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.