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Solving a partial differential equation associated with the pricing of power options with time‐dependent parameters
Author(s) -
Okelola M. O.,
Govinder K. S.,
O'Hara J. G.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3249
Subject(s) - ansatz , partial differential equation , mathematics , constant (computer programming) , valuation of options , mathematical optimization , volatility (finance) , stock (firearms) , econometrics , mathematical economics , computer science , mathematical analysis , mechanical engineering , engineering , mathematical physics , programming language
Previous analysis and research on the power option – one of the exotic options – have focused on the interest rate of the stock and its volatility as constant parameters throughout the run of execution. In this paper, we attempt to extend these results to the more practical and realistic case of when these parameters are time dependent. By making no ansatz or relying on ad hoc methods, we are able to achieve this via an algorithmic method – the Lie group approach – leading to exact solutions for the power option problem. Copyright © 2014 John Wiley & Sons, Ltd.