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## Are we extracting the true risk neutral density from option prices?: a question with no easy answer

Research output: Working paper

Published

### Standard

Lancaster : Lancaster University, 2012.

Research output: Working paper

### Bibtex

@techreport{4aac98cfb89e4fa887b531968c4665fe,
title = "Are we extracting the true risk neutral density from option prices?: a question with no easy answer",
abstract = "In this paper we raise a question on the reliability of option implied risk neutral density. We prove that given any number of options, there exist numerous risk neutral densities which are piecewise constant, have only two values, either a lower bound or an upper bound on the true risk neutral density, and price all these options correctly. Similar results are proved with respect to the true risk neutral density's derivatives. These results show how difficult it is to ensure that the risk neutral density we extract from option prices is the true one and how large estimation errors can be.",
keywords = "option-implied risk neutral density, option pricing, estimation errors",
author = "James Huang",
year = "2012",
language = "English",
publisher = "Lancaster University",
type = "WorkingPaper",
institution = "Lancaster University",

}

### RIS

TY - UNPB

T1 - Are we extracting the true risk neutral density from option prices?

T2 - a question with no easy answer

AU - Huang, James

PY - 2012

Y1 - 2012

N2 - In this paper we raise a question on the reliability of option implied risk neutral density. We prove that given any number of options, there exist numerous risk neutral densities which are piecewise constant, have only two values, either a lower bound or an upper bound on the true risk neutral density, and price all these options correctly. Similar results are proved with respect to the true risk neutral density's derivatives. These results show how difficult it is to ensure that the risk neutral density we extract from option prices is the true one and how large estimation errors can be.

AB - In this paper we raise a question on the reliability of option implied risk neutral density. We prove that given any number of options, there exist numerous risk neutral densities which are piecewise constant, have only two values, either a lower bound or an upper bound on the true risk neutral density, and price all these options correctly. Similar results are proved with respect to the true risk neutral density's derivatives. These results show how difficult it is to ensure that the risk neutral density we extract from option prices is the true one and how large estimation errors can be.

KW - option-implied risk neutral density

KW - option pricing

KW - estimation errors

M3 - Working paper

BT - Are we extracting the true risk neutral density from option prices?

PB - Lancaster University

CY - Lancaster

ER -