# Chapter IV - Numerical Simulation Techniques in Finance FRE...

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Numerical & Simulation Techniques in Finance FRE 6251 Chapter IV – Interpolation, etc. Edward D. Weinberger, Ph.D, F.R.M. Adjunct Assoc. Professor Polytechnic University [email protected]

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OUTLINE Chapter IV – Interpolation, etc. Statement of Problem Relevance to finance Building yield curves Building volatility curves Tools Neville’s algorithm Splines Rational Interpolation
THE PROBLEM Find a “reasonable” curve that passes through the given series of points ( x 1 , y 1 ), ( x 2 , y 2 ), …, ( x N , y N ), where “reasonable” might mean (for example) passes through all points (or not) smooth (or not) easy to compute

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WHAT NOT TO DO Want to interpolate (1, 0), (2, 0), (3, 0), (4, 0), (5, 0). Try a quintic polynomial, e.g. P ( x ) = ( x 1)( x – 2)( x – 3)( x – 4)( x – 5)
RELEVANCE TO FINANCE ALL pricing formulas are a kind of interpolation, since they are attempts to base pricing of a particular instrument on benchmark prices.

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## This note was uploaded on 04/05/2010 for the course FINANCE AN FRE6251 taught by Professor Weinberger,edward during the Fall '09 term at NYU Poly.

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Chapter IV - Numerical Simulation Techniques in Finance FRE...

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