Bull Spread Option pricing using a mixed modified fractional process with stochastic volatility and interest rates

International audience; We price options so as to take into account the existence of memory (short or long) characterizing the stochastic processes that generate prices, volatility and interest rates. In particular, we propose a model for Bull Spread options in a Mixed Modified Fractional Hull-White-Vasicek stochastic volatility and stochastic interest rate model. We propose a specific Bull Spread Vulnerable option pricing based on MMFHWV model.