有信用風險的USV利率期間結構模型之研究

Abstract

本文一般化 Trolle and Schwartz (2009) 的模型假設， 加入信用風險因子的設定，利用Martingale的評價方式，可以得到無隨機波動因子的有、無信用風險零息債券價格，也就是說，只要給定參數和隨機波動度的曲線，就可以計算出有、無信用風險零息債券價格；因為信用風險假設符合Duffie, Pan and Singleton (2000) (簡稱DPS)提出的Affine Jump-Diffusions(簡稱AJD)條件，有信用風險的零息債劵選擇權評價公式具有解析解。

We provide a general form of Trolle and Schwartz(2009)’s model, a Heath–Jarrow–Morton model with unspanned stochastic volatility (USV), and add credit risk in our model. This model has finite dimension Markovian property and has the affine jump diffusion property (AJD) as Duffie, Pan and Singleton (2000) paper. Consequently, we can obtain defaultable bond option prices with analytic form. We also provide a defaultable/default free zero coupon bond price without random variables by the way of martingale pricing.