Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in the presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting.     

Asymptotics of the probability of minimizing ‘down-side’ risk under partial information

We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model under partial information and then study the asymptotic behavior of the minimizing probability as T → ∞. This problem is closely related to an ergodic risk-sensitive stochastic control problem under partial information in the risk-averse case. Indeed, in our main theorem we relate the former problem to the latter as its dual. As a result we obtain an explicit expression for the limit value of the former problem in the case of linear Gaussian models.     

Optimal consumption and investment for markets with random coefficients

We consider an optimal investment and consumption problem for a Black–Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamic programming approach leads to an investigation of the Hamilton–Jacobi–Bellman (HJB) equation which is a highly nonlinear partial differential equation (PDE) of the second order. By using the Feynman–Kac representation, we prove uniqueness and smoothness of the solution. Moreover, we study the optimal convergence rate of iterative numerical schemes for both the value function and the optimal portfolio. We show that in this case, the optimal convergence rate is super-geometric, i.e., more rapid than any geometric one. We apply our results to a stochastic volatility financial market.     

Information and option pricings

How can one relate stock fluctuations and information-based human activities? We present a model of an incomplete market by adjoining the Black-Scholes exponential Brownian motion model for stock fluctuations with a hidden Markov process, which represents the state of information in the investors' community. The drift and volatility parameters take different values depending on the state of this hidden Markov process. Standard option pricing procedure under this model becomes problematic. Yet, with an additional economic assumption, we provide an explicit closed-form formula for the arbitrage-free price of the European call option. Our model can be discretized via a Skorohod embedding technique. We conclude with an example of a simulation of IBM stock, which shows that, not surprisingly, information does affect the market.     

Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility

Given an investor maximizing utility from terminal wealth with respect to a power utility function, we present a verification result for portfolio problems with stochastic volatility. Applying this result, we solve the portfolio problem for Heston's stochastic volatility model. We find that only under a specific condition on the model parameters does the problem possess a unique solution leading to a partial equilibrium. Finally, it is demonstrated that the results critically hinge upon the specification of the market price of risk. We conclude that, in applications, one has to be very careful when exogenously specifying the form of the market price of risk.     

The partial adjustment of IPO prices to public information and issuing methods in Taiwan

Using 1997 to 2009 exchange-listed data, we examine the treatment of public information by underwriters throughout the entire initial public offering (IPO) price-setting process in Taiwan. We find that regardless of which mechanism (fixed-price, auctions, or book-building) an issuer has chosen, the partial adjustment of the IPO offer prices to public information is evident in our study. Although both fixed-price and book-built issues show a modest but statistically significant relationship between market returns and the level of initial returns, we find economically meaningful effects for both issuing methods. Our findings also demonstrate that auctioned IPOs exhibit strong evidence of partial adjustment to market returns. That is to say, the estimated effect is statistically and economically significant. Therefore, we attempt to provide rational explanations for such phenomena.     

The Minimal Entropy Martingale Measure (MEMM) for a Markov-Modulated Exponential Lévy Model

This paper deals with the characterization problem of the minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model. This model is characterized by the presence of a background process modulating the risky asset price movements between different regimes or market environments. This allows to stress the strong dependence of financial assets price with structural changes in the market conditions. Our main results are obtained from the key idea of working conditionally on the modulator-factor process. This reduces the problem to studying the simpler case of processes with independent increments. Our work generalizes some previous works in the literature dealing with either the exponential Lévy case or the exponential-additive case.     

Red chips or H shares: which China-backed securities process information the fastest?

This study examines the information flow between China-backed securities, namely H shares, red chips, Shanghai and Shenzhen listed common shares. We document several findings. We find that an exponential generalized autoregressive conditional heteroscedasticity in mean (EGARCH-M) model appears to describe adequately the return process of the China-backed securities. Our empirical findings show that both H shares and red chips (which are listed in Hong Kong) are more sensitive to ‘good’ news than ‘bad’ news, while stocks listed in the China market are more sensitive to ‘bad’ news than ‘good’ news. Using a multivariate EGARCH-M model, we have found significant return and volatility spillover effects among the China-backed securities. Our study indicates that the red chips appear to spread information to other China-backed markets ‘directly’ or ‘indirectly’. The results imply that the red chip market processes information faster than the other markets.     

Perpetual American options in incomplete markets: the infinitely divisible case

We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.     

Information-Based Model with Noisy Anticipation and Its Application in Finance

We focus on an information-based model with noisy anticipation motivated by asset valuation problem. Precisely, the price of an asset is computed from the expectation of the totality of discounted future dividend, conditioned on the market filtration generated by (1) the current and past value of dividend, and (2) a partial information of the future cash flow stream. As a result, we obtained a new solution method to compute a generalized asset pricing formula. Moreover, under a certain condition, the formula can be reduced to a simple form, a linear combination between dividend and noisy anticipation. The approach can be applied to approximate a reasonable price of the commodities even without knowing the actual demand and supply.     

Underpricing in the Corporate Bond Market

This article examines underpricing of initial public offerings(IPOs) and seasoned offerings in the corporate bond market.We investigate whether underpricing represents a solution toan information problem or a liquidity problem. We find thatunderpricing occurs with both IPOs and seasoned offerings andis highest among riskier, unknown firms. Our evidence suggeststhat information problems drive underpricing, with support forboth the bookbuilding view of underpricing and the asymmetricinformation theory. We do not find evidence in favor of theRock model of underpricing or any evidence that illiquiditycauses underpricing.     

Discrete time hedging with liquidity risk

We study a discrete time hedging and pricing problem in a market with liquidity costs. Using Leland’s discrete time replication scheme [Leland, H.E., 1985. Journal of Finance, 1283–1301], we consider a discrete time version of the Black–Scholes model and a delta hedging strategy. We derive a partial differential equation for the option price in the presence of liquidity costs and develop a modified option hedging strategy which depends on the size of the parameter for liquidity risk. We also discuss an analytic method of solving the pricing equation using a series solution.     

Spectral calibration of exponential Lévy models

We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit inversion of the option price formula in the spectral domain and a cut-off scheme for high frequencies as regularisation.     

Assessing the Information Content of Mark-to-Market Accounting with Mixed Attributes: The Case of Cash Flow Hedges

We examine how outsiders rationally interpret a reported loss on derivatives when the application of mark‐to‐market accounting to cash flow hedges creates a mixed attribute problem. We find that because of the mixed attribute problem, the information content of mark‐to‐market accounting is related to the information content of historical cost accounting in a very specific way. This relationship allows us to identify the circumstances under which mark‐to‐market accounting facilitates and when it detracts from the objective of providing an early warning of potential financial distress. We show that the reporting of an impending derivative loss by a distressed firm can actually lead outsiders to infer that the firm is in a better financial position than what they would have inferred under the silence associated with historical cost accounting. Without the mixed attribute problem, mark‐to‐market accounting would always yield more accurate assessments of the firm's financial position.     

Dynamic programming and mean-variance hedging with partial execution risk

In this paper I consider a hedging problem in an illiquid market where there is a risk that the hedger’s order to buy or sell the underlying asset may be executed only partially. In this setting, I find a mean-variance optimal hedging strategy by the dynamic programming method. The solution contains a new endogenous state variable representing the current position in the underlying. The exogenous coefficients in the solution are given by recursive formulas which can be calculated efficiently in Markov models. I illustrate effects of the partial execution risk in several examples.      

Optimal portfolios in commodity futures markets

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization.     

An example of a stochastic equilibrium with incomplete markets

We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and general Markovian random endowments. The incompleteness featured in our setting—the source of which can be thought of as a credit event or a catastrophe—is genuine in the sense that not only the prices, but also the family of replicable claims itself are determined as a part of the equilibrium. Consequently, equilibrium allocations are not necessarily Pareto optimal and the related representative-agent techniques cannot be used. Instead, we follow a novel route based on new stability results for a class of semilinear partial differential equations related to the Hamilton–Jacobi–Bellman equation for the agents’ utility maximization problems. This approach leads to a reformulation of the problem where the Banach fixed-point theorem can be used not only to show existence and uniqueness, but also to provide a simple and efficient numerical procedure for its computation.     

Insiders' hedging in a jump diffusion model

In this paper, we formulate the optimal hedging problem when the underlying stock price has jumps, especially for insiders who have more information than the general public. The jumps in the underlying price process depend on another diffusion process, which models a sequence of firm-specific information. This diffusion process is observed only by insiders. Nevertheless, the market is incomplete to insiders as well as to the general public. We use the local risk minimization method to find an optimal hedging strategy for insiders. We also numerically compare the value of the insider's hedging portfolio with the value of an honest trader's hedging portfolio for a simulated sample path of a stock price.     

Unemployment insurance and incentives

In this paper we present a partial economic equilibrium model of the labor market in which we maximize the workers' expected discounted utility level, while implying a zero expected profit for the firms. The model we use for the labor market takes into consideration transitions between the various states of employment and the time periods spent in each state. The probability distribution of these time periods may be arbitrary, not restricted to being exponential, as is the case for ordinary time-continuous Markov processes. The basic principles and difficulties arising from monitoring problems and moral hazard are discussed. In order to analyze unemployment insurance schemes that include incentives for workers to avoid unemployment, we depart from the simplest form of the principle of equivalence in insurance. Several different alternatives are discussed, all giving rise to partial insurance and thus incentives. We also analyze the effects that early retirement have on unemployment. Here, we include social security benefits in the economic model. Finally, we show that the optimal solutions entail quantity rationing.