Pricing options of security portfolio in cyclical economic environment

In this article, we present two option pricing models of optimal security portfolio in real-world measure. We capture the risk-adjusted prices with multi-Vasicek model, which is used to describe the change patterns of the return and the price of security portfolio with time-varying correlation. We assume certainty equivalence for the first pricing model and relax this assumption in the second pricing model. We obtain explicit expressions of option prices and carry out numerical analysis. We conclude that there exists difference in option price between our proposed models and extended Black–Scholes model; the latter overestimates the prices of options, and our model II is a more realistic option pricing model of security portfolio in real-world measure.