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216878_731439052_713762010 - This article was downloaded...

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PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [National Taiwan University] On: 18 June 2010 Access details: Access Details: [subscription number 917276087] Publisher Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37- 41 Mortimer Street, London W1T 3JH, UK Applied Mathematical Finance Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713694021 Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach Riccardo Rebonato; Ian Cooper To cite this Article Rebonato, Riccardo and Cooper, Ian(1998) 'Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach', Applied Mathematical Finance, 5: 2, 131 — 141 To link to this Article: DOI: 10.1080/135048698334691 URL: http://dx.doi.org/10.1080/135048698334691 Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
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Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach RI CCA RDO RE B ONATO 1 and IAN COOPER 2 1 Barclays Capital, 5 The North Colonnade, Canary Wharf, London E14 4BB, UK 2 London Business School, Sussex Place, Regent’s Park, London NW1 4SA, UK Received September 1996. Accepted February 1998 This note presents a simple, robust and computationally ef cient way to calculate expectations of arbitrary future payoffs within the context of a Monte Carlo forward-induction methodology. The technique complements existing approximation techniques: while virtually all existing approximation methodologies remain approximate irrespective of the computational effort, the technique presented here has the desirable feature of being asymptotically ‘correct’, as long as ‘weak’ convergence in distribution is required. The proposed technique is applicable for the evaluation of both American options and compound options. The paper uses the fast Fourier transform (FFT) to evaluate along a simulated path the expectation of future pay-offs for an American option, conditional on the optimal exercise strategy. This technique can recover in a single pass the value function for a particular option across a wide range of values of the state variable and all future dates up to the maturity of the option. An example is given for a single state variable following a Markov process. The technique is shown
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