Dynamic Derivative Strategies

This paper studies the optimal investment strategy of an investor who can access not only the bond and the stock markets, but also the derivatives market. We focus on the investment situation where, in addition to the usual diffusive price shocks, the stock market experiences sudden price jumps and stochastic volatility, and provide closed-form solutions to the dynamic portfolio problem involving a riskless bond, a risky stock, and two derivative securities on the stock. Our results show that, as an investment instrument, derivatives are important in providing access to the the risk and return tradeoffs associated with the volatility and jump risks. In addition, as a vehicle to the volatility risk, derivatives are used by non-myopic investors to exploit the timevarying opportunity set; as a vehicle to the jump risk, derivatives are used by investors to dis-entangle their simultaneous exposure to the diffusive and jump risks in the stock market. Moreover, because of the interaction between the two markets, derivatives investing further complicates investors’ stock position. Calibrating our model to the S&P 500 index and options markets, we find sizable portfolio improvement for taking advantage of derivatives. ∗Liu is with the Anderson School at UCLA, [email protected]. Pan is with the MIT Sloan School of Management, [email protected]. We benefited from discussions with Darrell Duffie, and comments from Harrison Hong, Leonid Kogan, Alex Shapiro, and seminar participants at Duke.