The fractional CEV model: Pricing credit derivatives with memory
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| Year of publication | 2019 |
| Type | Appeared in Conference without Proceedings |
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| Description | The CEV model is a well-known formulation in the option pricing literature, which extends the classical Black-Scholes approach, to address two empirical facts in financial markets: the negative relationship between price and volatility (leverage effect) and the 'volatility skew'. Another important feature of the CEV model is its capability to allow bankruptcy. Then, the CEV model could be suitable for to price Credit Default Swaps (CDS), which becomes an important and widely-used tool in the risk management of credits. However, at the CEV model, the probabilities of hitting zero are very small for real applications. Taking it, Carr and Linetsky introduce to the CEV dynamics an affine default intensity as a function of the instantaneous variance, naming the whole process as Jump- to-Default extended CEV model (JD-CEV). This new specification on the model keeps the tractability of the CEV model. However, several researchers find CDS presents long-range dependency or memory effect. To deal with this issue, this research extends the JD-CEV model, using a fractional Brownian motion instead of a classical one. With the help of the fractional Itô's calculus and the fractional Fokker-Planck, equation, we reduce the problem to a non-stationary Feller process with time-varying coefficients, given a solution for the CDS pricing with memory. Besides, the convergence to the fractional and classical CEV approaches is provided. |