Credit Spread Option European Valuation Under Derivative GARCH Model

This paper develops closed-form solutions for options on credit spreads with GARCH models. We extend the mean-reverting model proposed in Longstaff andSchwartz (1995) and we use the Heston and Nandi’s (1999) GARCH specificationrather than the traditional lognormal. Our model, being more flexible, captures better the empirical properties of observed credit spreads and contains Longstaff and Schwartz (1995) model as a special case. The new model provides the first readily computed option formula for a random volatility model in which current volatility is easily estimated from historical asset prices observed at discrete intervals. Empirical analysis on S&P500index options shows the single-factor version of the GARCH model to be a substantial improvement over the Black-Scholes (1973) model.Otherwise this article considers the conditions of the risk-neutral probability in the Heston and Nandi’s (1999), inversely proportional to the logarithm of credit spreads and the conditional variance of conditions, this paper develops closed-form solutions for options.