Generalized Minimal Market Model

The paper proposes a tractable financial market model with continuous security processes. Its basic independent securities, the factors, are modelled as squared radial Ornstein-Uhlenbeck processes. Its parameters are modelled as time-homogeneous, continuous-time Markov chains to capture regime switching. The volatilities of the factors, their growth optimal portfolio (GOP), and the portfolio of the sum of the factors follow 3/2-volatility dynamics in respective activity times. The GOP of the factors serves as the numéraire for benchmark-neutral pricing, which provides the minimal possible prices of contingent claims. Risk-neutral pricing would often lead to more expensive and never to less expensive prices.