本文旨在探究當存在市場與信用風險之交互影響下風險性證券之易脆選 擇權的評價與避險。本文模型假設違約強度函數服從二因子 Cox 過程，並同 時考量交易對手與標的資產違約風險間的交互性。本研究呈現之結果如下： 首先，交易對手違約風險導致了權證價格上的信用折耗；然而，標的資產違 約風險對選擇權價值產生信用補貼。標的資產違約風險效果明顯占優於對手 違約風險效果。其次，此兩不同種類違約風險對權證避險比率亦造成截然不 同之影響。究其原因，標的資產違約風險對權證所造成之不對稱影響係因正 向「槓桿效果」與負向「提前保值效果」之間的抵換均衡於買權與賣權此二 情況下並非一致所導致。另外，給定不同水準下的總體經濟變數，本文模型 證實標的物違約風險效果與對手違約風險效果之間存在正向的共移性。此發 現可對應實證文獻所探討的「信用感染」及「成串違約」等現象之經濟意 義。

This paper derives the pricing formulas and put-call parity for “hybrid options”—vulnerable options on defaultable securities—with the presence of the intersection of market and twofold default risk. Default intensities are modeled as a two-factor Cox process, and the dependency of option writers’ default on the underlying stock default is also captured. We find counterparty risk generates credit discount on option value, while reference risk generates credit premium. The latter significantly dominates the former. The impact of twofold default risk on option hedging ratios fails to replicate consistency in the price pattern. The asymmetric behavior of option deltas with respect to reference risk is attributed to the trade-off between negative early-fixed effect and positive leverage effect. Also, our model generates a positive co-movement between these two types of default risk impact with varied choices of economic variables. Such a model feature reflects the empirical implication of credit contagion as well as the clustering of default.

Option has long been regarded as one of the most popular financial instruments widely used in derivative market, due to the hybrid function of hedge and speculation. Option pricing, hence, receives considerable attention from academic research. In view of the relevance of riskiness on option underlying asset in the context of option pricing, most of existing literature on option pricing pays its attention on market risk, interest rate risk, liquidity risk, or credit risk. They believe that a pricing model considering more types of risk has a better performance in explaining the observed option-price pattern. In this paper we study option pricing from arguments concerning twofold default risk (counterparty risk and reference risk). This paper departs from literature in two dimensions: (i) the consideration of reference default risk; (ii) the consideration of the dependency of option writers’ default on the underlying asset default. Prior literature on option pricing usually treats the underlying asset as a default-free financial claim. Such a doing, however, is unrealistic. Corporate bond and levered firms’ common stock are the two counter examples. Issuing options on these two types of financial claims must bear reference-type default risk. Once the occurrence of reference default heavily knocks down the price of underlying asset to be zero, option’s moneyness could be deep in-the-money or out-the-money. Besides, since option writer and the owner of underlying asset could belong to a same economy, the simultaneous trigger of counterparty and reference default does exist, reflecting the empirical implication of credit contagion and the clustering of defaults. Pricing model proposed by this paper contribute to academic research and practitioners in three ways: (i) to understand the difference in the impact on option pricing between counterparty risk and reference risk; (ii) to understand how the co-movement between counterparty risk impact and reference risk impact affects option’s characters; (iii) to understand the difference in the impact on hedging strategy against underlying asset-price fluctuation between counterparty risk and reference risk. The proposed model admits a close-form solution that holds computational tractability and comparability with related literature.