Pricing CoCos in Fractional Brownian Motion Environment

Contingent Convertible Bonds (CoCos) are an important type of bail-in debts. The empirical results show that the price changes of the banks' stocks in the Shanghai Stock Exchange do exhibit a long-range serial autocorrelation and persistence in following a trend. The stock price of the underlying bank is described by a stochastic differential equation driven by a fractional Brownian motion with the Hurst parameter H satisfying 1/2 < H < 1, which characterizes the serial autocorrelation indicating a memory and the fractal character of the price. The preference based equilibrium approach and the conditional distribution of the fractional Brownian motion are employed to price the CoCos. The explicit pricing formula for CoCos is derived through pricing barrier options and forwards. The results indicate that the long-range serial autocorrelation in price changes of the underlying stock has a significant influence on the values of the equity-related components of the CoCos since the maturity is usually large, though the autocorrelation is weak. The values of the barrier options are significantly affected by the long-range autocorrelation of the returns on the underlying stocks.