A driver entering into a car lease agreement can obtain the right to buy the car in

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A driver entering into a car lease agreement can obtain the right to buy the car in four years for $10,000. The current value of the car is $30,000. The value of the car, S, is expected to follow the process

dS = µS dt + oS dz


where μ = – 0.25, σ = 0.15, and dz is a Wiener process. The market price of risk for the car price is estimated to be –0.1. What is the value of the option? Assume that the risk-free rate for all maturities is 6%. 

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