We consider the option pricing problem when the risky underlying assets are driven by Markov-modulated Geometric Brownian Motion (GBM). That is, the market parameters, for instance, the market interest rate, the appreciation rate and the volatility of the underlying risky asset, depend on unobservable states of the economy which are modelled by a continuous-time Hidden Markov process. The market described by the Markov-modulated GBM model is incomplete in general and, hence, the martingale measure is not unique. We adopt a regime switching random Esscher transform to determine an equivalent martingale pricing measure. As in Miyahara , we can justify our pricing result by the minimal entropy martingale measure (MEMM).
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.
Prudent upper and lower valuations from the literature on arbitrage free two price economies provide risk characteristics driving required returns. The risk characteristics assess the risk of price fluctuations. The difference between the upper and lower prudent valuations can be viewed as a capital charge. In addition the lower valuation assesses the down side tail risk. The required risk characteristics may be estimated on a daily basis from past data and we elaborate on how to perform such upper and lower valuations using distorted expectations. Details are provided for calculations using just the raw data, or by first fitting a probability distribution, or in terms of estimated arrival rates for jumps. The valuations are obtained with a dynamic calibration of a parametric distortion on the S&P 500 index options market. Results for required returns based on capital charges and down side risk compensation show an improvement when risk is represented by the arrival rates of jump sizes. For risk assessments based on arrival rates, capital charges constitute between 67 and 85% of the required return. The rest being a charge for downside risk exposures. After the introduction of risk characteristics into required returns there is little scope for covariation measures like asset betas. Different proposed constructions for required returns deliver differences in the value of an invested dollar and associated differences in asset rankings across time.
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.