Enhanced Finite-Difference Techniques for Early-Exercise Options on Single and Multiple Underlyings

31 Pages Posted: 23 Aug 2007

See all articles by Paul V. Johnson

Paul V. Johnson

University of Manchester; University of Manchester

Nick J. Sharp

Nottingham University Business School (NUBS)

Peter Duck

University of Manchester - Department of Mathematics

David Newton

University of Bath - School of Management

Date Written: August 17, 2007

Abstract

This paper develops improvements to existing finite-difference methods for pricing derivatives (on single and also multiple underlying factors) which contain early-exercise features. Both fixed-grid methods (based on Projected Successive Over Relaxation) and moving-grid methods (based on boundary-fitted coordinates), are considered exploiting some prior (but limited) knowledge of the topology of the pricing in time and underlying price(s). These techniques can be quite readily applied to ensure pricing is both highly accurate and very efficient.

Keywords: American options, multi asset, finite difference, PSOR

JEL Classification: C63

Suggested Citation

Johnson, Paul V. and Sharp, Nick J. and Duck, Peter and Newton, David, Enhanced Finite-Difference Techniques for Early-Exercise Options on Single and Multiple Underlyings (August 17, 2007). 20th Australasian Finance & Banking Conference 2007 Paper, Available at SSRN: https://ssrn.com/abstract=1007721 or http://dx.doi.org/10.2139/ssrn.1007721

Paul V. Johnson

University of Manchester ( email )

Oxford Road
Manchester, N/A M13 9PL
United Kingdom
+44 (0) 161 306 3660 (Phone)

HOME PAGE: http://www.maths.manchester.ac.uk/~pjohnson/

University of Manchester ( email )

Oxford Road
Manchester, N/A M13 9PL
United Kingdom
+44 (0) 161 306 3660 (Phone)

HOME PAGE: http://www.maths.manchester.ac.uk/~pjohnson/

Nick J. Sharp (Contact Author)

Nottingham University Business School (NUBS) ( email )

Jubilee Campus
Wollaton Road
Nottingham, NG8 1BB
United Kingdom
+441519515258 (Phone)

Peter Duck

University of Manchester - Department of Mathematics ( email )

Oxford Road
Manchester M60 1QD, N/A M13 9PL
United Kingdom

David Newton

University of Bath - School of Management ( email )

Claverton Down
Bath, BA2 7AY
United Kingdom

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