Valuation of Quanto Derivatives Using Bivariate GARCH-Jump Models

以二元GARCH跳躍模型評價匯率連動衍生性金融商品

10.6545/JFS.2014.22(4).1

何曉緯(Hsiao-Wei Ho)；廖子翔(Tzu-Hsiang Liao)

二元GARCH跳躍模型 ； 隨機波動度 ； 匯率連動衍生性金融商品 ； Bivariate GARCH-jump model ； stochastic volatility ； quanto derivatives

財務金融學刊

22卷4期（2014 / 12 / 31）

1 - 35

英文

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。

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.

1. Duan, Jin-Chuan, Peter Ritchken, and Zhiqiang Sun, 2007, Jump starting GARCH: Pricing and hedging options with jumps in returns and volatilities,Working paper.
2. Black, Fischer,Scholes, Myron(1973).The pricing of options and corporate liabilities.Journal of Political Economy,81,637-654.
3. Chan, Wing H.(2003).A correlated bivariate poisson jump model for foreign exchange.Empirical Economics,28,669-685.
4. Christoffersen, Peter,Elkamhi, Redouane,Feunou, Bruno(2010).Option valuation with conditional heteroskedasticity and nonnormality.Review of Financial Studies,23,2139-2183.
5. Christoffersen, Peter,Jacobs, Kris(2004).Which GARCH model for option valuation?.Management Science,50,1204-1221.
6. Duan, Jin-Chuan(1995).The GARCH option pricing model.Mathematical Finance,5,13-32.
7. Duan, Jin-Chuan,Ritchken, Peter,Sun, Zhiqiang(2006).Approximating GARCH-jump models, jump-diffusion processes, and option pricing.Mathematical Finance,16,21-52.
8. Duan, Jin-Chuan,Wei, Jason Z.(1999).Pricing foreign currency and crosscurrency options under GARCH.Journal of Derivatives,7,51-63.
9. Engle, Robert F.(1982).Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation.Econometrica,50,987-1008.
10. Merton, Robert C.(1976).Option pricing when underlying stock returns are discontinuous.Journal of Financial Economics,3,125-144.

1. 葉仕國、張森林、林丙輝(2016)。台灣衍生性金融商品定價、避險與套利文獻回顧與展望。臺大管理論叢，27(1)，255-304。