This paper presents a novel adaptive algorithm using mean reversion strategy without transaction cost. The antiocr algorithm only exploits the property of “reversal to the mean” and its performance not only significantly depends on the size of window but also fluctuates wildly according to the different size of window. To overcome these limitations, this proposed algorithm is designed to deal w...

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 m...

We study infinite–horizon, optimal switching problems under a general class of stochastic volatility models that exhibit “fast” mean–reversion by using techniques from homogenisation theory. This leads to perturbation theory, providing closed–form approximations to the full switching problem which is often intractable, both analytically and numerically. We apply our general results to certain, ...

We solve a Dixit and Pindyck type irreversible investment problem in continuous time under the assumption that the project value follows a Cox–Ingersoll–Ross process. This setup works well for modeling foreign direct investment in the framework of real options, when the exchange rate is uncertain and the project value fixed in a foreign currency. We indicate how the solution qualitatively diffe...

Many underlying assets of option contracts, such as currencies, commodities, energy, temperature and even some stocks, exhibit both mean reversion and stochastic volatility. This paper investigates the valuation of options when the underlying asset follows a mean-reverting lognormal process with stochastic volatility. A closed-form solution is derived for European options by means of Fourier tr...

We con...rm the presence of substantial non-linearities in real exchange rate dynamics at the sectoral level. There exists zones where arbitrage is not pro...table because of transaction costs, and thus mean reversion is inexistent. We compute the speed of mean reversion of sector speci...c real exchange rates, conditional on the existence of arbitrage as implied by our non-linear estimations, ...

This paper investigates changes in the long-horizon behaviour of stock prices. Using a time-varyingparameter framework, we find that any pre-World War II tendency for mean reversion disappearsduring the post-War period. Furthermore, when we account for changes in the market risk premiumdue to dramatic shifts in pre-War return volatility, the full sample evidence for mean reversion i...

In this paper, we study the McDonald-Siegel (MS) model for real options under the assumption that the spanning asset undergoes a stochastic volatility dynamics that reverts to a historical value according to an Ornstein-Uhlenbeck process driven by a second source of uncertainty. In this case, the market is not complete, and valuation, even for a perfectly correlated asset, is not as straightfor...

This work provides an optimal trading rule that allows buying and selling of an asset sequentially over time. The asset price follows a switchable mean-reversion model with a Markovian jump. Such model can be applied to assets with a “staircase” price behavior and yet simple enough to allow an analytic solution. The objective is to determine a sequence of trading times to maximize an overall re...