Time Charters with Purchase Options in Shipping: Valuation and Risk Management

Abstract

The paper studies the valuation and optimal management of Time Charters with Purchase Options (T/C--POPs) which is a specific type of asset lease with embedded options that is common in shipping markets. T/C--POPs are economically significant and sometimes account for more than half of the stock market value of listed shipping companies.

The main source of risk in markets for maritime transportation is the freight rate, and we therefore specify a single-factor continuous time model for the dynamic evolution of freight rates which allows us to price a wide variety of freight rate related derivatives including various forms of T/C--POPs using contingent claims valuation techniques.

Our model allows for the derivation of closed valuation formulas for some simple freight rate derivatives while the more complex ones are analyzed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed.

Keywords: Ship valuation, options on ships, leasing, lease contracts with options, optimal stopping

JEL Classification: G12, G13