Option premia harvesting
Foundations of mean reversion
Volatility is not merely a statistical descriptor of price fluctuations; it is a dynamic state variable that governs the pricing of derivatives, the calibration of risk models, and the design of trading strategies. Among its most consequential properties is its tendency to revert to a long-run average—a phenomenon widely exploited by option sellers but often understood only through empirical observation or heuristic reasoning. This essay provides a formal, mathematical exposition of volatility mean reversion, grounded in stochastic calculus and the theory of diffusion processes. By examining the structural constraints that define mean-reverting behavior and analyzing the canonical Cox-Ingersoll-Ross (CIR) model, we establish a theoretical justification for why elevated volatility presents a statistically favorable environment for premium-selling strategies.
I. Defining Mean Reversion: Stationarity and Boundedness
In mathematical finance, a process is said to exhibit mean reversion if it possesses a long-term equilibrium level toward which it is continuously drawn over time. However, not all processes that appear to “snap back” empirically qualify as mean-reverting in a formal sense. Two necessary conditions must be satisfied:
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