Modeling a Risk - Based Criterion for a Portfolio with Options ∗
نویسنده
چکیده
The presence of options in a portfolio fundamentally alters the portfolio’s risk and return profiles when compared to an all equity portfolio. In this paper, we advocate modeling a risk-based criterion for optioned portfolio selection and rebalancing problems. The criterion is inspired by Chicago Mercantile Exchange’s risk-based margining system which sets the collateralization requirements on margin accounts. The margin criterion computes the losses expected at the portfolio level using expected stock price and volatility variations, and is itself an optimization problem. Our contribution is to remodel the criterion as a quadratic programming subproblem of the main portfolio optimization problem using option Greeks. We also extend the margin subproblem to a continuous domain. The quadratic programming problems thus designed can be solved numerically or in closed-form with high efficiency, greatly facilitating the main portfolio selection problem. We present two extended practical examples of the application of our approach to obtain optimal portfolios with options. These examples include a study of liquidity effects (bid/ask spreads and limited order sizes) and sensitivity to changing market conditions. Our analysis shows that the approach advocated here is more stable and more efficient than discrete approaches to portfolio selection.
منابع مشابه
Optimal Portfolio Allocation based on two Novel Risk Measures and Genetic Algorithm
The problem of optimal portfolio selection has attracted a great attention in the finance and optimization field. The future stock price should be predicted in an acceptable precision, and a suitable model and criterion for risk and the expected return of the stock portfolio should be proposed in order to solve the optimization problem. In this paper, two new criterions for the risk of stock pr...
متن کاملHedging of Options in Jump-Diffusion Markets with Correlated Assets
We consider the hedging problem in a jump-diffusion market with correlated assets. For this purpose, we employ the locally risk-minimizing approach and obtain the hedging portfolio as a solution of a multidimensional system of linear equations. This system shows that in a continuous market, independence and correlation assumptions of assets lead to the same locally risk-minimizing portfolio. ...
متن کاملFinancial Risk Modeling with Markova Chain
Investors use different approaches to select optimal portfolio. so, Optimal investment choices according to return can be interpreted in different models. The traditional approach to allocate portfolio selection called a mean - variance explains. Another approach is Markov chain. Markov chain is a random process without memory. This means that the conditional probability distribution of the nex...
متن کاملThe Tail Mean-Variance Model and Extended Efficient Frontier
In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of r...
متن کاملمقایسه روش های فراابتکاری برای
Abstract With the introduction of mean-variance model Markowitz took a giant step in modeling and optimizing portfolio type problems. But his model is based upon some assumptions that rarely they can hold in practice. For this reason, many researchers have taken steps both theoretical and practical to make some improvements to his standard mean-variance model. Up to now different risk criteria...
متن کامل