On the Generalised Clark Haussmann Ocone Formula
Abstract
In this paper, exchange option and explicit computation of price of such option is examined. The variation of exchange option is investigated via the utilisation of the generalised Clark Haussmann Ocone Formula characterised by the Malliavin derivative. Thus, as an application, the European exchange price is explicitly computed thereby validating the efficiency of the Generalised Clark Hausmann Ocone Formula.
Keywords
Generalised Clark Haussman Ocone Formula
Malliavin derivative
Martingale
Representation Theorem
The Girsonov Theorem
References
[1] Aase, K., Oksendal, B., Privault, N. and Uboe, "White Noise Generalisations of the Clark Haussmann Ocone Theorem: with Application to Mathematical Finance", Journal of Economic Literature. Vol.X, No.X, (200X), pp.XX-XX. [2] Glover, E.N. "Analytical Pricing of American Options", MS.c Thesis, Department of Mathematics and Statistics, University of Rhodes, (2008) [3] Karatzas, I and Ocone, D. "A Generalised Clark Representation Formulation to Optimal Portfolio" Stochastic and Statistics Reports. Vol. 34 (1991), pp.187-220 [4] Kohatsu-Higa, A. and Montero, M Malliavin Calculus in Finance, Universitat Pompeu Fabre, Spain, (2002). [5] Kusuoka, S "Malliavin Calculus for Stochastic Differential equations driven by subordinated Brownian motions", Kyoto J. Math, Vol. 50, No. 3, (2010), pp. 491-520 [6] Oksendal, B Malliavin Calculus with Application to Economics,Institute of Finance and Management Science,Norwegian School of Economics and Business Administration,Bergen, 2014 [7] Margrabe, W "The Value of an Option to Exchange One Aset for Another", Journal of Finance,Vol. 33, No.2, (1978), pp.177-190 [8] Mataramvura, S "The Malliavin Derivative and Application to Pricing and Hedging a European Exchange Option", Journal of Mathematical Finance, Vol.2012, No.2, (2012), pp.280-290 [9] Nunno, D.G. Introduction to Malliavin Calculus and Applications to Finance,Part 1. Finance and Insurance,Sochastical Analysis an Practical Methods.,Spring School, Marie Curie, 2009. [10] Nuuno, D.G.,and Oksendal,B.(2009);Malliavin Calculus for Applications to Finance. Oslo University Norway text, Springer 2009.
