Model Uncertainty Effect on Asset Prices

• Date: 01 June 2017
• Author: Junya Jiang,Weidong Tian
• Published date: 01 June 2017
• DOI: http://doi.org/10.1111/irfi.12118

Model Uncertainty Effect on Asset

Prices*

JUNYA JIANG AND WEIDONG TIAN

Belk College of Business, University of North Carolina at Charlotte, Charlotte, NC, USA

ABSTRACT

We develop a weighted-average approach of pricing under model uncer-

tainty, where several plausible models are considered instead of a perfect

one. The model uncertainty effect from this weighted-average approach is

significantly different from the conventional wisdom, in which the true

price must be bounded by prices in all plausible models. We identify under

what circumstances the model uncertainty effect is significant and reveal

serious risk management challenges for researchers, regulators, and market

participants.

JEL Codes: G11; G12; G13; D52; D90

I. INTRODUCTION

All asset-pricing problems in modern finance depend on financial models, but

models are never perfect. Because of increasing market turmoil and growing

financial innovations, financial models have become increasingly complicated,

subject to model risk.

1

As a result, model risk has emerged as a very important

asset-pricing issue for regulators, market participants, and researchers.

According to the Board of Governors of the Federal Reserve System (SR Letter

11-7, April 4, 2011), “the term model refers to a quantitative method, system, or

approach that applies statistical, economic, financial, or mathematical theories,

techniques, and assumptions to process input data into quantitative estimates.

There are three components in a financial model: an information input

* We greatly thank Carole Bernard, Phelim Boyle, Peter Carr, Zengjing Chen, Gardner Doug,

Shaolin Ji, Larry Li, Jianjun Miao, Kevin Oden, Tan Wang, Hong Yan, Tong Yang, and Han Zhang

for their helpful comments.

1 Model risk or valuation risk is a major concern in risk management and stands alone as a

new class of risk even before the financial crisis 2007-2009. See, for instance, “How Street

Rode: The Risk Ledge and Fell Over,”Walls Street Journal, August 7, 2007. In the post-crisis

period, there are a wide variety of interests in practice on model risk; see the documents

in www.pwc.com/modelrisk, www.risk.net/journal-of-risk-model-validation, to name just a

few. Moreover, as documented in the work of Pfleiderer (2014) with several widely cited finan-

cial and economical models, a model can easily become a chameleon, with a substantial neg-

ative impact under unrealistic assumptions.

© 2017 International Review of Finance Ltd. 2017

International Review of Finance, 17:2, 2017: pp. 205–233

DOI: 10.1111/irfi.12118

component, which delivers assumptions and data to the model; a processing

component, which transforms inputs into estimates; and a reporting component,

which translates the estimates into useful business information.”

2

This paper

concerns the information and processing component of a model to deal with

asset-pricing and risk management problems, and the components are measured

using several plausible model assumptions and estimation methodologies.

Specifically, assuming two plausible models A and B are used at the same time

in one financial market. It can be the case that each model is appropriate in

terms of its model assumption as well as calibration, but both two are not perfect,

and excluding either one or the other is not in the best interest of model users. It

may also be the case that more than one model is selected for a model validation

purpose, and the agent is presumed to better calibrate the financial risk using

multiple models. Given a general contingent claim xin the financial market with

the price x

A

and x

B

in model A and B, respectively, the question we study in this

paper is: What can we say about the price of x under two plausible models from

both the pricing and validation perspectives? Because we do not have perfect

knowledge about which model is better, neither x

A

nor x

B

is the precise true

price.

The conventional wisdom in dealing with the model uncertainty issue is to

price a contingent claim in each plausible model, and the “true”price must be

bounded by the prices of all plausible asset-pricing models. In other words, the

true price punder two possible models satisfies

min xA;xB

fg

≤p≤max xA;xB

fg (1)

regardless of the pricing methodology and mechanism. While it seems intui-

tively straightforward, this premise has profound implications for asset pricing.

For example, the closer the prices x

A

and x

B

, the smaller the interval [min{x

A

,

x

B

}, max{x

A

,x

B

}]; therefore, one model is justified by the other in a model valida-

tion process even though the agent does not know which one is a true or better

model.

3

From a general economic perspective, equation (1) is closely related to an

“internality axiom”that the value of a risky project must lie between the

highest and lowest outcome. This internality axiom has been justified for virtu-

ally all important economic models of decision making under risk, such as ex-

pected utility, prospect theory (Kahneman and Tversky 1979), disappointment

2 Model risk denotes adverse consequences from decisions that are based on incorrect or misused

model outputs and reports. Model risk is pervasive for two important reasons: the model is fun-

damentally wrong and produces inaccurate outputs, or the model is used incorrectly or inap-

propriately even though the model itself is sound. See “Supervisory Guidance on Model Risk

Management,”SRLetter 11-7, April 4, 2011.

3 Indeed, there is a pool of models in big financial institutions. Some models are used for pricing

while other models serve the purpose of risk management and validation. The models in the

pool are often used independently.As shown in this paper, however, model uncertainty yields

significant issues for current valuation and validation practice.

International Review of Finance

© 2017 International Review of Finance Ltd. 2017206