Sub-fractional Model for Credit Risk Pricing

Abstract

A sub-fractional version of the well-known Merton's model is proposed in this paper. Default probability, values of bonds and equity and credit spreads are derived under some suitable assumptions.

The sub-fractional CEV model

“…Then, diffusion processes under sfBm could be considered to model some financial time-series which exhibits long-range dependency and non-stationarity increments [4,5]. Some attempts has been addressed in the literature extending the Black-Scholes (B-S) model under sfBm [6][7][8][9][10]. However, in this communication, we consider a sub-fractional extension for Constant Elasticity of Variance (CEV) model, which is capable to address some shortcomings of the B-S approach as the leverage effect and the implied volatility skew [11].…”

Arbitrage opportunities in sub-fractional Black-Scholes model

“…文献 [25][26][27][28][29][30] 研 究了次分数 Brown 运动的许多性质及其应用. 文献 [31,32] 进一步利用文献 [33,34] 定义的关于次分 数 Brown 运动的随机积分, 研究了金融衍生品的定价问题. 近年来, 文献 [35] 研究了混合分数 Brown 运动下常方差弹性系数模型的期权定价问题.…”