Operator Calculation Of Present Value For Random Cash Flow And Real Option Pricing

We are already familiar with the mathematical methods of financialasset pricing and financial option pricing. But we also need to evaluatephysical assets as well as real options in actual life. It’s more complicatedand challenging than a simple research on financial assets and optionsdepending on theoretical and idealized assumptions.In this paper we focus on two issues. The first is about physical assetspricing. It only contains assets which can generate cash flow. So we need touse the method of discounted cash flow calculations. The traditional NPVmethod doesn’t consider the future fluctuation. This paper introduces amethod of random variables, making the assets’ future cash flows random.This approach is more flexible and prepares for our later calculations for realoptions. Only under random condition, the research of option is meaningful.In the calculation of NPV, we introduce a specific operator approach toavoid the difficulty in calculation the answer of the expectation of NPV forperpetual random cash flow.The second question is about real option pricing. I firstly follow theprevious calculation and deduce the exercise conditions as well as the valueof abandonment option with a theoretical approach. Then I also discusssome other real options. For options of limited period, I use the recursivecalculation method to estimate the value. For perpetual American option, Iintroduce the concept like the probabilities of arriving in random process,and calculate exhaustive probability and corresponding cash flow in limitedperiod by computer program or through recursive method. Taking the convergence of the sequence into account, we can get an approximation ofthe exercise conditions and the value for certain real option.