Novel Analytic Representations for Caps, Floors, Collars, and Exchange Options on Continuous Flows, Arbitrage-Free Relations, and Optimal Investments

Abstract

We offer analytic formulae for valuing finite maturity profit caps and floors that are contingent on continuous flows without the need for subtracting the risk-neutral expectation of the forward starting perpetual solution from the corresponding perpetual solution. The related price caps, floors, and collars are easily obtained from any analytic representation of profit caps and floors using some arbitrage-free relations. Finally, we offer two novel methods for calculating the optimal triggers of investment projects in the presence of price floors and collars regimes in a way that is much simpler than the ones currently used.