Multi-stage Option Pricing With Different Volatilities And Different Risk-free Rates And Its Simulation

Real Option is one of the most important methods to manage and make decision flexibly. In recent years there have been many kinds of option pricing models to estimate asset value in the field of business and project management decision. An enterprise or a project always has a multi-stage development, and it has different market environment and competitors. So a Venture Capital company always uses multi-stage option pricing models to estimate the value of multi-stage investment.The research topic of this paper is about multi-stage real option pricing and its simulation. Namely the theories and methods of stock option pricing are applied to analyze the value of multi-stage project and being simulated.In discrete situation the traditional binomial model of option pricing can’t be fit for multi-stage condition because its volatilities and risk-free rates are same in the time of live option. This paper assumes that volatilities and risk-free rates are different from each other, and uses no-arbitrage principle, risk-neutral measure and delta hedging to build a European call option pricing binomial model with different volatilities and different risk-free rates. And it is an improved binomial model of option pricing.In continues situation the traditional Black-Scholes model of option pricing can’t be fit for multi-stage condition. This paper assumes that volatilities and risk-free rates are different from each other, and uses It? integration, It? formula and delta hedging to build a European call option pricing dividend Black-Scholes model with different volatilities and different risk-free rates. And it is an improved Black-Scholes model of option pricing on multi-stage condition.At simulation part, this paper uses continued fraction to approximate the distribution function of standard normal distribution. And the approximation of that is applied to simulate the dividend paying European call option pricing Black-Scholes model with different volatilities and different risk-free rates. And the intrinsic value of the project from the result of this simulation is higher than that from the result of NPV method.