Valuation of time charter contracts for ships

Abstract

This article describes a valuation method for time charter contracts for ships, i.e. leasing contracts for ships with embedded Bermudan options for buying the ship and extending the contract. As there often are embedded foreign exchange options in the buy options on the ship, a two factor stochastic model is developed and it is shown how the price can be determined applying techniques from contingent claim analysis such as dynamic programming.

Forecasting spot freight rates based on forward freight agreement and time charter contract

“…The results suggest that freight differentiation has become visible in the booming market due to the high rates. Rygaard (2009) proposed a method for the valuation of TC contracts for ships with embedded options. Proposing a stochastic model for charter rates, Rygaard (2009) demonstrated how the value of a TC contract can be determined using a dynamic programming approach.…”

“…Accordingly, the TC can be regarded as a form of forward freight. Problems such as the dynamics of structure and volatility (Alizadeh and Nomikos, 2011), the relation of trip and TC freight rates (Goulielmos and Psifia, 2007) and the value of TC contracts with embedded options (Rygaard, 2009) have been studied. However, to the best of our knowledge, there are no extant studies that have investigated the price discovery of TC rates, namely, the lead-lag relationship in returns and volatilities between spot and TC freight markets.…”

Optimal investment timing in the dry bulk shipping sector

“…Sødal et al (2008Sødal et al ( , 2009 derive a real options model to valuing the option to switch between the dry bulk market and wet bulk market for a combination carrier. Ryaard (2009) uses dynamic programming to develop a valuation model for time charter contracts for ships. However, although these studies overcome the limitations of the DCF methodology, neglect the competitive context in which investment decisions take place.…”

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

“…Bjerksund and Steinar modeled the spot freight rate as a mean reverting process and used a contingent claim analysis to value a European option to extend the TC contract. 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.…”