Stochastic Programming Models for Optimal Risk Control with Financial Derivatives

Stochastic optimization models have been extensively applied to financial portfolios and have proven their effectiveness in asset and asset-liability management; however, derivatives have not been studied much in detail within the context of dynamic stochastic programming. Derivatives such as options have non-linear payoff profile and their presence in the portfolio makes constraints in the optimization problems complex. In this research, we focus on European options contracts (cash and physically-settled) within dynamic stochastic programming framework, starting from the single-stage models developed by other researchers, we develop multi-stage models where traditional asset classes are modeled with options available on them. We present a general model where not only long positions on derivatives are considered but also short-positions are modeled, we also verify that the general model we developed in particular cases reduces to the models developed by other researchers. We also developed models where we utilize physically-settled options contracts to manage the inventory dynamically. All the models developed are validated on the real data.