The valuation of projects:a real-option approach

Abstract

Valuation of R&D projects is quite complex due to the substantial uncertainties in a project`s life-cycle phases. The sequential nature of R&D projects continuously provides decision-makers with choices regarding whether and when to undertake future potential investment opportunities. This means that when valuing R&D projects decision-makers should take these factors into account. But R&D project usually takes long time to complete processes for commercialization. If the time to complete is longer, it is easier to trigger the crisis for capital shortage. So it seems very important modeling the capital shortage risk to induce the probability of failure in the pricing model. In this thesis we try to apply the analogy of financial securities subject to credit risk of Jarrow & Turnbull (1995) and attempt to value patents with capital shortage risk in an arbitrage free environment using the martingale measure technique. Furthermore, derive closed form formula for patents valuation which makes application easier than that of the theoretic option model. The major findings are: (1) when considering the effect of the failure frequency (capital shortage risk), the patent value will grow rapidly and then converge in the short run, no matter how other parameters incorporated into the robust analysis; (2) when increasing in the volatility of market revenues with synchronized higher volatility of investment cost, the volatility curve will be distorted to be U-shaped. Meanwhile, lower failure frequency could aggravate the decreasing in the option value.\r\nAnother issue is when the manager exercises the project with multiple underlying assets, where the assets returns are of non-linear correlation particularly in the non-Normal environment. Non-parametric dependence measures may better employed when explaining co-movement. We focus on the value of a (such as resources development) project in general depends on the price of the multiple products; these are usually correlated to some extent. So the project was treated as having a rainbow option, whose underlying asset prices correlate with each other, and also as having uncertainties that decrease according to the project stage. Based on Cherubini and Luciano’s framework (2002), the risk-neutral copula models are derived to figure decision flexibilities out easily. The main framework studies the valuation of a project (call on Max) by determining the joint risk-neutral distribution of the underlying assets (products) using copulas. Monte-Carlo simulations show that the higher default risk and association among the assets and the expected cost to completion contributes the higher risk premium in our model with dependence structure of Archimedean copula family than traditional Black-Scholes environment.

Valuation of R&D projects is quite complex due to the substantial uncertainties in a project`s life-cycle phases. The sequential nature of R&D projects continuously provides decision-makers with choices regarding whether and when to undertake future potential investment opportunities. This means that when valuing R&D projects decision-makers should take these factors into account. But R&D project usually takes long time to complete processes for commercialization. If the time to complete is longer, it is easier to trigger the crisis for capital shortage. So it seems very important modeling the capital shortage risk to induce the probability of failure in the pricing model. In this thesis we try to apply the analogy of financial securities subject to credit risk of Jarrow & Turnbull (1995) and attempt to value patents with capital shortage risk in an arbitrage free environment using the martingale measure technique. Furthermore, derive closed form formula for patents valuation which makes application easier than that of the theoretic option model. The major findings are: (1) when considering the effect of the failure frequency (capital shortage risk), the patent value will grow rapidly and then converge in the short run, no matter how other parameters incorporated into the robust analysis; (2) when increasing in the volatility of market revenues with synchronized higher volatility of investment cost, the volatility curve will be distorted to be U-shaped. Meanwhile, lower failure frequency could aggravate the decreasing in the option value.\r\nAnother issue is when the manager exercises the project with multiple underlying assets, where the assets returns are of non-linear correlation particularly in the non-Normal environment. Non-parametric dependence measures may better employed when explaining co-movement. We focus on the value of a (such as resources development) project in general depends on the price of the multiple products; these are usually correlated to some extent. So the project was treated as having a rainbow option, whose underlying asset prices correlate with each other, and also as having uncertainties that decrease according to the project stage. Based on Cherubini and Luciano’s framework (2002), the risk-neutral copula models are derived to figure decision flexibilities out easily. The main framework studies the valuation of a project (call on Max) by determining the joint risk-neutral distribution of the underlying assets (products) using copulas. Monte-Carlo simulations show that the higher default risk and association among the assets and the expected cost to completion contributes the higher risk premium in our model with dependence structure of Archimedean copula family than traditional Black-Scholes environment.