arXiv subjects

Harry Zheng

Publications and source records attributed to Harry Zheng.

43 records · Page 3Linked to original sources

arXiv2013

On Reduced Form Intensity-based Model with Trigger Events

Corporate defaults may be triggered by some major market news or events such as financial crises or collapses of major banks or financial institutions. With a view to develop a more realistic model for credit risk analysis, we introduce a new type of reduced-form intensity-based model that can incorporate the impacts of both observable "trigger" events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. Both single-default and multiple-default cases are considered in this paper. In the former case, a simple expression for the distribution of the default time is obtained. Applications of the proposed model to price defaultable bonds and multi-name Credit Default Swaps (CDSs) are provided.

q-fin.CP↗

arXiv2012

Smooth Value Function with Applications in Wealth-CVaR Efficient Portfolio and Turnpike Property

In this paper we continue the study of Bian-Miao-Zheng (2011) and extend the results there to a more general class of utility functions which may be bounded and non-strictly-concave and show that there is a classical solution to the HJB equation with the dual control method. We then apply the results to study the efficient frontier of wealth and conditional VaR (CVaR) problem and the turnpike property problem. For the former we construct explicitly the optimal control and discuss the choice of the optimal threadshold level and illustrate that the wealth and the CVaR are positively correlated. For the latter we give a simple proof to the turnpike property of the optimal policy of long-run investors and generalize the results of Huang-Zariphopoulou (1999).

q-fin.PM↗

arXiv2012

On Pricing Basket Credit Default Swaps

In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive formulas for the coefficients, which makes the calculation fast and efficient in finding rates of basket CDSs. In the homogeneous case, we explore the ordered default time in limiting case and further include the exponential decay and the multistate stochastic intensity process. The numerical study indicates that, in the valuation of the swap rates and their sensitivities with respect to underlying parameters, our proposed model outperforms the Monte Carlo method.

q-fin.PR↗

arXiv2010

A la Carte of Correlation Models: Which One to Choose?

In this paper we propose a copula contagion mixture model for correlated default times. The model includes the well known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the marginal default times to follow some contagion intensity processes coupled with copula dependence structure. We apply the total hazard construction method to generate ordered default times and numerically compare the pricing impact of different models on basket CDSs and CDOs in the presence of exponential decay and counterparty risk.

q-fin.PR↗

arXiv2010

Constrained NonSmooth Utility Maximization on the Positive Real Line

We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their dual relationship. We simplify the present proofs in this area and extend the existing duality theory to the constrained nonsmooth setting.

q-fin.CP↗

arXiv2010

Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.

q-fin.CP↗

arXiv2010

Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expansion method to approximate the conditional expectation of the stochastic variance associated with the basket value process. The numerical tests show that the suggested method is fast and accurate in comparison with the Monte Carlo and other methods in most cases.

q-fin.CP↗