Basket CDS pricing with default intensities using a regime-switching shot-noise model

In this paper, we employ an intensity-based credit risk model with regime-switching to study the valuation of basket CDS in a homogeneous portfolio. We assume that the default intensities are described by some dependent regime-switching shot-noise processes and the individual jumps of the intensity are driven by a common factor. By using the conditional Laplace transform of the regime-switching shot-noise process, we obtain the closed form results for pricing the fair spreads of the basket CDS. We present some numerical examples to illustrate the effect of the model parameters on the fair spreads.     

An FFT approach for option pricing under a regime-switching stochastic interest rate model

In this article, we investigate the pricing of European-style options under a Markovian regime-switching Hull–White interest rate model. The parameters of this model, including the mean-reversion level, the volatility of the stochastic interest rate, and the volatility of an asset’s value, are modulated by an observable, continuous-time, finite-state Markov chain. A closed-form expression for the characteristic function of the logarithmic terminal asset price is derived. Then, using the fast Fourier transform, a price of a European-style option is computed. In a two-state Markov chain case, numerical examples and empirical studies are presented to illustrate the practical implementation of the model.     

Mean-variance problem for an insurer with default risk under a jump-diffusion risk model

Abstract

This paper considers an optimal investment-reinsurance problem with default risk under the mean-variance criterion. We assume that the insurer is allowed to purchase proportional reinsurance and invest his/her surplus in a risk-free asset, a stock and a defaultable bond. The goal is to maximize the expectation and minimize the variance of the terminal wealth. We first formulate the problem to stochastic linear-quadratic (LQ) control problem with constraints. Then the optimal investment-reinsurance strategies and the corresponding value functions are obtained via the viscosity solutions of Hamilton-Jacobi-Bellman (HJB) equations for the post-default case and pre-default case, respectively. Finally, we provide numerical examples to illustrate the effects of model parameters on the optimal strategies and value functions.     

Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

This paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.     

On a discrete interaction risk model with delayed claims and stochastic incomes under random discount rates

In this paper, we study a discrete interaction risk model with delayed claims and stochastic incomes in the framework of the compound binomial model. A generalized Gerber-Shiu discounted penalty function is proposed to analyse this risk model in which the interest rates follow a Markov chain with finite state space. We derive an explicit expression for the generating function of this Gerber-Shiu discounted penalty function. Furthermore, we derive a recursive formula and a defective renewal equation for the original Gerber-Shiu discounted penalty function. As an application, the joint distributions of the surplus one period prior to ruin and the deficit at ruin, as well as the probabilities of ruin are obtained. Finally, some numerical illustrations from a specific example are also given.     

The ruin probabilities of a discrete time risk model with one-sided linear claim sizes and dependent risks

This article investigates the ruin probabilities of a discrete time risk model with dependent claim sizes and dependent relation between insurance risks and financial risks. The risk-free and risky investments of an insurer lead to stochastic discount factors {θ_n}_{n ? 1}. The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations {?_n}_{n ? 1}. The i.i.d. random pairs {(?_n, θ_n)}_{n ? 1} follow a common bivariate Sarmanov-dependent distribution. When the common distribution of the innovations is heavy tailed, we establish some asymptotic estimates for the ruin probabilities of this discrete time risk model.