The Pricing Formula Of Compound Options And Multi-stage Investment

Multi-stage investment decision is always carried out in an uncertain environment. The traditional Net Present Value pricing model (NPV model)always underestimate the value of the project, which is always lost valuable investment opportunities . The compound option pricing theory under uncertain environment for the evaluation of multi-stage investment decision provides a new thinking and quantitative tools. With the multi-stage investment decision described by the compound option pricing theory, each stage of decision corresponds to whether a particular option of the compound option is exercised or not. The compound option pricing theory which is used to describe the multi-stage investment decision, provides a more flexible and rational decision method for the enterprises. Therefore, it is particularly important to price the compound option reasonably.This paper extends the pricing formula of compound options and provides the sensitivity analysis of the pricing formula. The theoretical basis of the paper is Black-Scholes model and Geske's compound option pricing model, using risk-neutral pricing method. The paper begins with the multi-stage investment decisions and combines with the characteristics and realities of investment decisions, whose assumptions are closer to the actual environment. The specific features of the paper are as follows: First, the number of folds of the compound option is extended from 2-fold to multi-fold. Second, the call/put feature of the compound option is extended to be assigned arbitrarily. Third, interest rates, dividend ratio, variance of the asset prices are defined as the time-dependent deterministic functions, not constants. Wish the paper can be an extension of the existing theoretical research and a referenced theory of multi-stage investment decisions .