Affine LIBOR models driven by real-valued affine processes

The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative, and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by nonnegative affine processes, a restriction that makes it hard to produce volatility smiles. We modify the affine LIBOR models in such a way that real-valued affine processes can be used without destroying the nonnegativity of interest rates. Numerical examples show that in this class of models, pronounced volatility smiles are possible.     

LEVY-LIBOR市场模型的蒙特卡罗模拟参数校准与估计

基于远期LIBOR利率的随机波动与无限跳跃特征，针对标准化LIBOR市场模型（LMM）和随机波动率LIBOR市场模型（SV-LMM）应用局限，进一步引入Levy无限跳跃过程，建立多因子非标准化Levy 跳跃随机波动率LIBOR市场模型（SVLEVY-LMM）。在此基础上，基于非参数化相关矩阵假设，运用互换期权（Swaption）、利率上限（Cap）等主要市场校准工具和蒙特卡罗模拟技术，对模型局部波动率和瞬间相关系数等参数进行有效市场校准；应用自适应马尔科夫链蒙特卡罗模拟方法（A-MCMC）对Levy跳跃与随机波动参数进行有效理论估计。实证认为，对远期利率波动率校准，分段固定波动率结构较为符合市场实际情况；对远期利率相关系数矩阵校准，非参数化相关系数矩阵具有最小估计误差和最佳的市场适应性；SVLEVY-LMM能够最好拟合远期LIBOR利率。     

Do Central Bank Liquidity Facilities Affect Interbank Lending Rates?

In response to the global financial crisis that started in August 2007, central banks provided extraordinary amounts of liquidity to the financial system. To investigate the effect of central bank liquidity facilities on term interbank lending rates near the start of the crisis, we estimate a six-factor arbitrage-free model of U.S. Treasury yields, financial corporate bond yields, and term interbank rates. This model can account for fluctuations in the term structure of credit and liquidity spreads observed in the data. A significant shift in model estimates after the announcement of the liquidity facilities suggests that these central bank actions did help lower the liquidity premium in term interbank rates.     

The unaccountable risks of LIBOR

One of the on‐going consequences of recent financial crises seems to be that the conventional ‘anchor’ measures of global finance (such as the US dollar, treasury bonds and AAA rated securities) are no longer playing the anchoring role once believed of them. LIBOR now needs to be added to this list and not just because it has been tarnished by illegal practices, but because it is looking increasingly surpassed by financial market practices. LIBOR was believed to provide a risk‐free rate of interest, but has been revealed to be risk‐laden. Moreover, LIBOR is a measure of the costs of borrowing, whilst market concern is increasingly with measures of interest rate volatility. This paper looks at why, in the context of crisis, financial market focus on interest rates is turning towards other benchmarks, notably the overnight indexed swap (OIS) market, and what this shift might be telling us about the anchoring requirements of global financial markets.     

基于多因子LIBOR模型的CMS数字范围债券定价

论文在鞅论和测度变换的基础上，在多因子LIBOR市场模型的框架下，通过二阶变差的方法获得了CMS利率的近似分布，巧妙的解决了CMS利率在LIBOR市场模型下不满足对数正态分布的问题。在此基础上，利用CMS利率的近似概率分布，求解得出CMS范围数字债券的定价，避免了Monte Carlo大数据模拟的情况，在对浮动利率产品进行研究的过程中，论文使用了两种不同的方法进行比较，主要是引理法和Girsanov法，这为投资者的定价过程提供了选择，有利于投资者获得更好的投资回报。