Optimal consumption and investment with Epstein–Zin recursive utility

We study continuous-time optimal consumption and investment with Epstein–Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton–Jacobi–Bellman equation by a fixed point argument and makes it possible to compute both the indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.     

Can utility optimization explain the demand for structured investment products?

In this paper, we first show that for classical rational investors with correct beliefs and constant absolute or constant relative risk aversion, the utility gains from structured products over and above a portfolio consisting of the risk-free asset and the market portfolio are typically much smaller than their fees. This result holds irrespectively of whether the investors can continuously trade the risk-free asset and the market portfolio at no costs or whether they can just buy the assets and hold them to maturity of the structured product. However, when considering behavioural utility functions, such as prospect theory, or investors with incorrect beliefs (arising from probability weighting or probability misestimation), the utility gain can be sizable.     

Decision-making in incomplete markets with ambiguity—a case study of a gas field acquisition

We apply utility indifference pricing to solve a contingent claim problem, valuing a connected pair of gas fields where the underlying process is not standard Geometric Brownian Motion and the assumption of complete markets is not fulfilled. First, empirical data are often characterized by time-varying volatility and fat tails; therefore, we use Gaussian generalized autoregressive score (GAS) and GARCH models, extending them to Student’s t-GARCH and t-GAS. Second, an important risk (reservoir size) is not hedgeable. As a result, markets are incomplete which makes preference free pricing impossible and thus standard option pricing methodology inapplicable. Therefore, we parametrize the investor’s risk preference and use utility indifference pricing techniques. We use Least Squares Monte Carlo simulations as a dimension reduction technique in solving the resulting stochastic dynamic programming problems. Moreover, an investor often only has an approximate idea of the true probabilistic model underlying variables, making model ambiguity a relevant problem. We show empirically how model ambiguity affects project values, and importantly, how option values change as model ambiguity gets resolved in later phases of the projects. We show that traditional valuation approaches will consistently underestimate the value of project flexibility and in general lead to overly conservative investment decisions in the presence of time-dependent stochastic structures.     

MDP algorithms for portfolio optimization problems in pure jump markets

We consider the problem of maximizing the expected utility of the terminal wealth of a portfolio in a continuous-time pure jump market with general utility function. This leads to an optimal control problem for piecewise deterministic Markov processes. Using an embedding procedure we solve the problem by looking at a discrete-time contracting Markov decision process. Our aim is to show that this point of view has a number of advantages, in particular as far as computational aspects are concerned. We characterize the value function as the unique fixed point of the dynamic programming operator and prove the existence of optimal portfolios. Moreover, we show that value iteration as well as Howard’s policy improvement algorithm works. Finally, we give error bounds when the utility function is approximated and when we discretize the state space. A numerical example is presented and our approach is compared to the approximating Markov chain method.      

HARA utility maximization in a Markov-switching bond–stock market

We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor’s risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.     

The anatomy of buyer–seller dynamics in decentralized markets

In this paper I investigate the nexus between buyer–seller dynamics, financial frictions and market efficiency in decentralized markets. To do so, I introduce financial frictions in a dynamic market with heterogeneous traders. Heterogeneously constrained buyers sequentially enter the market to acquire units of a generic good from heterogeneously endowed sellers. I characterize two closely related classes of equilibria, respectively called homogeneous equilibrium with no entry (HEWNE) and homogeneous equilibrium with entry (HEWE). Both equilibria prescribe a market where only the efficiently endowed type of seller exists in the limit. However, the two equilibria diverge in the specification of agents’ behavior subsequent to trade. In HEWNE, sellers and buyers exit the market upon successful trading. In HEWE, like in supply chains, in every period certain types of buyers replace exiting sellers, thus becoming potential sellers for subsequent waves of buyers. First, I identify the critical role of frictions in steering the complex evolution of market heterogeneity for both classes of equilibria. Secondly, I operationalize the combined study of HEWNE and HEWE to obtain sharp predictions on market efficiency for a range of empirically-relevant situations in which buyer–seller dynamics are decoupled, for example when entry of new sellers is delayed or stopped. Third, I test the theoretical findings against a simulated artificial market.     

Return–volume nexus in financial markets: A survey of research

This paper provides a systematic review of the return–volume literature, broadly defined to include theoretical and empirical research relating to the intramarket and cross-market interlinkages between security return and trading volume characteristics in four financial markets, namely, the stock, bond, foreign exchange, and futures markets. Viewed through this lens, this paper attempts to review previous empirical research within a unified theoretical framework that relates the interlinkages between return and volume characteristics in various financial markets. Overall, this paper marks several interesting areas of debate and controversy based on several controversial theories and empirical findings in the literature, suggesting directions for future research.     

Does reinforcement learning outperform deep learning and traditional portfolio optimization models in frontier and developed financial markets?

Advancements in machine learning have opened up a wide range of new possibilities for using advanced computer algorithms, such as reinforcement learning in portfolio risk management. However, very little evidence has been provided on the superior performance of reinforcement learning models over traditional optimization models following the mean-variance framework in different financial market settings. This study uses two experiments with data from the Vietnamese and U.S. securities markets to justify whether advanced machine learning models could outperform traditional portfolios' cumulative returns while optimizing the Sharpe ratio. The results suggest that reinforcement learning consistently outperforms the established methods and benchmarks in both experiments, even when using a very similar degree of diversification in portfolio construction and the same input data. This study confirms the ability of reinforcement learning to provide dynamic responses to market conditions and redefine the risk-return standard in the financial system.     

Relation between bid–ask spread,impact and volatility in order-driven markets

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid–ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility per trade, with R ²s exceeding 0.9. This correlation suggests both that the main determinant of the bid–ask spread is adverse selection, and that most of the volatility comes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the NYSE, a liquid market with specialists, where monopoly rents appear to be present.     

The lead–lag relationship between the spot and futures markets in China

Based on daily and one-minute high-frequency returns, this paper examines the lead–lag dependence between the CSI 300 index spot and futures markets from 2010 to 2014. A nonparametric and non-linear method based on the thermal optimal path method is adopted. Empirical results of the daily data indicate that the lead–lag relationship between the two markets is within one day but this relationship is volatile since neither of the two possible situations (the futures leads or lags behind the spot market) takes a dominant place. Our results using the high-frequency data demonstrate that there is a price discovery in the Chinese futures market: the intraday one-minute futures return leads the cash return by 0–5 min regardless of the price trend of the market.     

Explaining the intra-day variation in the bid–ask spread in competitive dealership markets – A research note

There are many possible explanations for variation in the inside bid–ask spread during the trading day, including informed trading, price inelastic market demand, price discovery, statistical artefact and market concentration. Each of these explanations is examined for consistency with respect to both the inside and average bid–ask spread, observed both inside and outside the mandatory quote period in the London Stock Exchange.     

Does q-theory with investment frictions explain anomalies in the cross section of returns?

Q-theory predicts that investment frictions steepen the relation between expected returns and firm investment. Using financing constraints to proxy for investment frictions, we show only weak evidence that the investment-to-assets and asset growth effects in the cross section of returns are stronger in financially more constrained firms than in financially less constrained firms. There is no evidence that q-theory with investment frictions explains the investment growth, net stock issues, abnormal corporate investment, or net operating assets anomalies. Limits-to-arbitrage proxies dominate q-theory with investment frictions in explaining the magnitude of the investment-to-assets and asset growth anomalies in direct comparisons.     

Impact of financial market uncertainty and macroeconomic factors on stock–bond correlation in emerging markets

This paper examines the impact of global financial market uncertainty and domestic macroeconomic factors on stock–bond correlation in emerging markets. In particular, by applying the wavelet analysis approach, we are able to examine stock–bond correlations over different time horizons in ten emerging markets. We find that stock–bond correlation patterns vary significantly between the time horizons. In particular, the correlation in short horizon changes the sign rapidly showing sustainable negative episodes while the correlation in long horizon stays positive most of the time. The most important factor influencing stock–bond correlation in short horizon is the monetary policy stance, while the factors with the greatest long-term impact are inflation and stock market uncertainty. Finally, global stock market uncertainty plays a more significant role than global bond market uncertainty in explaining stock–bond correlations in emerging markets.     

Time-varying risk premia in foreign exchange and equity markets: evidence from Asia–Pacific countries

This paper examines the validity of the risk premia hypothesis in explaining deviations from Uncovered Interest Parity (UIP) and the role of deviations from Purchasing Power Parity (PPP) in the pricing of foreign exchange rates and equity securities in five Asia–Pacific countries and the US. Using weekly data from 1 January, 1988 to 27 February, 1998, I find that conditional variances are not related to the deviations from UIP in any statistical sense based on an univariate GARCH(1,1)-M model. As I consider both foreign exchange and equity markets together and test a conditional international CAPM (ICAPM) in the absence of PPP, I cannot reject the model based on the J-test by Hansen (Econometrica 50 (1982), 1029–1054) and find significant time-varying foreign exchange risk premia present in the data. This empirical evidence supports the notion of time-varying risk premia in explaining the deviations from UIP. It also supports the idea that the foreign exchange risk is not diversifiable and hence should be priced in both markets.     

Underwriting and investment risks in the property-liability insurance industry: evidence prior to the 9–11 event

Underwriting and investment are two important and related business activities of insurance companies. However, studies on the interrelation between underwriting and investment risks of Property-Liability (P-L) insurance companies are sparse in the literature. Using a sample of US P-L insurers, this article conducts an empirical investigation of how these two risks are associated with each other in the 1994–2000 period (before the September 11th terrorist attack in 2001). Our results, robust to various estimations, suggest that there is no significant relationship between the underwriting and investment risks among our sample firms. Such results based on pre 9–11 event period provide some support for the conjecture of Achleitner et al. (Geneva Pap Risk Insur Issues Pract 27:275–282, 2002) that many insurance companies may have failed to take an integrated approach to risk management. This resulted in a heavy loss due to dual exposures in both underwriting and investment in the 9–11 event. In the aftermath of the recent global financial crisis, risk taking and risk management of financial institutions have received more attention and increasing scrutiny. We believe the current paper provides some useful insights in this vein.     

Optimal execution with uncertain order fills in Almgren–Chriss framework

The classical price impact model of Almgren and Chriss is extended to incorporate the uncertainty of order fills. The extended model can be recast as alternatives to uncertain impact models and stochastic liquidity models. Optimal strategies are determined by maximizing the expected final profit and loss (P&L) and various P&L-risk tradeoffs including utility maximization. Closed form expressions for optimal strategies are obtained in linear cases. The results suggest a type of adaptive volume weighted average price, adaptive percentage of volume and adaptive Almgren–Chriss strategies. VWAP and classical Almgren–Chriss strategies are recovered as limiting cases with a different characteristic time scale of liquidation for the latter.     

Comparison of Black–Scholes Formula with Fractional Black–Scholes Formula in the Foreign Exchange Option Market with Changing Volatility

In this paper, the authors discuss the fractional option pricing with Black–Scholes formula, deduce the Fractional Black–Scholes formula, show the empirical results by using China merchants bank foreign exchange call option price, and find when the volatility is smaller, the asymptotic mean squared error of Fractional Black–Scholes is bigger than the Traditional Black–Scholes’, while the volatility is bigger—the market mechanism has a full play, the result is reverse. Namely when the market mechanism is given a full scope, the estimating effect of Fractional Black–Scholes is better than Traditional Black–Scholes’.     

Valuing fade-in options with default risk in Heston–Nandi GARCH models

Review of Derivatives Research - In this paper, we present a pricing model to value fade-in options with default risk, where the underlying asset price is driven by the Heston–Nandi GARCH...     

Dynamic asset–liability management in a Markov market with stochastic cash flows

This paper provides a general model to investigate an asset–liability management (ALM) problem in a Markov regime-switching market in a multi-period mean–variance (M–V) framework. Emphasis is placed on the stochastic cash flows in both wealth and liability dynamic processes, and the optimal investment and liquidity management strategies in achieving the M–V bi-objective of terminal surplus are evaluated. In this model, not only the asset returns and liability returns, but also the cash flows depend on the stochastic market states, which are assumed to follow a discrete-time Markov chain. Adopting the dynamic programming approach, the matrix theory and the Lagrange dual principle, we obtain closed-form expressions for the efficient investment strategy. Our proposed model is examined through empirical studies of a defined contribution pension fund. In-sample results show that, given the same risk level, an ALM investor (a) starting in a bear market can expect a higher return compared to beginning in a bull market and (b) has a lower expected return when there are major cash flow problems. The effects of the investment horizon and state-switching probability on the efficient frontier are also discussed. Out-of-sample analyses show the dynamic optimal liquidity management process. An ALM investor using our model can achieve his or her surplus objective in advance and with a minimum variance close to zero.