标题： 信用紧缩后的利率：多曲线普通衍生品和SABR 显示英文标题

标题： Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR

摘要： 我们对信贷紧缩危机期间市场和模型的演变进行了定量研究。 特别是，我们关注固定收益市场，并分析了关于Libor和OIS利率差异、基差互换利差的激增以及抵押协议和CSA贴现的扩散的最相关实证证据，从信用和流动性效应的角度进行分析。 我们还回顾了目前从业者中流行的新的现代定价方法，该方法基于多条收益率曲线，反映了不同期限的Libor利率的不同信用和流动性风险，以及在有抵押品且每日保证金的情况下衍生品交易产生的现金流的隔夜贴现。 我们报告了普通利率衍生品的经典和现代无套利定价公式，以及具有随机波动率的市场标准SABR模型的多曲线推广。 然后，我们报告了对最近市场数据的实证分析，比较了信贷紧缩前后的定价方法，并展示了市场实践从经典框架向现代框架的转变。 特别是，我们证明自2010年3月以来，利率互换市场已放弃了信贷紧缩前利率世界典型的经典单曲线定价方法，采用了现代的多曲线CSA方法，从而将信用和流动性效应纳入市场价格中。 同样的分析也应用于欧洲的看涨期权/看跌期权，发现完全转向现代多曲线CSA方法推迟到了2010年8月。 最后，我们展示了SABR模型在与新市场证据一致地校准市场波动率微笑方面的稳健性。 显示英文摘要

摘要： We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review the new modern pricing approach prevailing among practitioners, based on multiple yield curves reflecting the different credit and liquidity risk of Libor rates with different tenors and the overnight discounting of cash flows originated by derivative transactions under collateral with daily margination. We report the classical and modern no-arbitrage pricing formulas for plain vanilla interest rate derivatives, and the multiple-curve generalization of the market standard SABR model with stochastic volatility. We then report the results of an empirical analysis on recent market data comparing pre- and post-credit crunch pricing methodologies and showing the transition of the market practice from the classical to the modern framework. In particular, we prove that the market of Interest Rate Swaps has abandoned since March 2010 the classical Single-Curve pricing approach, typical of the pre-credit crunch interest rate world, and has adopted the modern Multiple-Curve CSA approach, thus incorporating credit and liquidity effects into market prices. The same analysis is applied to European Caps/Floors, finding that the full transition to the modern Multiple-Curve CSA approach has retarded up to August 2010. Finally, we show the robustness of the SABR model to calibrate the market volatility smile coherently with the new market evidences.