histogram/pdf -incompatible- binomial tree

This is not really restricted to option pricing. Actually, forget about option pricing! I’m thinking about the relationship of a pdf/histogram and a standard diamond-filled binomial tree.

http://bigblog.tanbin.com/2012/05/underlier-expiry-price-pdf-option.html mentions but doesn’t explain the10,000 simulations. One way to simulate is via the binomial tree.

To get 2001 nodes (each corresponding to a range described in that blog), we need 2000 steps to grow our tree. However, the standard CRR btree has the 2001 price points equally spaced logarithmically. A small CRR btree might grow to these price levels.

$32.0
$16.0
$8.0
$4.0
$2.0
$1.0
$0.5
$0.25

Therefore the 2001 ranges in http://bigblog.tanbin.com/2012/05/underlier-expiry-price-pdf-option.html will not map 1-to-1 to 2001 price nodes in a btree. Multiple high price Ranges will map to the highest tree Node, and many low Nodes will fall into the lowest Range of $0~$1.

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