I was trading professionally in the years 2006-2014 in the equity derivatives market. This thesis deals with two of the ideas inspired by my experience as a professional trader. The first topic deals with the pricing of a derivatives product in the market with a specific risk concentration. We call the product that causes the concentration a market driver. When the market driver exists, not only the market driver itself, but any derivatives product will not be priced fairly. We introduced a new model based on the Heston model that accounts for the concentration. The model leads to a pair of partial differential equations (PDEs): one semilinear parabolic PDE to price the market driver and one linear parabolic PDE to price all the other products. In solving the semilinear PDE, we use the policy improvement algorithm (PIA) to approximate the solution with those of linear PDEs. We show that the approximated solutions satisfy quadratic local convergence (QLC) which explains the efficiency of the algorithm. This efficiency of the algorithm is proved in a more general setup. The other idea sparked by my experience that is explored in the last chapter of the thesis concerns modeling technical analysis. Technical analysis is a family of methods that traders use to make decisions to purchase/sell assets. There is no mathematical proof that shows that they are correct as far as I am aware. We focus on one of the methods, the method of support and resistance levels, and used the optimal stopping argument to show the validity of the method. As far as I know, this is one of the first results to mathematically prove the effectiveness of a method in technical analysis.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:759715 |
| Date | January 2018 |
| Creators | Maeda, Jun |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/111069/ |
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