A set-valued Markov chain approach to credit default

We propose a novel credit default model that takes into account the impact of macroeconomic factors and intergroup contagion on the defaults of obligors. We use a set-valued Markov chain to model the default process, which includes all defaulted obligors in the group. We obtain analytic characterizations for the default process and derive pricing formulas in explicit forms for synthetic collateralized debt obligations (CDOs). Furthermore, we use market data to calibrate the model and conduct numerical studies on the tranche spreads of CDOs. We find evidence to support that systematic default risk coupled with default contagion could have the leading component of the total default risk.     

A Markov model for valuing asset prices in a dynamic bargaining market

This paper proposes a Markov chain model for studying the impact on asset prices of illiquidity associated with search and bargaining in an economy. The economy consists of finitely many agents who can trade only when they find each other, and any trade between agents changes the population of the agent types which affects the asset price in the future. Assuming that the equilibrium utility as well as the trade price is proportional to the asset dividend, we obtain the asset prices in steady state. Through extensive numerical experiments, we observe that the equilibrium prices exhibit the cutoff phenomenon (i.e. crash) as the fraction of pessimistic agents becomes large. Models with a market maker as well as irrational agents are also considered.     

On a multivariate Markov chain model for credit risk measurement

In this paper, we use credibility theory to estimate credit transition matrices in a multivariate Markov chain model for credit rating. A transition matrix is estimated by a linear combination of the prior estimate of the transition matrix and the empirical transition matrix. These estimates can be easily computed by solving a set of linear programming (LP) problems. The estimation procedure can be implemented easily on Excel spreadsheets without requiring much computational effort and time. The number of parameters is O(s² m² ), where s is the dimension of the categorical time series for credit ratings and m is the number of possible credit ratings for a security. Numerical evaluations of credit risk measures based on our model are presented.     

Range-based multivariate volatility model with double smooth transition in conditional correlation

This paper proposes a multivariate model named Double Smooth Transition Conditional Correlation Conditional Autoregressive Range (DSTCC-CARR for short). Determined by two transition variables, the correlations smoothly transit from one state to another. Together with the DSTCC-GARCH model, the model is employed to investigate the interdependence between Hong Kong's and international stock markets. It is proved by the empirical analysis that the DSTCC-CARR model is more credible and efficient than the DSTCC-GARCH model. Linkages among Hong Kong's and other world's markets captured by these two models are testified to be consistent with history, and have meaningful interpretations.     

Dollar exchange rate and stock price: evidence from multivariate cointegration and error correction model

In this paper, we investigate existence of long-run equilibrium relationships among the aggregate stock price, industrial production, real exchange rate, interest rate, and inflation in the United States. Applying Johansen's cointegration analysis to monthly data for the 1974:01-1998:12 period, we find that the S&P 500 stock price is positively related to the industrial production but negatively to the real exchange rate, interest rate, and inflation. Analysis of error correction mechanism reveals that the stock price, industrial production, and inflation adjust to correct disequilibrium among the five variables, while variance decompositions indicate that the stock price is driven to a considerable extent by innovations in the interest rate. Structural stability tests show that the parameters of the cointegrating system and the error correction term are stationary.     

Novel advancements in the Markov chain stock model: analysis and inference

In this paper we propose further advancements in the Markov chain stock model. First, we provide a formula for the second order moment of the fundamental price process with transversality conditions that avoid the presence of speculative bubbles. Second, we assume that the process of the dividend growth is governed by a finite state discrete time Markov chain and, under this hypothesis, we are able to compute the moments of the price process. We impose assumptions on the dividend growth process that guarantee finiteness of price and risk and the fulfilment of the transversality conditions. Subsequently, we develop non parametric statistical techniques for the inferential analysis of the model. We propose estimators of price, risk and forecasted prices and for each estimator we demonstrate that they are strongly consistent and that properly centralized and normalized they converge in distribution to normal random variables, then we give also the interval estimators. An application that demonstrate the practical implementation of methods and results to real dividend data concludes the paper.     

What drives Markov regime-switching behavior of stock markets? The Swiss case

To optimally account for dynamic and nonlinear changes in the stock market return distribution we evaluate competing Markov regime-switching model setups for the Swiss stock market. We find that the stochastic movement is optimally tracked by time-varying first and second moments and including a memory effect. Besides the superior dynamic properties, this setup exhibits appealing economic interpretations.     

A multivariate jump-driven financial asset model

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness, kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks or indexes and to study a multi-firm, value-based default model. Starting from an independent Brownian world, we introduce jumps and other deviations from normality, including non-Gaussian dependence. We use a stochastic time-change technique and provide the details for a Gamma change. The main feature of the model is the fact that—opposite to other, non-jointly Gaussian settings—its risk-neutral dependence can be calibrated from univariate derivative prices, providing a surprisingly good fit.     

价值链视角下的保险连锁营销模式研究

保险连锁营销模式是金融领域的一次重大创新。本文从价值链理论出发,分析了保险连锁营销模式的本质特征、运作特点,深入探讨了连锁营销网络如何整合保险企业资源,推动保险企业的流程优化和组织再造,指出连锁营销模式有利于实现保险企业的价值创造。     

COVID-19 and stock returns: Evidence from the Markov switching dependence approach

This paper aims to investigate the regime-switching and time-varying dependence between the COVID-19 pandemic and the US stock markets using a Markov-switching framework. It makes two contributions to the empirical literature by showing that: (a) the variations of the daily reported COVID-19 cases and cumulative COVID-19 deaths induced asymmetric lower (left) and upper (right) tail dependence with the stock markets, and its left and right tail dependence exhibited significant time-varying trends; and (b) the left and right tail dependence between the stock markets and the pandemic exhibited significant regime-switching behaviours, with its switching probabilities in the higher tail dependence stage all being greater than in the lower tail dependence stage after 1 December 2019. Moreover, given that there is concurrent but significant financial market reaction to any unexpected emergence of a transmittable respirational disease or a natural calamity, the outcomes have some vital implications to market players and policymakers.     

Optimal dividend problems for Sparre Andersen risk model with bounded dividend rates

ABSTRACT

This paper concerns the optimal dividend problem with bounded dividend rate for Sparre Andersen risk model. The analytic characterizations of admissible strategies and Markov strategies are given. We use the measure-valued generator theory to derive a measure-valued dynamic programming equation. The value function is proved to be of locally finite variation along the path, which belongs to the domain of the measure-valued generator. The verification theorem is proved without additional assumptions on the regularity of the value function. Actually, the value function may have jumps. Under certain conditions, the optimal strategy is presented as a Markov strategy with space-time band structure. We present an iterative algorithm to approximate the optimal value function and the optimal dividend strategy. As applications, some numerical examples are given.     

Ruin probabilities in models with a Markov chain dependence structure

In this paper we derive explicit expressions for the probability of ruin in a renewal risk model with dependence among the increments (Z _k ) _k>0. We study the case where the dependence structure among (Z _k ) _k>0 is driven by a Markov chain with a transition kernel that can be described via ordinary differential equations with constant coefficients.     

The multivariate Variance Gamma model: basket option pricing and calibration

In this paper, we propose a methodology for pricing basket options in the multivariate Variance Gamma model introduced in Luciano and Schoutens [Quant. Finance 6(5), 385–402]. The stock prices composing the basket are modelled by time-changed geometric Brownian motions with a common Gamma subordinator. Using the additivity property of comonotonic stop-loss premiums together with Gauss-Laguerre polynomials, we express the basket option price as a linear combination of Black & Scholes prices. Furthermore, our new basket option pricing formula enables us to calibrate the multivariate VG model in a fast way. As an illustration, we show that even in the constrained situation where the pairwise correlations between the Brownian motions are assumed to be equal, the multivariate VG model can closely match the observed Dow Jones index options.     

CB – Time Dependent Markov Model for Pricing Convertible Bonds

In this paper, we propose what we call the convertible bond (CB) – timedependent Markov model, which prices N given individual convertible bondssimultaneously, and apply it to Japanese convertible bond data. One of themain features of the model is that it makes full use of the correlationstructure of convertible bond prices. The empirical results show that themodel well describes individual prices in the market.     

Insurance ratemaking using a copula-based multivariate Tweedie model

The Tweedie distribution, featured with a mass probability at zero, is a convenient tool for insurance claims modeling and pure premium determination in general insurance. Motivated by the fact that an insurance policy typically provides multiple types of coverage, we propose a copula-based multivariate Tweedie regression for modeling the semi-continuous claims while accommodating the association among different types. The proposed approach also allows for dispersion modeling, resulting in a multivariate version of the double generalized linear model. We demonstrate the application in insurance ratemaking using a portfolio of policyholders of automobile insurance from the state of Massachusetts in the United States.     

Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain

We consider a multi-stock market model where prices satisfy a stochastic differential equation with instantaneous rates of return modeled as a continuous time Markov chain with finitely many states. Partial observation means that only the prices are observable. For the investors objective of maximizing the expected utility of the terminal wealth we derive an explicit representation of the optimal trading strategy in terms of the unnormalized filter of the drift process, using HMM filtering results and Malliavin calculus. The optimal strategy can be determined numerically and parameters can be estimated using the EM algorithm. The results are applied to historical prices.Received: March 2004, Mathematics Subject Classification (2000): 91B28, 60G44JEL Classification: G11Supported by NSERC under research grant 88051 and NCE grant 30354.     

The Cost of Equity Capital at the Corporate and Investor Levels Allowing a Rational Expectations Model with Personal Taxations

This paper argues that the conventional definition of the cost of equity at the corporate level is likely to be fundamentally flawed under conditions of personal taxation. A 'dimensionally consistent' definition is developed utilising the pioneering contributions of Auerbach and Elton and Gruber. Consequent benefits are straight-forward expressions for the cost of equity capital at the corporate level (for both retained earnings and new equity) as well as at the investor level (post personal tax) in terms of both the dividend discount and CAPM-type models, which are applicable to classical and imputation tax systems. A fundamental framework is thereby provided which succeeds in illuminating investor pesonal tax liabilities as they might be expected to impact on a firm's investment and related dividend policies.     

Approximation methods for piecewise deterministic Markov processes and their costs

In this paper, we analyse piecewise deterministic Markov processes (PDMPs), as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of PDMPs. There one is interested in computing certain quantities of interest such as the probability of ruin or the value of an insurance company. Instead of explicitly solving the related integro-(partial) differential equation (an approach which can only be used in few special cases), we adapt the problem in a manner that allows us to apply deterministic numerical integration algorithms such as quasi-Monte Carlo rules; this is in contrast to applying random integration algorithms such as Monte Carlo. To this end, we reformulate a general cost functional as a fixed point of a particular integral operator, which allows for iterative approximation of the functional. Furthermore, we introduce a smoothing technique which is applied to the integrands involved, in order to use error bounds for deterministic cubature rules. We prove a convergence result for our PDMPs approximation, which is of independent interest as it justifies phase-type approximations on the process level. We illustrate the smoothing technique for a risk-theoretic example, and compare deterministic and Monte Carlo integration.     

Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity

We analyze the counterparty risk for credit default swaps using the Markov chain model of portfolio credit risk of multiple obligors with interacting default intensity processes. The default correlation between the protection seller and underlying entity is modeled by an increment in default intensity upon the occurrence of an external shock event. The arrival of the shock event is a Cox process whose stochastic intensity is assumed to follow an affine diffusion process with jumps. We examine how the correlated default risks between the protection seller and the underlying entity may affect the credit default premium in a credit default swap.