Journal of Financial Engineering

Using a stochastic representation of the optimal wealth process in the classical Merton problem, we calculate its cumulative distribution and density functions and provide bounds and monotonicity results for these quantities under general risk preferences. We also show that the optimal wealth and portfolio processes for different utility functions are related through a deterministic transformation and appropriately modified initial conditions. We analyze the value at risk (VaR) and expected shortfall (ES) of the optimal wealth process and show how each can be used to infer a constant relative risk aversion (CRRA) investor's risk aversion coefficient. Drawing analogies to the option greeks, we study the sensitivities of the optimal wealth process with respect to the cumulative excess stock return, time, and market parameters. We conclude with a study of how sensitivities of the excess return on the optimal wealth process relate to the portfolio's beta.

Merton's optimal portfolio problem is solved, i.e., optimal portfolio formulas are derived for some new underlying price models of mean reversion type. The mean-reversion price models are proposed as an alternative to the well-known log-normal type and related models, possibly for a situation when an investor has a strong point of view about the future price-evolution.

In this paper, with the notion of independent and identically distributed (IID) random variables under sublinear expectations initiated by Peng, we develop a law of the iterated logarithm (LIL) for capacities. It turns out that our theorem is a natural extension of the Kolmogorov and the Hartman–Wintner LIL.

Valuation of American options is a difficult and challenging problem encountered in financial engineering. Longstaff and Schwartz [Longstaff, FA and ES Schwartz (2001). Valuing American Options by Simulation: A Simple Least-squares Approach, Review of Financial Studies, 14(1), 113–147.] Proposed the least-squares Monte Carlo (LSM) method for valuing American options. As this approach is intuitive and easy to apply, it has received much attention in the finance literature. However, a drawback of the LSM method is the low efficiency. In order to overcome this problem, we propose the least-squares randomized quasi-Monte Carlo (LSRQM) methods which can be viewed as a use low-discrepancy sequences as a variance reduction technique in the LSM method for valuing American options in this paper. Numerical results demonstrate that our proposed LSRQM methods are more efficient than the LSM method in terms of the valuation accuracy, the computation time and the convergence rate.

This paper considers the stochastic models for pricing credit-sensitive financial derivatives using the joint equity-credit modeling approach. The modeling of credit risk is embedded into a stochastic asset dynamics model by adding the jump-to-default (JtD) feature. We discuss the class of stochastic affine jump-diffusion (AJD) models with JtD and apply the models to price defaultable European options and credit default swaps. Numerical studies of the equity-credit models are also considered. The impact on the pricing behavior of derivative products with the added JtD feature is examined.

We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion (DD). Optimal strategies in the adapted class under various risk criteria, namely value-at-risk (VaR), expected shortfall (ES) and a new criterion called squared asset expectation (SAE), related to a version of the cost variance measure, are derived and compared. It is well known that DDs exhibit dynamics that are in-between arithmetic Brownian motions (ABM) and geometric Brownian motions (GBM) depending of the choice of the shift parameter. Furthermore, DD allows for changes in the support of the mid asset price distribution, allowing one to include a minimum permitted value for the mid price, either positive or negative. We study the dependence of the optimal solution on the choice of the risk aversion criterion. Optimal solutions across criteria and asset dynamics are comparable although differences are not negligible for high levels of risk aversion and low market impact assets. This is illustrated with numerical examples.

This paper explores a simulation framework to examine the financial contagion on the creditee linkage networks, owing to a comprehensive loan-level database of China Banking Regulatory Commission (CBRC). We merge two kinds of connections together, i.e., loan guarantee and shareholding relationships, when constructing our underlying network. Default transmission probabilities are characterized by the two-parameter logistic function with a variant of leverage. Our main finding is that, under the above channel, contagion spreads in a linear form. To be precise, as the scale of the initial shock grows, the total number of default firms and the amount of bad loans incurred both increase linearly. The main reason for this is that the underlying network is rather sparse. Within the same ratio of initially default companies, the Manufacturing Industry is likely to cause the largest number of companies to fail and the largest amount of bad loans. We also find that the default contagion mostly spreads within the same industries, explaining again why the domino effect is very limited. We investigate the impacts on different regions from industry failures, and get many interesting findings, e.g., most industries may influence the Yangtze Delta Economic Circle significantly except for Agriculture and the Mining Industry.

This paper establishes axioms for concentration index (CI) and its allocation function. It proves that the Herfindahl index (HI) and the square allocation function are the only one that satisfies these rules.