Recently, the maximum drawdown (MD) has been proposed as an alternative
risk measure ideal for capturing downside risk. Furthermore, the maximum
drawdown is associated with a Pain ratio and therefore may be a desirable
insurance product. This thesis focuses on the pricing of the discrete maximum
drawdown option under jump-diffusion by solving the associated partial integro
differential equation (PIDE). To achieve this, a finite difference method is used
to solve a set of one-dimensional PIDEs and appropriate observation conditions
are applied at a set of observation dates. We handle arbitrary strikes on the
option for both the absolute and relative maximum drawdown and then show
that a similarity reduction is possible for the absolute maximum drawdown with
zero strike, and for the relative maximum drawdown with arbitrary strike. We
present numerical tests of validation and convergence for various grid types and
interpolation methods. These results are in agreement with previous results
for the maximum drawdown and indicate that scaled grids using a tri-linear
interpolation achieves the best rate of convergence. A comparison with mutual
fund fees is performed to illustrate a possible rationalization for why investors
continue to purchase such funds, with high management fees.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/6134 |
| Date | January 2011 |
| Creators | Fagnan, David Erik |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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