再论两因素赫尔-怀特模型:CVA计算中两因素利率模型的相关结构

ERN: Swaps & Forwards (Topic) Pub Date : 2019-03-16 DOI:10.2139/ssrn.3338987

Osamu Tsuchiya

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引用次数: 1

摘要

信贷估值调整(CVA)(估值调整[XVA]) [Green]的发展，提高了Hull-White模型[Tan14] [Tsuchiya]等简单利率模型的重要性。这是因为XVA模型是一个外汇混合模型，只有当利率部分是一个简单的高斯模型时才易于处理。对于利率工具的XVA计算，即使对于掉期投资组合，收益率曲线的去相关性也很重要。在双因素Hull-White模型中获取相关结构是CVA (XVA)建模的重要组成部分。然而，除了[AndersenPiterbarg]的分析外，双因素Hull-White模型的相关结构研究还不够。本文详细分析了双因素Hull-White模型的相关结构。采用近似公式和蒙特卡罗模拟相结合的方法研究了共初始掉期利率的相关结构。Hull-White模型只有在参数(波动率和均值回归强度)满足一定关系时才能捕捉收益率曲线的去相关性，使得双因素Hull-White模型对XVA的估值有效。

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Two-Factor Hull-White Model Revisited: Correlation Structure for Two-Factor Interest Rate Model in CVA Calculation

The development of credit valuation adjustment (CVA) (valuation adjustments [XVA]) [Green] has increased the importance of simple interest rate models such as the Hull-White model [Tan14] [Tsuchiya]. This is because the XVA model is an FX hybrid model, and is tractable only when the interest rate part is a simple Gaussian model.

For the XVA calculation of interest rate instruments, de-correlation of the yield curve can be important even for the swap portfolio. Capturing the correlation structure in the two-factor Hull-White model is an integral element of CVA (XVA) modeling. However, the correlation structure in two-factor Hull-White model has not studied enough except for the analysis in [AndersenPiterbarg].

In this study, the correlation structure of the two-factor Hull-White model is analyzed in detail. The correlation structure of co-initial swap rates is investigated using a combination of the approximation formula and Monte-Carlo simulation. The Hull-White model captures the de-correlation of the yield curve only when the parameters (volatilities and mean reversion strength) satisfy certain relationships, making the valuation of XVA by two-factor Hull-White model effective.

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ERN: Swaps & Forwards (Topic)

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