Valuation of Quanto Derivatives Using Bivariate GARCH-Jump Models

Abstract

We propose an unrestricted bivariate NGARCH-jump model to value quanto derivatives. In this model, jumps take place in pricing kernel and, consequently, in returns of foreign asset prices and exchange rates. In empirical examination, we compare this model with the following four model variations: (1) a bivariate discrete-time Merton model, (2) a bivariate generalized Merton model, (3) a bivariate NGARCH-normal model, and (4) a restricted bivariate NGARCH-jump model. The results suggest that the unrestricted bivariate NGARCH-jump model outperforms the others. This implies that the nonlinear asymmetric model with jumps best captures the dynamics of foreign asset prices and exchange rates.本文提出一非受限二元NGARCH跳躍模型，並用以評價匯率連動衍生性商品。模型中，跳躍發生於定價核、外國資產價格及匯率。此外，我們將此模型與以下模型進行實證比較：（1）二元離散Merton模型、（2）二元一般化Merton模型、（3）二元NGARCH常態模型，以及（4）受限二元NGARCH跳躍模型。結果顯示非線性的非對稱模型最能捕捉外國資產價格與匯率的動態過程。