PORTFOLIO OPTIMAL CHOICE UNDER VOLATILITY AND PRICE RISK IMPACT APPLIED TO DERIVATIVE TRANSACTIONS
PORTFOLIO OPTIMAL CHOICE UNDER VOLATILITY AND PRICE RISK IMPACT APPLIED TO DERIVATIVE TRANSACTIONS

Summary/Abstract: The idea that derivatives can complete the market and increase the efficiency of the portfolio has been debated for a long time in the literature of specialty. Our contribution in this study is to build upon these intuitions and to choose an explicit case for a realistic model of the incomplete market with a realist set of derivatives. In particular, we push the existent intuition a step forward, asking ourselves: which are the optimal dynamical strategies for an investor to control not only his holdings, but also the derivative ones? Which is the benefit resulted from the inclusion of the derivatives? We ask these questions focusing on two specific aspects of the incomplete market that have been very good documented in the empiric literature for the aggregated stock market: the stock volatility and the price jumps. In a specific way, we adopted an empiric realistic model for the aggregated stock market that includes three types of risk factors: the risk of the impacts of the prices’ diffusion, the risk of the prices jumps and the volatility risk. Considering this condition of the market as already given, we resolve the dynamic allocation problem (Merton 1971) of an investor with a large utility of which opportunity of investment includes not only the risky stock and the usual bonds without risk, but also the stock derivatives.

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