Strategic investment decisions under fast mean-reversion stochastic volatility

Max O. Souza, Jorge P. Zubelli

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We are concerned with investment decisions when the spanning asset that correlates with the investment value undergoes a stochastic volatility dynamics. The project value in this case corresponds to the value of an American call with dividends, which can be priced by solving a generalized Black-Scholes free-boundary value problem. Following ideas of Fouque et al. under the hypothesis of fast mean-reversion, we obtain the formal asymptotic expansion of the project value and compute the adjustment of the price due to the stochastic volatility. We show that the presence of the stochastic volatility can alter the optimal time investment curve in a significative way, which in turn implies that caution should be taken with the assumption of constant volatility prevalent in many real option models. Additionally, we also present analytical results for the perpetual case. We also indicate how to calibrate to market data the model in the asymptotic regime.

Original languageBritish English
Pages (from-to)61-69
Number of pages9
JournalApplied Stochastic Models in Business and Industry
Volume27
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • asymptotic analysis
  • perpetual American options
  • real options
  • stochastic volatility

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