A new default intensity model with fuzziness and hesitation

Abstract

With the increased financial market volatility, corporate defaults will suffer from the double impact of the external shocks and internal contagion effects. In the existing stochastic default intensity models, the valuation of sensitivity parameters requires a lot of historical data, however, the limited market data does not guarantee the accuracy of parameter estimation, meanwhile, due to the people have a lot of fuzziness and hesitation judgements on the default process, it is necessary for us to let the corresponding random parameter of the default intensity to be a triangular intuitionistic fuzzy interval value. In this paper, we propose a new default intensity model based on the external shocks and internal contagion effects, and introduce the triangular intuitionistic fuzzy numbers into the credit default swaps (CDS) pricing modeling to describe the fuzziness and hesitation of the default process. In the end, we get a new fuzzy form pricing formula for CDS, and by the simulation analysis, we obtain that, all kinds of fuzziness and hesitation of the market have significant impact on credit spreads, and a model result with a consideration of the fair price of CDS in a fuzzy random environment including a pure random environment result. Compared with the existing stochastic model, these proper interval results can offer the investors more flexible options and can more reflect the impact of market environment on credit spreads.