A Simple Mean-variance Model for Equities and Equity Options under Inflation Rate Dynamics

抄録

Recently, portfolio managers have to optimize their portfolios taking the inflation rate into consideration because many central banks have adopted inflation targeting policies and the asset returns should be influenced by the target inflation rate. In such an investment environment, we model the equity process so that it can depend on an inflation rate that follows the OU process. Accordingly, we derive the expected returns, the volatilities and the correlation matrix, which are key ingredients for the use of the mean-variance model. We also provide an option pricing formula based on our equity model under the hedge-neutral probability measure and generate the future paths of not only the equity prices and the inflation rate but also the option prices. Using the proposed model, it is possible to optimize portfolios including the equity options under several inflation scenarios.