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# Algorithm for Compensating Discontinuities of Values which Arise in Pricing of Derivative Securities

IP.com Disclosure Number: IPCOM000116711D
Original Publication Date: 1995-Oct-01
Included in the Prior Art Database: 2005-Mar-31
Document File: 4 page(s) / 92K

IBM

## Related People

Ninomiya, S: AUTHOR

## Abstract

Disclosed is an algorithm for compensating those discontinuities of values which arise in pricing of derivative securities by Monte Carlo method on multinomial trees. The important points of this new algorithm are that it: 1. Uses backwardation method together with Monte Carlo method on multinomial tree. 2. Interpolates the values on those nodes which locate on the same time-slice in the tree.

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Algorithm for Compensating Discontinuities of Values which Arise
in Pricing of Derivative Securities

Disclosed is an algorithm for compensating those
discontinuities of values which arise in pricing of derivative
securities by

Monte Carlo

method on multinomial trees.  The important
points of this new algorithm are that it:
1.  Uses backwardation method together with

Monte Carlo

method on
multinomial tree.
2.  Interpolates the values on those nodes which locate on the same
time-slice in the tree.

Multinomial trees are widely used in the calculation of price
and risks of derivative securities.  There are two calculation schema
on multinomial trees: Backwardation and Monte Carlo method.
Conventional calculation methods on multinomial trees have the
following problem.  When parameters of a security (i.e., barrier
rate, strike, etc.) changes continuously, theoretical values of the
price and the risks of this security must change continuously, but
those obtained from conventional calculation methods on multinomial
trees do not.  For example, in Fig. 1 when the strike changes
continuously from A to B, the value of Delta calculated by this tree
does not change.  This is a fatal problem especially in the case of
risk calculation.

The disclosed algorithm solves the above problem when the Monte
Carlo method on multinomial tree is used.  Fig. 3

The modified algorithm of calculation for the price of a derivative
security by the Monte Carlo method on multinomial tree follows:
Step 1.  Generate a sample path on the tree by use of pseudo random
sequences or low-discrepancy sequences.  The important
point
is to stop generating this path when the path reaches one
time-step bef... 