Financial density forecasts: A comprehensive comparison of risk‐neutral and historical schemes

• Date: 01 August 2018
• DOI: http://doi.org/10.1002/for.2521
• Author: Lorena Couso,Ricardo Crisóstomo
• Published date: 01 August 2018

RESEARCH ARTICLE

Financial density forecasts: A comprehensive comparison of

risk‐neutral and historical schemes

Ricardo Crisóstomo

1,2

| Lorena Couso

3

1

Comisión Nacional del Mercado de

Valores (CNMV), Madrid, Spain

2

National Distance Education University

(UNED), Madrid, Spain

3

CaixaBank Asset Management, Madrid,

Spain

Correspondence

Ricardo Crisóstomo, Comisión Nacional

del Mercado de Valores (CNMV), Edison

4, 28006 Madrid, Spain.

Email: rcayala@cnmv.es

[Correction added on 26 April 2018, after

first online publication: The text “line

below is too”cited at the top of Table 6 has

been deleted].

Abstract

We investigate the forecasting ability of the most commonly used benchmarks

in financial economics. We approach the usual caveats of probabilistic forecasts

studies—small samples, limited models, and nonholistic validations—by

performing a comprehensive comparison of 15 predictive schemes during a

time period of over 21 years. All densities are evaluated in terms of their statis-

tical consistency, local accuracy and forecasting errors. Using a new composite

indicator, the integrated forecast score, we show that risk‐neutral densities out-

perform historical‐based predictions in terms of information content. We find

that the variance gamma model generates the highest out‐of‐sample likelihood

of observed prices and the lowest predictive errors, whereas the GARCH‐based

GJR‐FHS delivers the most consistent forecasts across the entire density range.

In contrast, lognormal densities, the Heston model, or the nonparametric

Breeden–Litzenberger formula yield biased predictions and are rejected in sta-

tistical tests.

KEYWORDS

ARCH models, ensemblepredictions, forecast verification,probabilistic forecasting, risk‐neutral

densities

1|INTRODUCTION

Forecasting future asset prices is arguably one of the most

relevant problems for risk managers, central bankers, and

investors. Historical and risk‐neutral methods are the

most widely used techniques in financial forecasting.

Yet, when it comes to evaluate predictions across the

entire density range, comprehensive comparisons are

scarce and there is no consensus on which models provide

better forecasts.

Historical methods generate future predictions based

on past prices. These models are easy to implement and

extensively used in risk management and stress testing.

However, it is well‐known that historical patterns do not

repeat themselves, particularly in times of economic tur-

moil. Furthermore, historical models may yield different

estimates depending on the length of the calibration win-

dow, introducing uncertainty and possible cherry‐picking

concerns.

Risk‐neutral estimates, on the other hand, contain for-

ward‐looking expectations and react immediately to

changing market conditions, thus being conceptually bet-

ter suited for forecasting purposes. However, risk‐neutral

models do not explicitly consider the investors’risk pref-

erences across different future states. Consequently, some

agents rapidly dismiss risk‐neutral models as the basis for

financial predictions.

The previous literature on financial forecasts has been

mainly devoted to volatility predictions. Poon and

Granger (2003) compare the results from 18 academic

papers showing that in 17 of them implied volatilities pro-

duce better forecasts than generalized autoregressive

Received: 28 December 2017 Accepted: 11 February 2018

DOI: 10.1002/for.2521

Journal of Forecasting. 2018;37:589–603. Copyright © 2018 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for 589