Multistage portfolio optimization with stocks and options

Abstract

We develop a multistage portfolio optimization model that utilizes options for mitigating market risk in a dynamic setting. Due to the key role of scenarios in the quality of investment decisions, a new scenario generation method is proposed that characterizes the dynamic behavior of asset returns. This methodology takes the dependence structure of different asset returns into account, and also considers serial correlations of each of the asset returns. Moreover, it preserves marginal distributions of asset returns. Also, it precludes arbitrage opportunities. To investigate the role of options, we implement the scenario generation method on a set of stocks selected from the New York Stock Exchange. Results show the high performance of the proposed scenario generation method. Afterwards, the generated set of scenarios is used as the uncertainty set for the multistage portfolio optimization model. Static and dynamic assessments are used for measuring the performance of options in mitigating market risks and generating additional returns. Finally, backtesting simulations are used for assessing different trading strategies of options.

Practical arbitrage‐free scenario tree reduction methods and their applications in financial optimization

“…In this case, Algorithm 1 might not be efficient. To overcome this difficulty, we propose the other method to solve problem (9). As we know, to solve model (9) is to determine the optimal I m and m for m = 1, 2, · · · , M 1 .…”

“…Step 6 Take I (n+1) m and (n+1) m , m = 1, 2, · · · , M 1 , as a solution to model (9), and the probability of node (n+1)…”

“…Proof. From the expression of the objective function of model (9) and equations (16) and (17), we have…”

“…In Section 2, we proposed a stage-wise approximate method to solve model (5), which relies on the solution of model (9). On the basis of Algorithm 3, we design the following algorithm to solve model (5), or equivalently a multiperiod arbitrage-free scenario tree reduction algorithm.…”

“…Then we test Algorithm 3, the arbitrage-free hybrid method. These 3 algorithms are single-period scenario tree reduction methods to solve problem (9). Finally, we test Algorithm 4, the arbitrage-free multiperiod scenario tree reduction method.…”