基于无套利对冲原理的信用风险期权定价

文章拓展了Klein假设中关于固定违约门槛的假设,构造可变违约门槛,根据无套利对冲原理,通过偏微分方程这种数学工具,推导出含信用风险的欧式脆弱期权价格波动的偏微分方程组和期权定价模型,进而求其显示解,得到类似于Black-Scholes公式的定价公式,该公式的推导过程比使用鞅理论推导更加浅显易懂。     

Valuing spread options with counterparty risk and jump risk

In this paper, we investigate spread options with counterparty risk in a jump-diffusion model. Due to the fact that there is no closed-form formula of spread options with counterparty risk, we obtain analytical expressions of lower and upper bounds by employing the measure-change technique. Finally, we numerically check the accuracy of the bounds and analyze the impacts of counterparty risk and jump risk on spread option prices.     

Pricing basket spread options with default risk under Heston–Nandi GARCH models

In this paper, we investigate basket spread options under the Heston–Nandi GARCH model. Moreover, we adopt the reduced-form model to capture default risk, which is correlated with all underlying assets. Because of the nonexistence of the analytical fair values, we obtain a closed-form approximated pricing formula of basket spread options with default risk. Finally, we examine the accuracy of approximations and then use the proposed formulae to illustrate the effect of the number of the underlying assets and default risk as well.     

Jumps in intensity models: investigating the performance of Ornstein-Uhlenbeck processes in credit risk modeling

This work presents intensity-based credit risk models where the default intensity of the point process is modeled by an Ornstein-Uhlenbeck type process completely driven by jumps. Under this model we compute the default probability over time by linking it to the characteristic function of the integrated intensity process. In case of the Gamma and the Inverse Gaussian Ornstein-Uhlenbeck processes this leads to a closed-form expression for the default probability and to a straightforward estimate of credit default swaps prices. The model is calibrated to a series of real-market term structures and then used to price a digital default put option. Results are compared with the well known cases of Poisson and CIR dynamics. Possible extensions of the model to the multivariate setting are finally discussed.     

Exchange options for catastrophe risk management

In this paper, we investigate the pricing issue and catastrophe risk management of exchange options. Exchange options allow the holder to exchange its stocks for another at maturity and can be seen as an extended version of catastrophe equity put options with another traded asset price as strike prices. Since option holders have to issue new shares to exercise the option, we illustrate the differences between option prices calculated using pre-exercise and post-exercise share prices. The effects of default risk on option prices and risk management are also considered. Finally, risk management analysis shows that exchange options can effectively hedge catastrophe risk.     

Explicit expressions to counterparty credit exposures for Forward and European Option

With the fast development of over the counter (OTC) derivatives market, counterparty credit risk (CCR) has become one of the main risks that can even affect the survival of banks. As a result, it is essential to measure and manage CCR exposures. Giant financial institutions apply numerical methods such as the Monte Carlo to calculate exposures. However, the numerical methods usually cost a significant amount of time, and some advanced algorithms like distributed and parallel processing are usually used to accelerate the calculation. Nevertheless, for small banks, they cannot afford the calculation cost. In order to make small banks manage CCR more efficiently, this paper puts forward analytic models to measure CCR exposures and derives the explicit expressions to exposures for Forward contract and European Option, which are represented in the OTC market. The explicit expressions to credit exposures for Forward contract are derived under the assumption that the underlying market risk factors follow Geometric Brown Motion. For European Option case, the problem turns to be difficult since the analytic formula involves double-definite integral of Gaussian function that cannot be simplified into elementary functions. An approximating normal distribution function with integrability is proposed, then the analytic approximations of European Call Option’s credit exposures and maximum errors are presented.     

Market perception of sovereign credit risk in the euro area during the financial crisis

We study market perception of sovereign credit risk in the euro area during the financial crisis. In our analysis we use a parsimonious CDS pricing model to estimate the probability of default (PD) and the loss given default (LGD) as perceived by financial markets. In our empirical results the estimated LGDs perceived by financial markets stay comfortably below 40% in most of the samples. Global financial indicators are positively and strongly correlated with the market perception of sovereign credit risk; whilst macroeconomic and institutional developments were at best only weakly correlated with the market perception of sovereign credit risk.     

Valuation of double trigger catastrophe options with counterparty risk

This study presents a novel catastrophe option pricing model that considers counterparty risk. Asset prices are modeled through a jump-diffusion process which is correlated to counterparty loss process and collateral assets. Because of the long term of catastrophe options, this study also examines the model in the stochastic interest rate environment. The numerical results indicate that counterparty risk significantly affects the value of options. Recently, numerous serious financial events have demonstrated the importance of counterparty risk when valuing financial products.     

Valuation of options on the maximum of two prices with default risk under GARCH models

In this paper, we work under GARCH models to value options on the maximum or the minimum of two prices. In addition, we consider not only two underlying asset prices but also geometric average ones. Further, default risk is also incorporated in a reduced-form model. In the proposed framework, closed-form pricing formulae of options on the maximum with or without default risk are derived and then used to perform numerical examples.     

Density approximations for multivariate affine jump-diffusion processes

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in option pricing, credit risk, and likelihood inference highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.     

Pricing vulnerable options with stochastic liquidity risk

In this paper, we consider vulnerable options with stochastic liquidity risk. We employ liquidity-adjusted pricing models to describe the underlying stock price and option issuer’s assets. In addition, the correlation between these assets is stochastic, depending on the market liquidity measures. In the proposed framework, we derive closed forms of vulnerable European options with stochastic liquidity risk and then use them to illustrate the effects of stochastic liquidity risk on vulnerable option prices. Numerical results show that the effects of liquidity risk on the prices of out-of-the-money options or the options with a short maturity are not negligible.     

Pricing European continuous-installment currency options with mean-reversion

In this paper, we consider European continuous-installment currency option under the mean-reversion environment. Specifically, we provide efficient pricing formula of installment currency put option via a partial differential equation (PDE) approach when the exchange rate follows the mean reverting lognormal model. Using the Mellin transform techniques, we derive the integral equation representation for the optimal stopping boundary from the PDE for pricing of the option. To verify the efficiency and accuracy of our approach, we provide computational results with the least square Monte Carlo method proposed by Longstaff and Schwartz (2001). We also present some numerical examples to examine the characteristics of the optimal boundaries and prices.     

带Poisson跳的Black-Scholes模型的期权定价

主要讨论欧式期权的定价公式。首先给出一个B-S期权定价公式的简化方法,使具有一般微积分知识的读者就能理解;并假定股票价格过程遵循带Poisson跳的扩散过程,在股票预期收益率、波动率和无风险利率均为时间函数的情况下,得到欧式期权定价公式和买权与卖权之间的平价关系。     

考虑违约风险的可转换债券定价新模型

随着近几年我国证券市场可转换债券的发展,对其进行定价成为学界的一个热门课题。利用期权定价方法对可转换债券进行定价,并得到了一个考虑违约风险的可转换债券定价新模型。     

Stability in consumer credit scores: Level and direction of FICO score drift as a precursor to mortgage default and prepayment

This article represents an extension of the expansive credit risk and credit migration literature, prominent in the corporate bond and securities risk pricing literature, to an analysis of the drift of consumer credit scores. A rich data set of residential mortgages is used to observe credit score migration post loan origination and in a test of the ability of credit score transition to serve as a precursor to potential default and prepayment. The results indicate credit scores provide signals and information to investors and servicing agents in a fashion similar to credit ratings on commercial paper as to default potential.     

基于Stackelberg博弈的供应链信用风险分析

讨论了由一个供应商和一个销售商组成的简单供应链,在销售商还款不确定的前提下,基于供应商和销售商订货过程是Stackelberg博弈,给出了他们的最优定价和订货策略,并说明了通过合理定价,供应商可以有效地防范信用风险;然后分析了销售商违约对供销双方及供应链的影响,并通过算例进行了说明。     

A model of the topology of the bank – firm credit network and its role as channel of contagion

This paper proposes a stochastic model of a bipartite credit network between banks and the non-bank corporate sector that encapsulates basic stylized facts found in comprehensive data sets for bank-firm loans for a number of countries. When performing computational experiments with this model, we find that it shows a pronounced non-linear behavior under shocks: the default of a single unit will mostly have practically no knock-on effects, but might lead to an almost full-scale collapse of the entire system in a certain number of cases. The dependency of the overall outcome on firm characteristics like size or number of loans seems fuzzy. Distinguishing between contagion due to interbank credit and due to joint exposures to counterparty risk via loans to firms, the later channel appears more important for contagious spread of defaults.     

信息不完全的信用风险定价模型及其在我国的应用

基于信息不完全的信用风险定价模型与传统的结构化模型和约化模型的最大区别在于它将信息不完全这一前提引入了以信息完全为前提的结构化模型,同时它又考虑了约化模型中强度的优点,引入短期信用风险的度量,成为当前最切合现实的信用风险定价模型。本文认为,应用基于信息不完全的信用风险定价模型来测度信用风险,将具有十分重要的现实意义。     

A revised version of the Cathcart & El-Jahel model and its application to CDS market

Decisions in Economics and Finance - The paper considers the pricing of credit default swaps (CDSs) using a revised version of the credit risk model proposed in Cathcart and El-Jahel (2003)....