Affine model of inflation-indexed derivatives and inflation risk premium

This paper proposes an affine-based approach which jointly captures the nominal interest rate, the real interest rate, and the inflation risk premium to price inflation-indexed derivatives, including zero-coupon inflation-indexed swaps, year-on-year inflation-indexed swaps, inflation-indexed swaptions, and inflation-indexed caps and floors. We provide an example and explain how to use traded zero-coupon inflation-indexed swap rates to estimate inflation risk premiums.     

人民币利率互换中风险的市场价格

为研究人民币利率互换市场中流动性风险和违约风险的市场价格,运用三因子广义高斯仿射模型,同时对人民币国债市场利率、银行间质押式回购市场利率和利率互换市场利率进行模拟,并采用极大似然估计方法估计众多参数。结果发现,在目前的人民币利率互换定价过程中,流动性要素相对违约要素更加重要,市场给予流动性风险以显著的风险溢价。如采用互换利差定价法为人民币利率互换定价的话,可以以回购利率作为基准,在此基础上考虑信用风险来进行。     

Variance swaps under the threshold Ornstein–Uhlenbeck model

Variance swap is a typical financial tool for managing volatility risk. In this paper, we evaluate different types of variance swaps under a threshold Ornstein–Uhlenbeck model, which exhibits both mean reversion and regime switching features in the underlying asset price. We derive the analytical solution for the joint moment generating function of log‐asset prices at two distinct time points. This enables us to price various types of variance swaps analytically. Copyright © 2017 John Wiley & Sons, Ltd.     

金融危机下中美两国利率互换市场的特征及互动性分析

以2008～2009年中美两国利率互换市场的日交易数据为样本,分析比较了影响两国利率互换利差的主要因素,进而实证研究了危机期间中美两国利率互换市场的动态互动效应。结果表明:两国利率的水平和利率期限结构斜率是影响互换利差的主要因素,另外,中国的流动性溢价和美国的违约溢价对互换利差的影响也较为显著;研究发现:中美两国互换利差均受对方市场因素的影响,特别地,在金融危机期间,中美两国利率互换市场间存在着明显的互动效应,一方面,美国利率互换市场信息能够对中国利率互换市场产生较强的冲击,虽然冲击的程度受制于美国的经济状况;另一方面,中国市场对美国市场也形成了一定的反向冲击,且程度受制于中国的货币政策。     

Restructuring risk in credit default swaps: An empirical analysis

This paper estimates the price for restructuring risk in the US corporate bond market during 1999–2005. Comparing quotes from default swap (CDS) contracts with a restructuring event and without, we find that the average premium for restructuring risk represents 6%–8% of the swap rate without restructuring. We show that the restructuring premium depends on firm-specific balance-sheet and macroeconomic variables. And, when default swap rates without a restructuring event increase, the increase in restructuring premia is higher for low-credit-quality firms than for high-credit-quality firms. We propose a reduced-form arbitrage-free model for pricing default swaps that explicitly incorporates the distinction between restructuring and default events. A case study illustrating the model’s implementation is provided.     

利用传染模型对含有对手风险的信用证券定价(英文)

本文利用传染模型研究了可违约债券和含有对手风险的信用违约互换的定价。我们在约化模型中引入具有违约相关性的传染模型,该模型假设违约过程的强度依赖于由随机微分方程驱动的随机利率过程和交易对手的违约过程.本文模型可视为Jarrow和Yu(2001)及Hao和Ye(2011)中模型的推广.进一步地,我们利用随机指数的性质导出了可违约债券和含有对手风险的信用违约互换的定价公式并进行了数值分析.     

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本文讨论了信用衍生产品之一的总收益互换的定价问题. 其中涉及到利率风险和违约风险, 本文利用HJM利率模型来刻画利率风险, 并利用强度模型和混合模型对违约风险进行建模. 分别考虑了违约时间与利率无关时总收益互换合约的定价问题, 以及违约时间与利率相关时总收益互换合约的定价问题, 给出了相应的定价模型, 并用蒙特卡罗模拟方法得到定价问题的数值解.     

Prices and Asymptotics for Discrete Variance Swaps

Abstract

We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull–White and Schöbel–Zhu stochastic volatility models, we give simple explicit expressions (improving Broadie and Jain (2008a). The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761–797) in the case of the Heston model). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than that of the continuous variance swap. The interest rate and the correlation between the underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a. The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761–797), Jarrow et al. (2013. Discretely sampled variance and volatility swaps versus their continuous approximations. Finance and Stochastics, 17(2), 305–324) and Keller-Ressel and Griessler (2012. Convex order of discrete, continuous and predictable quadratic variation and applications to options on variance. Working paper. Retrieved from http://arxiv.org/abs/1103.2310).     

Pricing model of interest rate swap with a bilateral default risk

Under the foundation of Duffie & Huang (1996) [7], this paper integrates the reduced form model and the structure model for a default risk measure, giving rise to a new pricing model of interest rate swap with a bilateral default risk. This model avoids the shortcomings of ignoring the dynamic movements of the firm’s assets of the reduced form model but adds only a little complexity and simplifies the pricing formula significantly when compared with Li (1998) [10]. With the help of the Crank-Nicholson difference method, we give the numerical solutions of the new model to study the default risk effects on the swap rate. We find that for a one year interest rate swap with the coupon paid per quarter, the variance of the default fixed rate payer decreases from 0.1 to 0.01 only causing about a 1.35%’s increase in the swap rate. This is consistent with previous results.     

The affine inflation market models

Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data.