; Comment: 20 pages, to appear in "Mathematical Finance"

## Consistent price systems and face-lifting pricing under transaction costs

Guasoni, Paolo; Rásonyi, Miklós; Schachermayer, Walter
Tipo: Artigo de Revista Científica
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In markets with transaction costs, consistent price systems play the same role as martingale measures in frictionless markets. We prove that if a continuous price process has conditional full support, then it admits consistent price systems for arbitrarily small transaction costs. This result applies to a large class of Markovian and non-Markovian models, including geometric fractional Brownian motion. Using the constructed price systems, we show, under very general assumptions, the following face-lifting'' result: the asymptotic superreplication price of a European contingent claim $g(S_T)$ equals $\hat{g}(S_0)$, where $\hat{g}$ is the concave envelope of $g$ and $S_t$ is the price of the asset at time $t$. This theorem generalizes similar results obtained for diffusion processes to processes with conditional full support.; Comment: Published in at http://dx.doi.org/10.1214/07-AAP461 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

## Hedging of claims with physical delivery under convex transaction costs

Pennanen, Teemu; Penner, Irina
Tipo: Artigo de Revista Científica
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We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no arbitrage condition implies that the set of claims hedgeable with zero cost is closed in probability. Combined with classical techniques of convex analysis, the closedness yields a dual characterization of premium processes that are sufficient to superhedge a given claim process. We also extend the fundamental theorem of asset pricing for general conical models.

## Functionals of Exponential Brownian Motion and Divided Differences

Tipo: Artigo de Revista Científica
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We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and its time average, and we find the use of divided differences greatly elucidates formulae, providing a path to several new results. As applications, we find that this correlation coefficient is always at least $1/\sqrt{2}$ and, via the Hermite--Genocchi integral relation, demonstrate that all moments of the time average are certain divided differences of the exponential function. We also prove that these moments agree with the somewhat more complex formulae obtained by Oshanin and Yor.

## Pricing the European call option in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Exact formulas

Kuchuk-Iatsenko, Sergii; Mishura, Yuliya
Tipo: Artigo de Revista Científica