JOINT CALIBRATION OF MARKET RISK, CREDIT RISK, AND INTEREST RATE RISK

市場風險、信用風險與利率風險的聯合校準

韓傳祥(Chuan-Hsiang Han) ； 戴慧欣(Hui-Hsin Tai) ； 吳慶堂(Ching-Tang Wu)

《中國統計學報》 55卷4期 (2017/12) Pp. 160-187

摘要

Recent literature has highlighted joint movements between the credit default swap (CDS for short) spread and its corresponding option price. Some dynamically consistent frameworks have been proposed for the joint evaluation and estimation of stock options and their CDS spreads in order to integrate both market information. This paper extends previous studies and provides a new methodology for joint evaluation of stock option prices, CDS spreads and bond prices based on three separate calibration methods. They include (1) a two-step Monte Carlo procedure for calibration to the term structure of implied volatilities, (2) an approximated default intensity rate for the credit risk calibration, and (3) a closed-form of zero coupon bond price for the interest rate risk calibration. Various innovative combinations of these three calibration methods are proposed to allow a genuine robust and efficient estimation for the joint dynamics of multiple risk factors. Our investigation discloses the importance of cross-market information to fit the implied volatility surfaces by means of a joint dynamic model which includes market risk, credit risk and the interest risk.

關鍵字

Instantaneous volatility ； implied volatility surface ； default intensity ； model calibration ； martingale control variate ； vulnerable option

並列摘要

最近的文獻指出了信用違約交換(簡稱CDS)價差與其相應的選擇權價格有聯合變動的特性。為了整合市場訊息，一些動態具一致性的框架被提出，用來聯合衡量和估計股票權選擇權和CDS之間的價差。本文在過往研究的基礎上，提出了一種新的方法對股票選擇權價格、CDS價差和債券價格進行聯合衡量。基於三種各自不同的校準方法，包括(1)對隱含波動率的期限結構使用兩階段蒙地卡羅法進行校準，(2)在信用風險的縮減式模型下使用近似法來校準信用違約強度，(3)在利率風險下的零息票債券價格的封閉解進行校準。本文提出了這三種校準方法的創新組合，為多種風險因素的聯合動態提供了一種穩定有效的估計方法。我們的研究顯示了交叉市場訊息的重要性，通過一個包含市場風險、信用風險和利率風險的聯合動態模型，能夠最適地擬合隱含波動率曲面。

並列關鍵字

瞬時波動率 ； 隱含波動曲面 ； 違約密度 ； 平賭控制變異 ； 違約選擇權

參考文獻

Black, F.,Cox, J.(1976).Valuing corporate securities: some effects of bondin-denture provisions.Journal of Finance.31,351-367.

Berndt, A. and Ostrovnaya, A. (2007). Information flow between credit default swap, option and equity markets. Working paper, Tepper School of Business, Carnegie Mellon University

Brigo, D.,Auréelien, A.(2005).Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model.Finance Stochast.9,29-42.

Brigo, D. and Morini, M. (2005). CDS market formulas and models. Working paper, Banca IMI.

Carr, P.,Wu, L.(2010).Stock options and Credit Default Swaps: a joint frame-work for valuation and estimation.Journal of Financial Econometrics.8(4),409-449.