Strategic Exercise Of Options On Non-traded Assets And Stochastic Volatility In An Incomplete Market: Indifference Pricing And Entropy Methods

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Title: Strategic Exercise Of Options On Non-traded Assets And Stochastic Volatility In An Incomplete Market: Indifference Pricing And Entropy Methods
Author: Hoe, Singru
Abstract: The first study explores optimal investment policies for strategic option exercise when the underlying project is not traded . A duopoly model captures strategic interactions , while a partial spanning asset models market incompleteness . The option value to invest is obtained through indifference pricing , i .e . , certainty equivalent value . I find that incompleteness narrows the gap between leader and follower entry dates . The follower enters much sooner , and the leader delays slightly compared to classic real options models . Modeling investment income stream as an Arithmetic Brownian motion is a better fit than Geometric Brownian motion , while reducing the necessary numerical approximations for obtaining the results in the incomplete market situation . As a byproduct of modeling two different stochastic income streams , I investigate the impact of market share and uncertainty on the relative investment trigger as well as the option value to invest . Results are sensitive to these factors ; thus , it is important to model stochastic processes to accurately reflect the real world circumstances . The second study explores the valuation consequences of incompleteness resulting from stochastic volatility in a real options setting . The optimal policy is obtained through q -optimal measures as well as indifference pricing . I examine the efficacy of different approaches to finding and justifying a particular martingale measure . Stochastic volatility induced market incompleteness affects the investment /abandonment decision in several important ways . In addition , I demonstrate that indifference prices for the option value to invest and the abandonment option solve quasilinear variational inequalities with obstacle terms . With the exponential utility function , the utility -based indifference price admits a new pricing measure , which is the minimal relative entropy martingale measure minimizing the relative entropy between the historical measure and the Q martingale measure . I also show that the indifference price is non -increasing with respect to risk aversion . As the risk aversion parameter converges to zero , the indifference price converges to the unique bounded viscosity solution of the linear variational inequality with obstacle term .
URI: http : / /hdl .handle .net /10106 /8
Date: 2007-08-23

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Strategic Exercise Of Options On Non-traded Assets And Stochastic Volatility In An Incomplete Market: Indifference Pricing And Entropy Methods. Available electronically from http : / /hdl .handle .net /10106 /8 .

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