Stochastic Programming Models for Optimal Risk Control with Financial Derivatives

Abstract

Stochastic optimization models have been extensively applied to financial portfolios and have proven their effectiveness in asset and asset-liability management; hardly however they have been applied to decision universe including not only financial but also derivatives written on the underlying, derivatives such as options or futures with their dedicated risk profiles and associated modeling complexities. Including options in the portfolio gives us the opportunity to hedge the underlying and to speculate on them to increase the profit potential given a certain risk level. The modeling of options in multistage stochastic programming framework would have many advantages, for instance, a put option can be used for insuring a portfolio against any downside movement in the market, high volatility in options prices is risky but rewarding if captured accurately, in-the-money call/put options at maturity can be used to buy/sell the underlying security at a price lower/higher than the market price, optimally increasing and reducing inventory. We present here multistage models to include cash and physical settled call and put options in a portfolio along with other asset classes.