The Lévy LIBOR model

Models driven by Lévy processes are attractive because of their greater flexibility compared to classical diffusion models. First we derive the dynamics of the LIBOR rate process in a semimartingale as well as a Lévy Heath-Jarrow-Morton setting. Then we introduce a Lévy LIBOR market model. In order to guarantee positive rates, the LIBOR rate process is constructed as an ordinary exponential. Via backward induction we get that the rates are martingales under the corresponding forward measures. An explicit formula to price caps and floors which uses bilateral Laplace transforms is derived.     

Convergence of numerical methods for valuing path-dependent options using interpolation

One method for valuing path-dependent options is the augmented state space approach described in Hull and White (1993) and Barraquand and Pudet (1996), among others. In certain cases, interpolation is required because the number of possible values of the additional state variable grows exponentially. We provide a detailed analysis of the convergence of these algorithms. We show that it is possible for the algorithm to be non-convergent, or to converge to an incorrect answer, if the interpolation scheme is selected in appropriately. We concentrate on Asian options, due to their popularity and because of some errors in the previous literature. This revised version was published online in June 2006 with corrections to the Cover Date.     

The minimum variance hedge and the bankruptcy risk of the firm

In this paper, we analyze the influence of hedging with forward contracts on the firm's probability of bankruptcy (POB). The minimization of this probability can serve as a substitute for the maximization of shareholders' wealth. It is shown that the popular minimum variance hedge is generally neither necessary nor sufficient for the minimization of the firm's POB. Moreover, our model suggests a correction of the widespread view that a reduction in the variance of the future value of the firm is inevitably accompanied by a reduction in its default risk. We derive an analytical solution for the variance-minimizing hedge ratio of a firm exposed to both input and output price uncertainty that takes into account the issue of correlation. Based on this solution, we provide a graphical analysis to prove our claim that there is a fundamental difference between hedging policies focused on bankruptcy risk and those following conventional wisdom even if positive correlation constitutes a “natural” hedge.     

Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields

Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998), de Jong and Santa-Clara (1999), Björk and Svensson (2001) and Chiarella and Kwon (2001a). However, these models usually required the introduction of a large number of state variables which, at first sight, did not appear to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models are affine functions of the state variables, and conversely that the state variables in these models can be expressed as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain affine representations for a number of popular interest rate models.     

The effectiveness of interest-rate futures contracts for hedging Japanese bonds of different credit quality and duration

This study investigates the effectiveness of the Tokyo Stock Exchange (TSE)-traded Japanese 10-year JGB futures contract to hedge portfolios of Japanese bonds of differing maturity and credit quality. The bond portfolios examined are Government, AAA-, and AA-rated Eurobonds with maturities of 2, 3, 5, 7, 10, and 20 years. Consistent with the recent literature, the study employs univariate methods for calculating hedge ratios based on levels, first differences, and percentage change of each series. Out-of-sample forecasting is used to determine the effectiveness of the calculated hedge ratios for each of the bond portfolios and to determine which approach to calculating hedge ratios is the most effective. The results show that this particular futures contract does provide a good hedge, particularly for those bond terms closest to the 10-year term of the contract. There is some evidence, although not strong, that JGBs are better hedged than AAA and AA bonds. Investors should take some caution when using this futures contract to hedge bond portfolios of different maturities and credit ratings.     

薪酬合约的激励有效性研究:一个理论综述

薪酬激励是组织中最常用的激励手段之一，薪酬合约的激励效果直接影响组织效率。本文尝试用激励理论系统阐述各类薪酬合约的激励有效性条件，为这方面研究梳理出一个统一的理论框架。     

Pricing mortgage insurance contracts under housing price cycles with jump risk: evidence from the U.K. housing market

Previous studies have investigated the determinants of housing price cycles in the housing market; however, we observed the phenomenon of housing price jumps in the 2007 subprime crisis. This paper presents a discussion on the housing price cycle and abnormal price jumps to describe the behavior of housing prices in the United Kingdom. The empirical results show that the impact factors of housing cycles are market risk and the switching factor. Furthermore, the impact factors of jump risks include the bursting of the housing bubble and financial crises. Therefore, in this paper, we employ the Markov switching model with jump risks to value the MI contracts and analyze the influences of housing price cycles, jump risks, risks of market interest rate, and the prepayment risks on MI premiums. The results of sensitivity analysis show that more volatile housing price index returns, as well as longer periods of higher volatility in housing prices, raise MI premiums. Moreover, the MI premium is positively related to the absolute value of the average jump amplitude and the shock frequency of abnormal events. There is the tradeoff between the market interest rate and the prepayment risk. The influences of market interest rate are different on MI premium with/without prepayment risks.     

Liquidity operations during the financial crisis 2008/09: evidence from the relations between Korean won onshore and offshore markets

This paper addresses the interrelation of onshore and offshore markets before and after the Bank of Korea intervened in 2008/09. During the financial crisis, Korea faced a liquidity crunch and leveraged its high level of reserves to conduct swap agreements in late 2008. To analyse how the reforms affected the mean and volatility spillover in between the spot and NDF markets, an extended GARCH model is used. The main findings of this paper are that prior to the financial crisis, the spot market dominated the offshore market. This changed after South Korea addressed the won’s liquidity crunch at the height of the crisis. Mean and volatility spillover between the markets diminished and the price gap narrowed. In addition to the empirical results, the paper also underlines the significance of liquidity and robust capital requirements for central banks.