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Strategic investment decisions under fast mean‐reversion stochastic volatility
Author(s) -
Souza Max O.,
Zubelli Jorge P.
Publication year - 2011
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.833
Subject(s) - mean reversion , stochastic volatility , economics , volatility (finance) , econometrics , volatility smile , implied volatility , dividend , investment strategy , volatility swap , financial economics , sabr volatility model , stochastic investment model , asset allocation , finance , market liquidity , portfolio
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. Copyright © 2010 John Wiley & Sons, Ltd.