Financial time series exhibit a set of characteristics, known in the economic community as stylized facts, without a clearly confirmed explanation [1, 2]. Among these are:

- heavy tails of returns,

- volatility clustering,

- gain/loss asymmetry,

- absence of autocorrelations in returns,

- slow decay of the autocorrelation function (ACF) of absolute returns.

There have been a multitude of models attempting to reproduce or explain some or all of the above observed phenomena, ranging from the GARCH family of models [3] to agent-based simulation techniques [4].

We present a much simpler approach. We start with an observation of different properties of "uptrend" and "downtrend" market regimes in terms of volatility and heaviness of tails (different stability parameter of the Lévy-stable distribution). We build upon this observation to construct a bootstrap-style, stochastic stock market index. We arrive at a market index with 2 distinct market regimes and all the listed above stylized facts. An ACF profile of absolute returns similar to that of the S&P500 index is obtained.

[1] Cont, R. (2001). "Empirical properties of asset returns: stylized facts and statistical issues", Quantitative Finance

[2] Cont, R. (2005). "Long range dependence in financial markets", Fractals in Engineering

[3] Mikosch, M.; Starica, C. (2003). "Long range dependence effects and ARCH modelling", Long-Range Dependence: Theory and Applications

[4] Cont, R. (2005). "Volatility clustering in financial markets: Empirical facts and agent-based models", Long Memory in Economics

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