A Hedged Monte Carlo Approach to Real Option Pricing
In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs.
It is based on the Hedged Monte Carlo strategy proposed by Potters, Bouchaud, Sestovic (Phys. A Stat. Mech. Appl. 289(3–4):517–525, 2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.
KeywordsEntropy Filtration Volatility Vanilla Hedging
E.B. developed this work while visiting IMPA under the Cooperation Agreement between IMPA and Petrobras. MOS was partially supported by CNPq grant 308113/2012-8 and FAPERJ. JPZ was supported by CNPq grants 302161/2003-1 and 474085/2003-1 and by FAPERJ through the programs Cientistas do Nosso Estado and Pensa Rio. All authors acknowledge the IMPA-PETROBRAS cooperation agreement.
The authors would like to acknowledge and thank a number of discussions with Fernando Aiube (PUC-RJ and Petrobras). We also thank Milene Mondek for the implementation of a number of preliminary examples of the HMC algorithm and Luca P. Mertens for help with the R software and the calibration procedure in the examples.
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