Abstract: We compute the optimal investment and consumption strategies for an individual who wishes to maximize her expected discounted exponential utility of lifetime consumption, while imposing a constraint on the expected time her wealth spends below a poverty threshold b. First, we compute the optimal strategies for the corresponding (unconstrained) problem with a running penalty for time that wealth spends below b. This penalty acts as a Lagrange multiplier for our original constrained problem, so we recover the optimal strategies for our original problem from the recast problem. We show that (1) if the current wealth is greater than b, then the optimal investment strategy becomes more conservative as the poverty constraint becomes sharper; and (2) if the current wealth is less than b, then the optimal investment strategy is either independent of the poverty constraint or becomes more aggressive as the poverty constraint becomes sharper, depending on the value b. We also show that the optimal rate of consumption (weakly) decreases as the poverty constraint becomes sharper. PubDate: 2019-11-08
Abstract: This paper investigates whether short-term momentum and long-term reversal may emerge from the wealth reallocation process taking place in speculative markets. We assume that there are two classes of investors who trade long-lived assets by holding constantly rebalanced portfolios based on their beliefs. Provided beliefs, and thus portfolios, are sufficiently diversified, all investors survive in the long-run and, due to waves of mispricing, the resulting equilibrium returns exhibit long-term reversal. If, moreover, asset dividends are positively correlated, investors’ profitable trades become positively correlated too, thus generating short-term momentum in equilibrium returns. We use the model to replicate the performance of the Winners and Losers portfolios highlighted by the empirical literature and to provide insights on how to improve upon them. Finally, we show that dividend positive autocorrelation is positively related to momentum and negatively related to reversal while diversity of beliefs is positively related to both momentum and reversal. PubDate: 2019-10-08
Abstract: We employ a simple numerical scheme to compute optimal portfolios and utilities of informed and uninformed investors in a mispriced Carr–Geman–Madan–Yor (CGMY) Lévy market under information asymmetry using instantaneous centralized moments of returns (ICMR). We also investigate the impact on investors’ demand for stocks and indices at different levels of asymmetric information, mispricing, investment horizon, jump intensity, and volatility. Our simulations not only confirm that uninformed expected demand falls as information asymmetry increases but also offer strong evidence that informed expected demand behaves in a similar manner. In particular, expected demand of informed investors falls whenever information asymmetry exceeds 50%. The investor that demands more of the risky asset maintains that position over the entire investment horizon at each level of mispricing and information asymmetry. The absolute difference in expected demand between the uninformed and informed investors increases with the investment horizon, but decreases with the level of information asymmetry. PubDate: 2019-09-01
Abstract: In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple \( (\lambda (t), X(t) ) \) is affine, this property allows to extend the general methodology introduced by Hubalek et al. (Quant Finance 17:873–888, 2017) for Geometric Asian option pricing to jump-diffusion models with stochastic jump intensity. Although the system of ordinary differential equations providing the characteristic function of the related affine process cannot be solved in closed form, a COS-type algorithm allows to obtain the relevant quantities needed for options valuation. We describe, by means of graphical illustrations, the dependence of Asian options prices by the main parameters of the driving Hawkes process. Finally, by using Geometric Asian options values as control variates, we show that Arithmetic Asian options prices can be computed in a fast and efficient way by a standard Monte Carlo method. PubDate: 2019-08-28
Abstract: We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean–Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves. PubDate: 2019-08-20
Abstract: Rational expectations equilibrium seeks a proper treatment of behavior under private information by assuming that the information revealed by prices is taken into account by consumers in their decisions. Typically agents are supposed to maximize a conditional expectation of state-dependent utility function and to consume the same bundles in indistiguishable states [see Allen (Econometrica 49(5):1173–1199, 1981), Radner (Econometrica 47(3):655–678, 1979)]. A problem with this model is that a rational expectations equilibrium may not exist even under very restrictive assumptions, may not be efficient, may not be incentive compatible, and may not be implementable as a perfect Bayesian equilibrium (Glycopantis et al. in Econ Theory 26(4):765–791, 2005). We introduce a notion of rational expectations equilibrium with two main features: agents may consume different bundles in indistinguishable states and ambiguity is allowed in individuals’ preferences. We show that such an equilibrium exists universally and not only generically without freezing a particular preferences representation. Moreover, if we particularize the preferences to a specific form of the maxmin expected utility model introduced in Gilboa and Schmeidler (J Math Econ 18(2):141–153, 1989), then we are able to prove efficiency and incentive compatibility. These properties do not hold for the traditional (Bayesian) Rational Expectation Equilibrium. PubDate: 2019-07-20
Abstract: This paper presents the first continuous-time model to feature a flexible dependence structure among jump intensity, stock variance, and stock returns. In particular, it addresses a gap in the financial portfolio optimization literature concerning the non-trivial correlation between stock return variance and the intensity of price jumps. The model permits closed-form representations for the optimal strategy and value functions in an expected utility theory setting. It also produces analytical expressions for the value function associated with relevant suboptimal strategies. Such an analytical setting allows for the first wealth-equivalent utility loss (WEL) analysis of the pitfalls of ignoring the aforementioned dependence. The model and results can be easily extended to the pair intensity-covariance in multi-assets. The WEL analysis is carried out for three different suboptimal classes: tailor-made incomplete markets, misspecifications in the parameters of the model, and time-independent (myopic) strategies. For the numerical section, we focus on the correlation between jump intensity and stock variance, which is assumed to be either zero or one in the existing literature. We demonstrate that simplistic assumptions like perfect dependence or independence could lead to wealth-equivalent losses of up to 61%. Similarly, a failure to hedge these variances and intensity drivers could cause losses of up to 95% (in particular, up to 60% due to the factors driving the dependence). PubDate: 2019-07-02
Abstract: We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion risk preferences. By analyzing the associated Hamilton–Jacobi–Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters. PubDate: 2019-06-10
Abstract: I develop an analytical general-equilibrium model to explain economic sources of business-cycle pattern of aggregate stock market returns. With concave production functions and capital accumulation, a technology shock has a pro-cyclical direct effect and a counter-cyclical indirect effect on expected returns. The indirect effect, reflecting the “feedback” effect of consumers’ behavior on asset returns, dominates the direct effect and causes counter-cyclical variations of expected returns. I show that the conditional mean, volatility, and Sharpe ratios of asset returns all vary counter-cyclically and they are persistent and predictable, and that stock market behavior has forecasting power for real economic activity. PubDate: 2019-06-03
Abstract: The theory of conic finance replaces the classical one-price model by a two-price model by determining bid and ask prices for future terminal cash flows in a consistent manner. In this framework, we derive closed-form solutions for bid and ask prices of plain vanilla European options, when the density of the log-returns is log-concave. Assuming that log-returns are normally or Laplace distributed, we apply the results to a time-series of real market data and compute an implied liquidity risk premium to describe the bid–ask spread. We compare this approach to the classical attempt of describing the spread by quoting Black–Scholes implied bid and ask volatilities and demonstrate that the new approach characterize liquidity over time significantly better. PubDate: 2019-06-01
Abstract: We show how the impact of a government bailout in the form of liquidity assistance on the ex ante effort of a representative bank depends on the volatility of its investment. The bank’s investment delivers a cashflow that follows a geometric Brownian motion and the government guarantees the bank’s liabilities. To counter the bank’s expectations of a bailout, the government may choose a tighter liquidity policy when the bank’s effort is not observable. This tighter liquidity induces more prudent ex ante behavior by the bank, but it may have the opposite effect when investment volatility is high. This novel effect arises because the bank could be discouraged to be prudent precisely because the chances of receiving liquidity assistance are low. PubDate: 2019-05-15
Abstract: We study the potential role of correlated refinancing abilities among different countries for the disruption of government bond markets in a currency union. Following Morris and Shin (Eur Econ Rev 48(1):133–153, 2004) we use a global games framework and model the simultaneous investment decision into two assets, which are subject to correlated fundamental states, as a coordination problem with correlated imperfect information. Based on this model we evaluate the role of information about one country for the coordination of creditors of another country. We find, however, that the contagious effects on the price of debt precipitated through correlation are modest. Hence, assuming that investors behave as modeled in the global game, we conclude that correlated fundamentals that precipitate informational spillovers appear to be unlikely to play a major role for e.g. the disruption of some Eurozone government bond markets in the aftermath of the recent financial and economic crisis. PubDate: 2019-04-09
Authors:Paulo Rogério Faustino Matos Abstract: I incorporate household debt and delinquency decisions into a standard model of lifecycle consumption-saving-investment. I also impose a punishment to the delinquent behavior by assuming that the percentage of endowment available is a linear function of the default decision. Theoretically such additional investor decisions are playing a relevant role in terms of completing markets. In practice, it enables me to derive an extended system of Euler equations which does not alter consumption-based fundamental asset pricing equation. It imposes the pricing kernel to account jointly for two additional first-order conditions. I perform empirical exercises aiming to price equity premium in United States from 1987:1 to 2018:1. I find significant elasticity of intertemporal substitution in consumption of the representative agent ranging from 0.24 to 0.55 and risk aversion from 1.82 to 3.51. This approach is also useful to account for the cross-section behavior of domestic assets. I can also use this framework to draw bounds for the household decisions on loan and delinquency and to propose a new rule of thumb relating preferences parameters and credit variables. PubDate: 2019-02-19 DOI: 10.1007/s10436-019-00344-1
Authors:Mark Whitmeyer Abstract: This paper examines the strategic interaction of n portfolio managers with relative performance concerns. We characterize the unique constant Nash equilibrium and derive some compelling results. Surprisingly, in equilibrium, more risk tolerant players do not generally take riskier positions than less risk tolerant players. We derive sufficient conditions under which this relation does hold. We also examine the effects of adding new players to the game on the equilibrium, and look at the equilibrium in the limiting case as the number of players goes to infinity. We show that for a symmetric population, the equilibrium strategy of the players converges pointwise to some limiting equilibrium policy. PubDate: 2019-02-07 DOI: 10.1007/s10436-019-00343-2
Authors:Berardino Palazzo Abstract: This paper explores the effects of a firm’s cash flow systematic risk on its optimal capital structure. In a model where firms are allowed to borrow resources from a competitive lending sector, those with cash flows more correlated with the aggregate economy (i.e., firms with riskier assets in place) choose a lower leverage given their higher expected financing costs. On the other hand, less risky firms, having lower expected financing costs, optimally choose to issue more debt to exploit a tax advantage. The model predicts that cash flow systematic risk is negatively correlated with leverage and corporate bond yields. PubDate: 2019-01-07 DOI: 10.1007/s10436-018-00342-9
Authors:Guglielmo D’Amico; Ada Lika; Filippo Petroni Abstract: This paper uses an Indexed Markov Chain to model high frequency price returns of quoted rms. Introducing an Index process permits consideration of endogenous market volatility, and two important stylized facts of financial time series can be taken into account: long memory and volatility clustering. This paper rst proposes a method to optimally determine the state space of the Index process, which is based on a change-point approach for Markov chains. Furthermore, we provide an explicit formula for the probability distribution function of the rst change of state of the Index process. Results are illustrated with an application to intra-day firm prices. PubDate: 2018-10-13 DOI: 10.1007/s10436-018-0337-0
Authors:Archil Gulisashvili; Frederi Viens; Xin Zhang Abstract: We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen–Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or small values of the variable, and study the wing behavior of the implied volatility in these models. Our main result provides explicit expressions for the first three terms in the expansion of the implied volatility, based on three basic spectral-type statistics of the Gaussian process: the top eigenvalue of its covariance operator, the multiplicity of this eigenvalue, and the \(L^{2}\) norm of the projection of the mean function on the top eigenspace. Numerical illustrations using the Stein–Stein and fractional Stein–Stein models are presented, including strategies for parameter calibration. PubDate: 2018-10-01 DOI: 10.1007/s10436-018-0338-z
Authors:Donatien Hainaut; Franck Moraux Abstract: This study proposes a new Markov switching process with clustering effects. In this approach, a hidden Markov chain with a finite number of states modulates the parameters of a self-excited jump process combined to a geometric Brownian motion. Each regime corresponds to a particular economic cycle determining the expected return, the diffusion coefficient and the long-run frequency of clustered jumps. We study first the theoretical properties of this process and we propose a sequential Monte-Carlo method to filter the hidden state variables. We next develop a Markov Chain Monte-Carlo procedure to fit the model to the S&P 500. We find that self-exciting jumps occur mainly during economic recession and nearly disappear in periods of economic growth. Finally, we analyse the impact of such a jump clustering on implied volatilities of European options. PubDate: 2018-09-29 DOI: 10.1007/s10436-018-0340-5
Authors:Tim Leung; Zheng Wang Abstract: This paper studies the optimal risk-averse timing to sell a risky asset. The investor’s risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price— the geometric Brownian motion and exponential Ornstein–Uhlenbeck models—to account for, respectively, the trending and mean-reverting price dynamics. In all cases, we derive the optimal thresholds and certainty equivalents to sell the asset, and compare them across models and utilities, with emphasis on their dependence on asset price, risk aversion, and quantity. We find that the timing option may render the investor’s value function and certainty equivalent non-concave in price. Numerical results are provided to illustrate the investor’s strategies and the premium associated with optimally timing to sell. PubDate: 2018-09-11 DOI: 10.1007/s10436-018-0336-1
Authors:Adriana Gama; Isabelle Maret; Virginie Masson Abstract: This paper examines the standard symmetric two-period R&D duopoly model, but with a deterministic one-way spillover structure. Though the two firms are ex-ante identical, one obtains a unique pair of asymmetric equilibria of R&D investments, leading to inter-firm heterogeneity in the industry, in R&D roles as well as in unit costs. We analyze the impact of a change in the spillover parameter and R&D costs on firms’ levels of R&D and profits. We find that higher spillovers need not lead to lower R&D investments for both firms. In addition, equilibrium profits may improve due to the presence of spillovers, and it may be advantageous to be the R&D imitator rather than the R&D innovator. PubDate: 2018-08-21 DOI: 10.1007/s10436-018-0329-0
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