Real options with non-linear dynamics
The value of a real or financial option depends among other factors on the assumption of the underlying stochastic process. Linear and loglinear processes are most common, such as the arithmetic Brownian motion, the geometric Brownian motion and the Ornstein-Uhlenbeck process. In the time series literature, non-linear continuous time models have been developed. One such class of models is the threshold-autoregressive model, where the dynamic process changes character depending on whether the process is above or below a certain threshold. In this paper we investigate real option modelling when uncertainty can be described by a continuous time threshold autoregression. Closed form solutions to perpetual American options on such processes are derived. Various applications are studied, focusing on how uncertainty and non-linearity can a?ect option valuation and investment. This includes examples where uncertainty encourages investment, contrary to the result with most real options models.
Publisert i 11th international conference on real options, Real Options Group, 2007
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