Option Portfolio Management as a Chance Constrained Problem

Dmitry Golembiovsky and Anatoliy Abramov
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Dmitry Golembiovsky: Department of Risks, Bank ZENIT, Moscow Financial-Industrial University “Sinergy” 9, Banny Lane, Moscow 129110, Russia
Anatoliy Abramov: Department of Risks, Bank ZENIT, Moscow Financial-Industrial University “Sinergy” 9, Banny Lane, Moscow 129110, Russia

Chapter 7 in Stochastic Programming:Applications in Finance, Energy, Planning and Logistics, 2013, pp 155-172 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn a risk-neutral world the price of an option is equal to its expected payoff discounted at the risk-free interest rate. So, the expected return from investment in any static option portfolio corresponds with the risk-free rate. However, it is possible to manage the portfolio dynamically in such a way that it provides higher return with a probability close to unity and lower return (possibly large negative return) with a given low probability. For this purpose stochastic programming with chance constraints can be used.In the paper the problem of option portfolio management is investigated. The hypothetical market considered includes European options expiring in the nearest month. It is a risk-neutral market where the underlying asset follows a geometric Brownian motion and prices of all options are calculated on the basis of the Black-Scholes formula. A stochastic chance constrained program for option portfolio management is developed along with the corresponding multinomial scenario tree.The results of a Monte-Carlo simulation of the portfolio management are presented. They confirm that it is possible to make more than the risk-free return in a risk-neutral options market.

Keywords: Stochastic Programming; Optimization with Scenarios; Finance; Energy; Production and Logistics Applications (search for similar items in EconPapers)
Date: 2013
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