Computational Methods for Maximum Drawdown Options Under Jump-Diffusion

computational finance;scientific computing;Computer Science

Fagnan, David Erik

University of Waterloo

关键词: computational finance;    scientific computing;    Computer Science;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/6134/1/Fagnan_David.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Recently, the maximum drawdown (MD) has been proposed as an alternativerisk measure ideal for capturing downside risk. Furthermore, the maximumdrawdown is associated with a Pain ratio and therefore may be a desirableinsurance product. This thesis focuses on the pricing of the discrete maximumdrawdown option under jump-diffusion by solving the associated partial integrodifferential equation (PIDE). To achieve this, a finite difference method is usedto solve a set of one-dimensional PIDEs and appropriate observation conditionsare applied at a set of observation dates. We handle arbitrary strikes on theoption for both the absolute and relative maximum drawdown and then showthat a similarity reduction is possible for the absolute maximum drawdown withzero strike, and for the relative maximum drawdown with arbitrary strike. Wepresent numerical tests of validation and convergence for various grid types andinterpolation methods. These results are in agreement with previous resultsfor the maximum drawdown and indicate that scaled grids using a tri-linearinterpolation achieves the best rate of convergence. A comparison with mutualfund fees is performed to illustrate a possible rationalization for why investorscontinue to purchase such funds, with high management fees.