Abstract
By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise, by several orders of magnitude. To maximize the sensitivity to volatility, a simple formulation of Merton’s model is proposed that employs deep out-of-the-money option implied volatilities. The methodology also eliminates the use of historic data to specify the default barrier, thereby leading to a full risk-neutral calibration. Subsequently, a new technique for identifying and hedging capital structure arbitrage opportunities is illustrated. The approach seeks to hedge the volatility risk, or vega, as opposed to the exposure from the underlying equity itself, or delta. The results question the efficacy of the common arbitrage strategy of only executing the delta hedge.
Highlights
The concept of capital structure arbitrage is well understood
Stamicar and Finger [10] showed the potential for exploiting that sensitivity by calibrating the CreditGrades model [11] to equity implied volatility in place of historic volatility
Quantifying credit risk through structural models has been investigated by Eom, Helwege and Huang [15], Huang and Zhou [16], as well as Huang and Huang [17]
Summary
The concept of capital structure arbitrage is well understood. Using Merton’s model of firm value [1], mispricing between the equity and debt of a company can be sought. All of the studies mentioned above, except for [6], employed the CreditGrades model [11], where the default barrier is held constant with random jumps introduced by assuming that the recovery rate follows a log-normal distribution Calibrating such an approach is problematic as data are scarce. We illustrate a volatility hedging technique with several case studies to show the effectiveness of focusing the hedging strategy on the implied volatility This is extended and back tested across all applicable CDS. This includes several case studies to explicitly illustrate the technique.
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