Stochastic Market Cycles and Option Valuation

摘要: A new Jump-Diffusion model of security price evolution is proposed. The posits that asset processes can be decomposed into a deterministic drift, Wiener process, and two compound Poisson representing discontinuous movements due to the arrivals “good” “bad” news during periods economic expansion contraction. Expansionary periods–Bull Markets–are characterized by more frequent arrival “good news” cause large increases (jumps). Contractionary periods–Bear “bad decreases. Market conditions change at random points in time causing regime. During each market epoch, jump magnitudes are determined draws from stationary distributions. This form information dynamics permits simple returns’ predictability, where conditional on current phase market, relative frequency direction may anticipated. We derive option pricing formula for this process investigate bias misspecification error. then generalize allow rate regime vary stochastically over time. also outline several strategies estimation simulation proposed but cannot report any results as work still progress.