Состоялось очередное заседание общемосковского научного семинара "МАТЕМАТИЧЕСКИЕ МЕТОДЫ АНАЛИЗА РЕШЕНИЙ В ЭКОНОМИКЕ, БИЗНЕСЕ И ПОЛИТИКЕ"

Автор доклада: Голембиовский Дмитрий Юрьевич (Банк ЗЕНИТ)
Тема: Динамическое управление портфелем опционов в риск-нейтральном мире

19 марта 2014 года в рамках очередного заседания общемосковского научного семинара "МАТЕМАТИЧЕСКИЕ МЕТОДЫ АНАЛИЗА РЕШЕНИЙ В ЭКОНОМИКЕ, БИЗНЕСЕ И ПОЛИТИКЕ" был заслушан доклад на тему "Динамическое управление портфелем опционов в риск-нейтральном мире".
         Автор доклада: Голембиовский Дмитрий Юрьевич (Банк ЗЕНИТ)

The risk-neutral world is a model of real financial markets reflecting the essential feature of arbitrage absence. In the 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 option portfolio corresponds with the risk-free rate. However, it is possible to manage 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. To construct the appropriate strategy stochastic programming with the so called safety-first criterion can be used. It minimizes the probability of getting a return lower than the defined level. Optimization with the safety-first criterion is a hard problem to solve. In the report an approximation for solving the option portfolio optimization problem is suggested. It makes the problem linear and permits us to deal with the portfolios of quite large dimentions even including options with dual consecutive expiration dates. A stochastic program with the safety-first criterion for option portfolio management is considered along with the corresponding multinomial scenario tree. The results of the Monte-Carlo simulation of the portfolio management are presented.