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In this paper, we study the risk aversion on valuing the single-name credit derivatives with the fast-scale stochastic volatility correction. Two specific utility forms, including the exponential utility and the power utility, are tested as examples in our work. We apply the asymptotic approximation to obtain the solution of the non-linear PDE, and make a comparison of the utility before and after the stochastic volatility modification, and we find that incorporation of fast-scale volatility will lower down the utility. By using the indifference price, we also give the yield spread impacted by the risk adverse valuation. We find that by considering the default risk, yield spread is sloping in a short period and converge in a long run.

The Study of Utility Valuation of Single-Name Credit Derivatives with the Fast-Scale Stochastic Volatility Correction