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

Abstract

The article 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 that 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, whereas the more complex ones are analysed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed.Ship valuation, options on ships, leasing, lease contracts with options, optimal stopping,

Double-sided price adjustment flexibility with a preemptive right to exercise

“…Rygaard (2009) proposed a valuation method for TC contracts with built-in Bermudan options to purchase chartered ships. Jørgensen and De Giovanni (2010) analyzed and priced TC contracts with extension and purchase options.…”

“…Boundary conditions must first be determined at each time step. This paper has adopted an improved FDM introduced by Vetzal (1998) and implemented by Jørgensen and De Giovanni (2010) to overcome the problem of the PDE being convection-dominated for mean reverting processes. This method uses an explicit approximation for the option value on the boundaries of X j instead of directly defining it.…”

Stochastic modeling of Supramax spot and forward freight rates

“…Various real option models in shipping have been studied by Mossin (1968), Tvedt (1997Tvedt ( , 2003 and Sødal et al (2008Sødal et al ( , 2009. Models for pricing financial options in shipping markets have been developed in the study by Tvedt (1998), Koekebakker et al (2007) and Jørgensen and De Giovanni (2010). Continuous-time shipping models typically assume fairly simple freight rate dynamics, because simple dynamics typically lead to wellknown closed-form solutions to valuation problems.…”

Freight derivatives pricing for decoupled mean-reverting diffusion and jumps

“…The option market also appeared popular with a trading volume of 280,000 cargo days for 2015 and an average weekly open interest of 140,000 cargo trading days (source: www.balticexchange.com). Therefore, it is not surprising that the valuation and hedging of freight contingent claims have received attention from practitioners and researchers (see, for example, Koekebakker et al, 2007, Jørgensen and De Giovanni, 2010, Prokopczuk, 2011, Nomikos et al, 2013, especially from 2008 onwards; a period which was characterized by a notoriously high volatility.…”