International Journal of Theoretical and Applied Finance

In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the stock market and borrow money in order to raise funds. We propose a simple model to find the maximum amount of new funds the banks can raise in these ways. To do this, we incorporate market confidence of the bank together with market confidence of all the other banks in the system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of Nash equilibrium point for all these problems. Finally, using this model we investigate if banks have become safer since the crisis. We calibrate this model with market data and conduct an empirical study to assess safety of the financial system before, during after the last financial crisis.

This paper studies the optimal investment problem for a behavioral investor with probability distortion functions and an S-shaped utility function whose utility on gains satisfies the Inada condition at infinity, albeit not necessarily at zero, in a complete continuous-time financial market model. In particular, a piecewise utility function with hyperbolic absolute risk aversion (HARA) is applied. The considered behavioral framework, cumulative prospect theory (CPT), was originally introduced by [A. Tversky & D. Kahneman (1992) Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (4), 297–323]. The utility model allows for increasing, constant or decreasing relative risk aversion. The continuous-time portfolio selection problem under the S-shaped HARA utility function in combination with probability distortion functions on gains and losses is solved theoretically for the first time, the optimal terminal wealth and its replicating wealth process and investment strategy are stated. In addition, conditions on the utility and the probability distortion functions for well-posedness and closed-form solutions are provided. A specific probability distortion function family is presented which fulfills all those requirements. This generalizes the work by [H. Jin & X. Y. Zhou (2008) Behavioral portfolio selection in continuous time, Mathematical Finance 18 (3), 385–426]. Finally, a numerical case study is carried out to illustrate the impact of the utility function and the probability distortion functions.

We consider an optimal liquidation problem with infinite horizon in the Almgren–Chriss framework, where the unaffected asset price follows a Lévy process. The temporary price impact is described by a general function that satisfies some reasonable conditions. We consider a market agent with constant absolute risk aversion, who wants to maximize the expected utility of the cash received from the sale of the agent’s assets, and show that this problem can be reduced to a deterministic optimization problem that we are able to solve explicitly. In order to compare our results with exponential Lévy models, which provide a very good statistical fit with observed asset price data for short time horizons, we derive the (linear) Lévy process approximation of such models. In particular we derive expressions for the Lévy process approximation of the exponential variance–gamma Lévy process, and study properties of the corresponding optimal liquidation strategy. We then provide a comparison of the liquidation trajectories for reasonable parameters between the Lévy process model and the classical Almgren–Chriss model. In particular, we obtain an explicit expression for the connection between the temporary impact function for the Lévy model and the temporary impact function for the Brownian motion model (the classical Almgren–Chriss model), for which the optimal liquidation trajectories for the two models coincide.

We present an algorithm to approximate moments for forward rates under a displaced lognormal forward-LIBOR model (DLFM). Since the joint distribution of rates is unknown, we use a multi-dimensional full weak order 2.0 Ito–Taylor expansion in combination with a second-order Delta method. This more accurately accounts for state dependence in the drift terms, improving upon previous approaches. To verify this improvement we conduct quasi-Monte Carlo simulations. We use the new mean approximation to provide an improved swaption volatility approximation, and compare this to the approaches of Rebonato, Hull–White and Kawai, adapted to price swaptions under the DLFM. Rebonato and Hull–White are found to be the least accurate. While Kawai is the most accurate, it is computationally inefficient. Numerical results show that our approach strikes a balance between accuracy and efficiency.

In practice, optimal portfolio construction for large stock markets has never been conclusively resolved because estimating the required means of returns with sufficient accuracy is a highly intractable task. By avoiding estimation, this paper approximates closely the growth optimal portfolio (GP) for the stocks of developed markets with a well-diversified, hierarchically weighted index (HWI). For stocks denominated in units of the HWI, their current value turns out to be strictly greater than their future expected values, which indicates the existence of stock price bubbles that could be systematically exploited for long-term asset management. It is shown that the HWI does not leave much room for significant performance improvements as proxy for the GP.

At odds with the common “rational expectations” framework for bubbles, economists like Hyman Minsky, Charles Kindleberger and Robert Shiller have documented that irrational behavior, ambiguous information or certain limits to arbitrage are essential drivers for bubble phenomena and financial crises. Following this understanding that asset price bubbles are generated by market failures, we present a framework for explosive semimartingales that is based on the antagonistic combination of (i) an excessive, unstable pre-crash process and (ii) a drawdown starting at some random time. This unifying framework allows one to accommodate and compare many discrete and continuous time bubble models in the literature that feature such market inefficiencies. Moreover, it significantly extends the range of feasible asset price processes during times of financial speculation and frenzy and provides a strong theoretical background for future model design in financial and risk management problem settings. This conception of bubbles also allows us to elucidate the status of rational expectation bubbles, which, by design, suffer from the paradox that a rational market should not allow for misvaluation. While the discrete time case has been extensively discussed in the literature and is most criticized for its failure to comply with rational expectations equilibria, we argue that this carries over to the finite time “strict local martingale”-approach to bubbles.

In this paper, we propose a new model for pricing stock and dividend derivatives. We jointly specify dynamics for the stock price and the dividend rate such that the stock price is positive and the dividend rate nonnegative. In its simplest form, the model features a dividend rate that is mean-reverting around a constant fraction of the stock price. The advantage of directly specifying dynamics for the dividend rate, as opposed to the more common approach of modeling the dividend yield, is that it is easier to keep the distribution of cumulative dividends tractable. The model is nonaffine but does belong to the more general class of polynomial processes, which allows us to compute all conditional moments of the stock price and the cumulative dividends explicitly. In particular, we have closed-form expressions for the prices of stock and dividend futures. Prices of stock and dividend options are accurately approximated using a moment matching technique based on the principle of maximal entropy.