Pricing counterparty default risks: Applications to FRNs and vulnerable options

This paper provides simple closed-form pricing models for floating-rate notes and vulnerable options under the counterparty risk framework of [Jarrow, R., Yu, F., 2001. Counterparty risk and the pricing of default risk. Journal of Finance 56, 1765-1799]. After deriving closed-form pricing models for them, this paper illustrates the impact of the default intensity of counterparty on the prices of floating-rate notes and vulnerable options. Numerical examples show that the default risk of counterparty is an important factor of the value of floating-rate notes and vulnerable options.     

Valuation of vulnerable American options with correlated credit risk

This article evaluates vulnerable American options based on the two-point Geske and Johnson method. In accordance with the Martingale approach, we provide analytical pricing formulas for European and multi-exercisable options under risk-neutral measures. Employing Richardson’s extrapolation gets the values of vulnerable American options. To demonstrate the accuracy of our proposed method, we use numerical examples to compare the values of vulnerable American options from our proposed method with the benchmark values from the least-square Monte Carlo simulation method. We also perform sensitivity analyses for vulnerable American options and show how the prices of vulnerable American options vary with the correlation between the underlying assets and the option writer’s assets.      

Fast estimation of true bounds on Bermudan option prices under jump-diffusion processes

Fast pricing of American-style options has been a difficult problem since it was first introduced to the financial markets in 1970s, especially when the underlying stocks’ prices follow some jump-diffusion processes. In this paper, we extend the ‘true martingale algorithm’ proposed by Belomestny et al. [Math. Finance, 2009, 19, 53–71] for the pure-diffusion models to the jump-diffusion models, to fast compute true tight upper bounds on the Bermudan option price in a non-nested simulation manner. By exploiting the martingale representation theorem on the optimal dual martingale driven by jump-diffusion processes, we are able to explore the unique structure of the optimal dual martingale and construct an approximation that preserves the martingale property. The resulting upper bound estimator avoids the nested Monte Carlo simulation suffered by the original primal–dual algorithm, therefore significantly improving the computational efficiency. Theoretical analysis is provided to guarantee the quality of the martingale approximation. Numerical experiments are conducted to verify the efficiency of our algorithm.     

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market

We study the numerical solutions for an integro-differential parabolic problem modeling a process with jumps and stochastic volatility in financial mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, a general-purpose, partial differential equation solver.     

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be a diffusion or a Markov process, as the examples in Sect. 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus. E. Alòs’ research is supported by grants MEC FEDER MTM 2006 06427 and SEJ2006-13537. J.A. León’s research is partially supported by the CONACyT grant 45684-F. J. Vives’ research is supported by grant MEC FEDER MTM 2006 06427.     

Growth options,macroeconomic conditions,and the cross section of credit risk

This paper develops a structural equilibrium model with intertemporal macroeconomic risk, incorporating the fact that firms are heterogeneous in their asset composition. Compared with firms that are mainly composed of invested assets, firms with growth options have higher costs of debt because they are more volatile and have a greater tendency to default during recession when marginal utility is high and recovery rates are low. Our model matches empirical facts regarding credit spreads, default probabilities, leverage ratios, equity premiums, and investment clustering. Importantly, it also makes predictions about the cross section of all these features.     

A Note on Option Pricing for the Constant Elasticity of Variance Model

We study the arbitrage free optionpricing problem for the constant elasticity of variance (CEV) model. To treatthestochastic aspect of the CEV model, we direct attention to the relationship between the CEV modeland squared Bessel processes. Then we show the existence of a unique equivalentmartingale measure and derive the Cox's arbitrage free option pricing formulathrough the properties of squared Bessel processes. Finally we show that the CEVmodel admits arbitrage opportunities when it is conditioned to be strictlypositive.     

Options on the minimum or the maximum of two average prices

This paper studies options on the minimum/maximum of two average prices. We provide a closed-form pricing formula for the option with geometric averaging starting at any time before maturity. We show overwhelming numerical evidence that the variance reduction technique with the help of the above closed-form solution dramatically improves the accuracy of the simulated price of an option with arithmetic averaging. The proposed options are found widely applicable in risk management and in the design of incentive contracts. The paper also discusses some parity relationships within the family of average-rate options and provides the upper and lower bounds for the proposed options with arithmetic averaging. This revised version was published online in June 2006 with corrections to the Cover Date.     

Pricing the Risks of Default: A Note on Madan and Unal

In their well-known article, Madan and Unal (1998) presented one of the first intensity-based credit risk models. In this approach the default intensity is directly linked to the market value of the firm's equity. In order to derive the probability of default Madan and Unal have to solve a partial differential equation (PDE). Here, we show that one of the transformations in the derivation of the solution of this PDE is not correct and analyze the difference between the correct solution of the PDE and the solution based on the incorrect transformation. As a consequence of the transformation error the credit risk of a debtor is systematically underestimated.     

Dynamical analysis of corporate bonds based on the yield spread term-quality surface

Our aim of this research is to propose a model which estimates implied relative credit reliability from the yield spread of defaultable bonds and evaluates their spread risk. We introduce “yield spread term-quality surface” (YSTQS) which is defined on the space of duration and credit reliability of the issuers, and express their yield spread. First, we review the general pricing theorem of defaultable bonds with unpredictable recovery in the no-arbitrage context based on the external hazard rates. Second, we show that the dynamics of state variables determine the shape of the YSTQS, and they drive the YSTQS if the loss-adjusted hazard rates are described by a function of them. Finally, we show an empirical analysis of our model with daily yield spread, duration, and the credit ratings of corporate bonds.

长寿风险对寿险和年金产品定价的对冲效应研究

作为老龄社会的重要风险,长寿风险专题研究是近20年来公共养老金领域、保险公司关注的热点。长寿风险引发的保险公司寿险产品定价高估和年金产品定价低估之间存在潜在的自然对冲效应。为了量化这种对冲效应的长期影响,本文基于构建的同时涵盖低龄、高龄和超高龄在内的整个生命跨度的全年龄人口动态死亡率模型,采用对冲弹性量化终身寿险与终身年金、两全保险与定期年金、递延寿险与递延年金三类保障型寿险产品和养老型年金产品对冲效应的动态演变,并通过敏感性分析扩展探讨利率变化对对冲效应的长期影响。研究发现,从单位寿险和年金产品组合的净对冲效应来看,由于保险公司的产品定价区分了性别差异,使得女性的对冲效应更明显,因而女性对应的产品组合中的长寿风险对保险公司的影响更不显著。作为系统性风险,利率风险和长寿风险也存在对冲,利率上升能抵消或对冲长寿风险的影响,低利率下长寿风险更显著。     

Pricing of Defaultable Bonds with Log-Normal Spread: Development of the Model and an Application to Argentinean and Brazilian Bonds During the Argentine Crisis

In this paper we describe a two-factor model for a defaultable discount bond, assuming log-normal dynamics with bounded volatility for the instantaneous short rate spread. Under some simplified hypothesis, we obtain an explicit barrier-type solution for zero recovery and constant recovery. We also present a numerical application for Argentinean and Brazilian Sovereign Bonds during the default crisis of Argentina.JEL Classification: G 13     

Discerning the Impact of Derivatives on Asset Risk: The Case of Canadian Banks

The Canadian banks have shown remarkable resilience to the financial crisis that intensified in the late 2008. The interesting question is whether this stability is due to their prudent lending practices to limit the original risk exposures or due to effective risk management through hedging by using financial derivatives. In this paper, we implement the option‐theoretic model of Merton to calculate the implied asset risk and discern the impact of these derivatives on the aggregate risk for Canadian banks over the period 1997–2008. An algorithm of iterative procedure is developed to impute asset value and risk from bank stock prices. Our estimates show that the risk for Canadian banks is low and even decreasing till the unfolding of the recent crises in 2008. Further analyses reveal that such low risks are not due to reliance on hedging, nor is it related to trading in derivatives, after disentangling the intertwined effects of hedging and trading. These results suggest that involvements in derivatives, in and of themselves, should not be blamed for causing the bank crises; rather, it is conservatism in controlling original risk exposures that remains fundamental for safeguarding a healthy financial system.     

A note on different models of stochastic processes dealt with in the collective theory of risk

Abstract

1. For the definition of general processes with special regard to those concerned in Collective Risk Theory reference is made to Cramér (Collective Risk Theory, Skandia Jubilee Volume, Stockholm, 1955). Let the independent parameter of such a process be denoted by τ, with the origin at the point of departure of the process and on a scale independent of the number of expected changes of the random function. Denote with p(τ, n)dt the asymptotic expression for the conditional probability of one change in the random function while the parameter passes from τ to τ + dτ: relative to the hypothesis that n changes have occurred, while the parameter passes from 0 to τ. Assume further—unless the contrary is stated—that the probability of more than one change, while the parameter passes from τ to τ + dτ, is of smaller order than dτ.     

The effects of tone at the top and coordination with external auditors on internal auditors’ fraud risk assessments

Prior research suggests that internal auditors’ judgements are subject to management influence resulting in compromised risk assessments. This study investigates the effects of the tone at the top and coordination with external auditors on internal auditors’ fraud risk assessments. Results of an experiment involving 64 internal auditors indicate that when the tone at the top is poor, rather than favouring management, internal auditors report a higher risk of intentional misstatements and that coordination with external auditors can further reduce expectations of the incidence of intentional misstatements.     

中国农业企业汇率风险应对行为的实证研究——基于企业竞争力视角

本文提出了一个涉外企业汇率风险应对行为的分析框架,并利用352家涉外农业企业调查数据与多元Logit模型,从企业竞争力视角实证检验中国农业企业汇率风险应对行为的影响因素。研究发现,企业竞争力对中国农业企业避险策略选择至关重要,且表征企业竞争力的诸多变量对汇率风险应对行为的影响各不相同:融资能力越强、在技术方面越有优势的农业企业越倾向于使用运营策略规避汇率风险,而国际化程度越高的农业企业越倾向于使用金融衍生工具管理汇率风险;同时,农业企业汇率风险应对行为存在较为明显的地区差异。在此基础上,本文提出中国涉外农业企业应对汇率风险、扩大出口的若干政策建议。