Classification of whether recovery of non-performing loans (NPL) is zero or positive is not only important in management of non-performing loans, but also is essential for estimating recovery rate and implementing the new Basel Capital Accord. Based on the largest database of NPL's recovering information in China, this paper tries to establish discriminant models to predict the loan with zero recovery. We first use Step-wise discrimination method to select variables; then give an in-depth analysis on why the selected variables are important factors influencing whether a loan is zero or positive recovery rate. Using the selected variables, we establish two-type discriminant models to classify the NPLs. Empirical results show that both models achieve high prediction accuracy, and the characteristics of obligors are the most important factors in determining whether a NPL is positively recovered or zero recovered.

Yue Tang

Hao Chen

Bo Wang

Muzi Chen

Min Chen

Xiaoguang Yang

Discriminant Analysis of Zero Recovery for China's NPL

We deal with the pricing of callable Russian options. A callable Russian option
is a contract in which both of the seller and the buyer have the rights to cancel and to exercise at any time,
respectively. The pricing of such an option can be formulated as an optimal stopping problem between the
seller and the buyer, and is analyzed as Dynkin game. We derive the value function of callable Russian
options and their optimal boundaries.

Atsuo Suzuki

Katsushige Sawaki

Callable Russian Options and Their Optimal Boundaries

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefan(free boundary) problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.

Lei Wang

Zhiming Jin

Valuation of Game Options in Jump-Diffusion Model and with Applications to Convertible Bonds

A product warranty is an agreement offered by a producer to a consumer
to replace or repair a faulty item, or to partially or fully reimburse
the consumer in the event of a failure. Warranties are very
widespread and serve many purposes, including protection for producer,
seller, and consumer. They are used as signals of quality and
as elements of marketing strategies. In this study we review the notion
of an online convex optimization algorithm and its variations,
and apply it in warranty context. We introduce a class of profit functions,
which are functions of warranty, and use it to formulate the
problem of maximizing the company's profit over time as an online
convex optimization problem. We use this formulation to present an
approach to setting the warranty based on an online algorithm with
low regret. Under a dynamic environment, this algorithm provides
a warranty strategy for the company that maximises its profit over
time.

Nedialko B. Dimitrov

Stefanka Chukova

Warranty Optimization in a Dynamic Environment

Most of the investments in practice are carried out without certain horizons. There are many factors to drive investment to a stop. In this paper, we consider a portfolio selection policy with market-related stopping time. Particularly, we assume that the investor exits the market once his wealth reaches a given investment target or falls below a bankruptcy threshold. Our objective is to minimize the expected time when the investment target is obtained, at the same time, we guarantee the probability that bankruptcy happens is no larger than a given level. We formulate the problem as a mix integer linear programming model and make analysis of the model by using a numerical example.

Jianfeng Liang

Discrete Analysis of Portfolio Selection with Optimal Stopping Time

This research work investigates the theoretical foundations and computational aspects of constructing optimal bespoke CDO structures. Due to the evolutionary nature of the CDO design process, stochastic search methods that
mimic the metaphor of natural biological evolution are applied. For efficient searching the optimal solution, the nondominating
sort genetic algorithm (NSGA-II) is used, which places emphasis on moving towards the true Paretooptimal
region. This is an essential part of real-world credit structuring problems. The algorithm further demonstrates
attractive constraint handling features among others, which is suitable for successfully solving the constrained portfolio
optimisation problem. Numerical analysis is conducted on a bespoke CDO collateral portfolio constructed from
constituents of the iTraxx Europe IG S5 CDS index. For comparative purposes, the default dependence structure is
modelled via Gaussian and Clayton copula assumptions. This research concludes that CDO tranche returns at all
levels of risk under the Clayton copula assumption performed better than the sub-optimal Gaussian assumption. It is
evident that our research has provided meaningful guidance to CDO traders, for seeking significant improvement of
returns over standardised CDOs tranches of similar rating.

Diresh Jewan

Renkuan Guo

Gareth Witten

Optimal Bespoke CDO Design via NSGA-II

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Advances in Decision Sciences