Managing a portfolio of securities using jump models and static hedging
Abstract
Managing a portfolio of securities using jump models and static hedging
Incoming article date: 12.12.2017The article investigates approaches to managing currency risks on the Moscow exchange based on static hedging and taking into account the features of the Russian derivatives market. For more delicate managing currency risks, it is proposed to use barrier options that are not traded on the Moscow exchange. It is shown that the barrier option can be replicated with the portfolio of European options, the strike prices of which are the barrier and the strike price of the barrier option. The main idea behind the approach applied is replication of zero price of the up-an-out call (in the case of crossing the barrier) by the linear combination of European call options with different time to expiry. Examples of constructing replicating portfolios of options on the futures contract for the US dollar - Russian ruble are given . Further analysis of the portfolio's value dynamics demonstrates the inadequacy of the classical Black-Scholes model for the Russian derivatives market. The approaches of static hedging barrier options in jump models are disscussed.
Keywords: mathematical modeling, numerical method, mathematical finance, barrier options, Black-Scholes model, static hedging, Levy models, derivatives market.