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January 8th, 2010, 09:44 AM
We develop a simple robust link between equity out-of-the-money American put options and a pure credit insurance contract on the same reference company. Assuming that the stock price stays above a barrier B > 0 before default but drops and remains below a lower barrier A < B after default, we show that the spread between two co-terminal American put options struck within the default corridor [A,B] scaled by their strike difference replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the presence of the default corridor, this simple replicating strategy is robust to the details of pre- and post-default stock price dynamics, interest rate movements, and default risk fluctuations. We use quotes on American puts to infer the value of the credit insurance contract and compare it to that estimated from the credit default swap spreads. Collecting data on several companies, we identify strong co-movements between the credit insurance values inferred from the two markets. We also find that deviations between the two estimates cannot be fully explained by common variables used for explaining American put values, such as the underlying stock price and stock return volatility, but the cross-market deviations can predict future movements in American puts.
In this paper, we propose a new, simple, and robust link between equity out-of-the-money American put options and a credit insurance contract on the same reference company. The link is established under a general class of stock price dynamics. The key assumption we make is that the stock price is bounded below by a strictly positive barrier B > 0 before default, but drops below a lower barrier A < B at default, and stays below A thereafter. The range [A,B] defines a default corridor in which the stock price can never reside. Given the existence of the default corridor, we show that the spread between any two American put options of the same maturity and with strike prices falling within the default corridor replicates a pure credit insurance contract that pays off when and only when the company defaults prior to the option expiry.
Our paper offers several new insights. First, many structural models with strategic default imply the existence of a default corridor, but the simple robust linkage that we identify in the presence of the corridor is new. Second, compared to the many linkages identified in the literature through parametric (structural or reduced-form) model specifications, our identified linkage between equity American put options and credit insurance is much simpler as it does not incur any significant computations involving Monte Carlo, Fourier transforms, or lattice constructions. Third, our linkage is also more robust as it does not depend on any particular parameterizations of pre- and post-default stock price dynamics, interest rates variations, and default risk fluctuations. Most importantly, the American put spread replicates the cash flow of the credit insurance contract. Hedging the credit insurance contract with the American put spread generates a static portfolio that is markedly different from dynamic hedging and rebalancing based on historical regression coefficients or gradients from an estimated parametric model.
The rest of the paper is structured as follows. The next section lays down the theoretical framework, under which we build the linkage between equity American put options and credit insurance. Section 3 describes the data that we use for our empirical work and the procedure that we follow to estimate the value of unit recovery claims. Section 4 compares the time-series behavior of the unit recovery claim values estimated from equity American puts and the CDS market. Section 5 offers concluding remarks and directions for future research.
In this paper, we propose a new, simple, and robust link between equity out-of-the-money American put options and a credit insurance contract on the same reference company. The link is established under a general class of stock price dynamics. The key assumption we make is that the stock price is bounded below by a strictly positive barrier B > 0 before default, but drops below a lower barrier A < B at default, and stays below A thereafter. The range [A,B] defines a default corridor in which the stock price can never reside. Given the existence of the default corridor, we show that the spread between any two American put options of the same maturity and with strike prices falling within the default corridor replicates a pure credit insurance contract that pays off when and only when the company defaults prior to the option expiry.
Our paper offers several new insights. First, many structural models with strategic default imply the existence of a default corridor, but the simple robust linkage that we identify in the presence of the corridor is new. Second, compared to the many linkages identified in the literature through parametric (structural or reduced-form) model specifications, our identified linkage between equity American put options and credit insurance is much simpler as it does not incur any significant computations involving Monte Carlo, Fourier transforms, or lattice constructions. Third, our linkage is also more robust as it does not depend on any particular parameterizations of pre- and post-default stock price dynamics, interest rates variations, and default risk fluctuations. Most importantly, the American put spread replicates the cash flow of the credit insurance contract. Hedging the credit insurance contract with the American put spread generates a static portfolio that is markedly different from dynamic hedging and rebalancing based on historical regression coefficients or gradients from an estimated parametric model.
The rest of the paper is structured as follows. The next section lays down the theoretical framework, under which we build the linkage between equity American put options and credit insurance. Section 3 describes the data that we use for our empirical work and the procedure that we follow to estimate the value of unit recovery claims. Section 4 compares the time-series behavior of the unit recovery claim values estimated from equity American puts and the CDS market. Section 5 offers concluding remarks and directions for future research.