Stylianos Z. Xanthopoulos

Scenarios for Price Determination in Incomplete Markets

We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios, based on utility pricing. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modeling the convergence of the buyer and seller prices to a unique price are proposed. The case of exponential utilities is treated in detail, in the simplest possible example of an incomplete market, the trinomial model.

A novel corporate credit rating system based on Student's-t hidden Markov models

We propose a credit rating system based on hidden Markov models.Our system captures strong temporal dynamics in the data.Robust to outliers in the training data.State-of-the-art results in corporate default prediction. Corporate credit rating systems have been an integral part of expert decision making of financial institutions for the last four decades. They are embedded into the pricing function determining the interest rate of a loan contact, and play crucial role in the credit approval process. However, the currently employed intelligent systems are based on assumptions that completely ignore two key characteristics of financial data, namely their heavy-tailed actual distributions, and their time-series nature. These unrealistic assumptions definitely undermine the performance of the resulting corporate credit rating systems used to inform expert decisions. To address these shortcomings, in this work we propose a novel corporate credit rating system based on Students-t hidden Markov models (SHMMs), which are a well-established method for modeling heavy-tailed time-series data: Under our approach, we use a properly selected set of financial ratios to perform credit scoring, which we model via SHMMs. We evaluate our method using a dataset pertaining to Greek corporations and SMEs; this dataset includes five-year financial data, and delinquency behavioral information. We perform extensive comparisons of the credit risk assessments obtained from our method with other models commonly used by financial institutions. As we show, our proposed system yields significantly more reliable predictions, offering a valuable new intelligent system to bank experts, to assist their decision making.

Behavioural and dynamical scenarios for contingent claims valuation in incomplete markets

We study the problem of determination of asset prices in an incomplete market proposing three different but related scenarios. One scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Dynamical schemes modelling the convergence of the buyers and of the sellers prices to a unique price are proposed.

A generalized ROC approach for the validation of credit rating systems and scorecards

Purpose - The purpose of this article is to introduce Receiver Operating Characteristic (ROC) surfaces and hyper-surfaces within a banking context as natural generalizations of the ROC curve. Design/methodology/approach - Nonparametric ROC analysis using Findings - Application of the proposed methodology on data from a small size Greek bank illustrates the usefulness of ROC analysis for scoring systems assessment. The area under the ROC curve and the volume under the ROC surface and hyper-surface are useful diagnostic indices for the assessment of credit rating systems and scorecards. The notion of statistical significance is not adequate for the evaluation of the loan granting strategy of a financial institution. Originality/value - This article will be of value to financial institutions during the process of evaluation/validation of rating models.

On a variational sequential bargaining pricing scheme

Abstract We propose a minimization problem as a model for the interaction between two agents trading a contingent claim in an incomplete discrete-time multiperiod financial market. The agents personal valuations for the contingent claim are assumed to depend on probability measures representing their beliefs concerning the future states of the world. The agents’ goal is to achieve a common price for the contingent claim to be traded, while deviating as litle as possible from their initial beliefs. Under appropriate conditions, we prove that the minimization problem under consideration admits at least one solution. Furthermore, we provide a detailed description for the minimizers – orbits of a finite horizon discrete-time dynamical system on the space of probability measures representing the agents beliefs.

A projected gradient dynamical system modelling the dynamics of bargaining

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations that do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world, and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents, beliefs during the bargaining period and is constructed so that an agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.

Minimum Regret Pricing of Contingent Claims in Incomplete Markets

In this paper we propose a contingent claim pricing scheme between two counterparties in an incomplete one period market. According to our approach the two counterparties of a non-marketed contingent claim select a pair of pricing kernels, in order to agree on a common price, by minimizing their joint regret function, which quantifies the departure from their initial beliefs. The joint regret function is a convex combination of entropy-like or norm-dependent functionals. The relevant optimization problem is posed in terms of a partially finite convex programming problem in the space of pricing kernels.

Contingent claim pricing through a continuous time variational bargaining scheme

We consider a variational problem modelling the evolution with time of two probability measures representing the subjective beliefs of a couple of agents engaged in a continuous-time bargaining pricing scheme with the goal of finding a unique price for a contingent claim in a continuous-time financial market. This optimization problem is coupled with two finite dimensional portfolio optimization problems, one for each agent involved in the bargaining scheme. Under mild conditions, we prove that the optimization problem under consideration here admits a unique solution, yielding a unique price for the contingent claim.

Relative Entropy Criterion and CAPM-Like Pricing

The minimal relative entropy criterion for the selection of an equivalent martingale measure in an incomplete market seems to still hold some mystique in its financial interpretation. In this paper we work toward this interpretation by suggesting and exploring the idea of relating a martingale measure selection criterion to a CAPM-like pricing scheme. We examine this idea in the case of the minimal relative entropy criterion and we present some preliminary results. We work within a one-period financial market and show that the minimal relative entropy pricing criterion is equivalent to some CAPM-like pricing scheme where the classical beta coefficient formula has been replaced by some “entropic beta” and the market portfolio by some “appropriate” reference portfolio. Furthermore, we show that if the assets involved have returns that are jointly normal, then this “entropic beta” formula coincides with the classical beta coefficient. Additionally and for comparison reasons, we briefly illustrate that if our criterion for the choice of the martingale measure was the minimization of the variance of the Radon–Nikodym derivative, then the resulting martingale pricing and the pricing implied by the classical CAPM scheme would be the same.

Three Behavioural Scenarios for Contingent Claims Valuation in Incomplete Markets

We describe three different but related scenarios for determination of asset prices in an incomplete market: one scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations.