We study options on short-term leases for capital-intensive equipment performing specific functions and services, such as leases for semi-submersible drilling rigs, marine seismic services, corporate real estate leasing, retail space leasing, and apartment leasing. We quantify the effect of an important factor in pricing options on these services: idle time between consecutive lease contracts. We show that while the expected, discounted value for a contract with options is unique, option prices

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... and option exercise prices must be given with respect to a payment structure for the whole contract. We prove that there exist payment schemes in which prices do not depend on exercise probabilities. We use a simple analytic model to derive closed-form solutions for option prices and illustrate our methodology by pricing options for leasing oil-drilling services in the North Sea.