Bareboat charters and ship leasing contracts with purchase options are important channels for ship owners and the operators obtaining their ships. This study develops an option pricing model to evaluate the trade-off relationship between the hire rates and the exercise prices of purchase options. Numerical analysis is conducted using four input variables namely the spot ship prices, the volatility of the spot ship prices, the time to maturity of the options and the discount rate. An actual example is also presented. The results show that as the exercise price decreases, it is very likely that this purchase option is exercised; and for this very reason, owners will ask for a higher hire rate in the charters with this kind of purchase option given to charterers, therefore the hire rate difference between the charters with and without this purchase option increases. Evidently it reveals a trade-off relationship between the exercise price and the hire rate. In addition, for a specific exercise price, applying higher spot ship prices, greater volatility, longer time to maturity and higher discount rates all manifest the trade-off relationship between the exercise prices and the charter rates.

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