多因子隨機波動率模型校準在信用、選擇權和風險管理上的應用

Calibration of Multifactor Heston Model with Applications in Credit Spreads, Equity Options, and Risk Management

石磊(Shi, Lei)

指導教授 ： 韓傳祥

國立清華大學/科技管理學院/計量財務金融系/碩士(2016年)

摘要

本文在Christoffersen et al. (2009)的框架下推導出多因子隨機波動率模型選擇權定價公式的封閉解。探討將該模型應用在信用，選擇權和風險管理上。我們主要研究隨機波動率對信用價差收益率曲線隨時間變化的影響。我們認為多因子的隨機波動率模型可以更好地擬合信用價差，因此，模型校準結果顯示出兩個隨機波動率因子更靈活，可以捕捉信用價差期限結構隨時間變化的特性，其中一個因子代表長期波動率，另外一個代表短期波動率。在對隱含波動率曲面的模型校準上，對比Han（2011）的兩階段蒙地卡羅校準方法，我們的模型有更小的加權平均MSE和更快的計算速度。最後，該模型還可以計算風險中性下的違約概率和VaR。

關鍵字

隨機波動率 ； 模型校準 ； 信用價差 ； 隱含波動率 ； 違約概率

並列摘要

This article develops a closed-form solution of multifactor stochastic volatility option pricing model which is developed from Christoffersen et al. (2009) framework. We apply this model on Credit Spreads, Equity Options, and Risk Management. In particular, we look at the effect of having stochastic volatility in the structural approach and study the effects of time scales on the credit spread yield curves for the stochastic volatility. We argue that this model with multifactor stochastic volatility can produce more realistic credit spreads. Thus, the calibration reveal how the introduction of two volatility factors can generate a wide range of combinations associated with short-term and long-term patterns corresponding to credit spreads. In Second application, we solve the calibration problem of implied volatility surfaces. The results reveal that our model has relatively lowest total MSE and faster computing speed. Finally, our model also can calculate risk-neutral default probability.

並列關鍵字

volatility ； model calibration ； stochastic volatility model ； Fourier transform method ； the term structure of credit spreads ； implied volatility surface ； default probability

參考文獻

1.Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of financial studies, 6(2), 327-343.

2.Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 637-659

3.Black, F., & Cox, J. C. (1976). Valuing corporate securities: Some effects of bond indenture provisions. The Journal of Finance, 31(2), 351-367.

4.Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates*. The Journal of Finance, 29(2), 449-470.

5.Christoffersen, P., Heston, S., & Jacobs, K. (2009). The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well. Management Science, 55(12), 1914-1932.