Hedging Strategies : Complete and Incomplete Systems of Markets

Papayiannis, Andreas (2010) Hedging Strategies : Complete and Incomplete Systems of Markets. Masters thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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We are motivated by the latest statistical facts that weather directly affects about 20% of the U.S. economy and, as a result energy companies experience enormous potential losses due to weather that is colder or warmer than expected for a certain period of a year. Incompleteness and illiquidity of markets renders hedging the exposure using energy as the underlying asset impossible. We attempt to price and hedge a written European call option with an asset that is highly correlated with the underlying asset; still, a significant amount of the total risk cannot be diversified. Yet, our analysis begins by considering hedging in a complete markets system that can be utilised as a theoretical point of reference, relative to which we can assess incompleteness. The Black-Scholes Model is introduced and the Monte Carlo approach is used to investigate the effects of three hedging strategies adopted; Delta hedging, Static hedging and a Stop-Loss strategy. Next, an incomplete system of markets is assumed and the Minimal Variance approach is demonstrated. This approach results in a non-linear PDE for the option price. We use the actuarial standard deviation principle to modify the PDE to account for the unhedgeable risk. Based on the derived PDE, two additional hedging schemes are examined: the Delta hedging and the Stop-loss hedging. We set up a risk-free bond to keep track of any money injected or removed from the portfolios and provide comparisons between the hedging schemes, based on the Profit/Loss distributions and their main statistical features, obtained at expiry.

Item Type: Thesis (Masters)
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Date Deposited: 21 Sep 2012
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1869

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