A commercial real estate company has an option to develop a parcel of land. Assuming the dynamics of land value, L, are described by geometric Brownian motion with drift a and volatility, and that the cost of developing the land is I, answer the following questions. Assume the economy is risk-neutral and the instantaneous risk-free rate of interest is r. a. Compute the value of the development option, F(L), and the optimal exercise policy, I, assuming the firm can exercise the option at any time. b. In a more realistic setting, the company may face competition that damages the value of its growth options. For simplicity, assume that the arrival of competition can be described as a Poisson process with intensity parameter 2; and that conditional on the arrival of competition, the development option becomes worthless (i.e., drops in value to zero). Compute the value of the option, F(L), and the optimal exercise policy, Î**, under this competition scenario. c. Compare the optimal exercise policies under parts a. and b. of this question. How does competition influence the optimal exercise policy?
A commercial real estate company has an option to develop a parcel of land. Assuming the dynamics of land value, L, are described by geometric Brownian motion with drift a and volatility, and that the cost of developing the land is I, answer the following questions. Assume the economy is risk-neutral and the instantaneous risk-free rate of interest is r. a. Compute the value of the development option, F(L), and the optimal exercise policy, I, assuming the firm can exercise the option at any time. b. In a more realistic setting, the company may face competition that damages the value of its growth options. For simplicity, assume that the arrival of competition can be described as a Poisson process with intensity parameter 2; and that conditional on the arrival of competition, the development option becomes worthless (i.e., drops in value to zero). Compute the value of the option, F(L), and the optimal exercise policy, Î**, under this competition scenario. c. Compare the optimal exercise policies under parts a. and b. of this question. How does competition influence the optimal exercise policy?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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Transcribed Image Text:A commercial real estate company has an option to develop a parcel of land. Assuming the
dynamics of land value, L, are described by geometric Brownian motion with drift a and
volatility o, and that the cost of developing the land is I, answer the following questions.
Assume the economy is risk-neutral and the instantaneous risk-free rate of interest is r.
a. Compute the value of the development option, F(L), and the optimal exercise policy, L,
assuming the firm can exercise the option at any time.
b. In a more realistic setting, the company may face competition that damages the value of its
growth options. For simplicity, assume that the arrival of competition can be described as
a Poisson process with intensity parameter 2; and that conditional on the arrival of
competition, the development option becomes worthless (i.e., drops in value to zero).
Compute the value of the option, F(L), and the optimal exercise policy, L, under this
competition scenario.
c. Compare the optimal exercise policies under parts a. and b. of this question. How does
competition influence the optimal exercise policy?
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