We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a...We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.展开更多
Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing form...Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.展开更多
文摘We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. Since this includes the Black-Scholes and the Vasicek (Ornstein-Uhlenbeck) return models, the considered deflator is called Black-Scholes- Vasicek deflator. Besides a new elementary proof of the Black-Scholes and Margrabe option pricing formulas a validation of these in a multiple risk economy is achieved.
文摘Under the assumption of the underlying asset is driven by the mixed fractional Brownian motion, we obtain the mixed fractionalBlack-Scholes partial differential equation by fractional Ito formula, and the pricing formula of perpetual American put option bythis partial differential equation theory.
