Option‐implied risk measures: An empirical examination on the S&P 500 index

• Published date: 01 October 2019
• Author: Chiara Legnazzi,Giovanni Barone‐Adesi,Carlo Sala
• DOI: http://doi.org/10.1002/ijfe.1743
• Date: 01 October 2019

DOI: 10.1002/ijfe.1743

RESEARCH ARTICLE

Option-implied risk measures: An empirical examination

on the S&P 500 index

Giovanni Barone-Adesi1Chiara Legnazzi1Carlo Sala2

1Swiss Finance Institute at Università

della Svizzera Italiana (USI), Institute of

Finance, Via G. Buffi 13, Lugano,

CH-6900, Switzerland

2Department of Financial Management

and Control, ESADE Business School,

Ramon LLull University, Avenidade

Torreblanca59, Barcelona, 08172, Spain

Correspondence

Carlo Sala, Department of Financial

Management and Control, ESADE

Business School, Ramon LLull University,

Avenida de Torreblanca59, 08172 Sant

Cugat, Barcelona, Spain.

Email: carlo.sala@esade.edu

Abstract

The forward-looking nature of option market data allows one to derive econom-

ically based and model-free risk measures. This article proposes an extensive

analysis of the performances of option-implied value at risk and conditional

value at risk and compares them with classical risk measures for the S&P 500

index. Delivering good results both at short and long time horizons, the proposed

option-implied risk metrics emerge as a convenient alternative to the existing

risk measures.

KEYWORDS

long and short-term risk measures, option prices, option-implied VaR and CVaR,S&P 500 index

JEL CLASSIFICATION

G13; G32; D81

1INTRODUCTION

“...risk management models generally covered only the past

two decades, a period of euphoria. Had instead the models

been fitted more appropriately to historic periods of stress,

capital requirements would have been much higher and the

financial world would be in far better shape today.”

Alan Greenspan, 1987–2006 Chairman of the US Federal

Reserve (FED)

Thanks to their ease of application and to different

empirical and theoretical convenient features,1the value

at risk (VaR) and the conditional value at risk (CVaR) are

to date the most widely used risk measures in finance.

Summarizing the market risk in a single value, both risk

measures assess the maximal loss at a specified probability

level over a fixed time horizon. The risk management lit-

erature proposes a wide variety of approaches to estimate

the VaR and CVaR. To date, most of the existing method-

ologies infer their estimates from past returns, using more

or less sophisticated statistical procedures (henceforth

“statistically based” models). Unfortunately, the use of

past returns leads to backward-looking final results that,

especially during crashes, may poorly predictthe dynamics

of financial markets. This is opposed to option market

data. Reflecting the investors' expectations over different

time horizons, option prices are by construction forward

looking, and so the estimation deriving from them.

Using option market data as input and proposing both a

nonparametric and a parametric approach, this paper tests

if the option-based (henceforth “option implied”) VaRand

CVaRcan deliver accurate risk forecasts and compare their

performances with those of the relative statistically based

risk measures. Performing well both at short and long time

horizons and at different risk levels, our results show that

option-implied risk measures can be considered as valid

alternatives to the classical statistically based risk metrics.

From a theoretical viewpoint, most of results coming

from the existing statistically based models might be prone

to economic and econometric biases linked to the estima-

tion of the future profit and loss (P&L) distribution. First,

even though at different extents, all statistically based risk

models involve errors in the modelling of the underlying

asset volatility,thus being exposed to the “risk that the risk

will change” (see Engle, 2009; 2011).

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BARONE-ADESI ET AL .

Second, as anticipated, statistically based risk models

use historical data as inputs, thus making the resulting

estimates backward looking by construction. More for-

mally, at each trading day, only one stock return is observ-

able. Being the observations just a single value (a scalar),

it is not possible to infer a density out of it. To tackle this

problem, a common approach is to enlarge the amount of

data used in the estimation process by adding historical

returns to the current value. Unfortunately, when piling

up historical returns to estimate the future P&L distribu-

tion, the last values become almost uninformative. The

obtained P&L distribution cannot be sensitive to the cur-

rent market situation; on the contrary,it is strongly depen-

dent to the time window and amount of data used in the

estimation process. As a consequence, the resulting statis-

tically based risk measures are biased by construction.

Third, it is well known that the statistical properties

of market prices depend on the general market outlook

(e.g., Danielsson, 2002; Brunnermeier & Pedersen, 2009,

and references therein). In stable periods, the heterogene-

ity among investors' behaviour increases, whereas during

high volatility periods, agents' actions become more sim-

ilar (e.g., bank runs and flights to safety). As a conse-

quence, the statistical analysis conducted in stable peri-

ods can rarely be helpful during highly volatile ones, and

vice versa.

Fourth, the time horizon of the estimates is a crucial ele-

ment in risk management, and the use of historical data

makes the estimation of long time horizon risk measures

challenging. From an econometric viewpoint, statistically

based risk metrics often need to rely on a proper estima-

tion of the market volatility. Brownlees et al. (2011) show

that several ARCH models perform well at short time hori-

zons, whereas results are often unsatisfactory at medium

and long time horizons. To date, statistically based risk

measures at time horizons longer than 1 day are obtained

with more or less complex numerical transformations.2

Unfortunately, how to economically justify most of these

transformations is still an open question. All these points

have great practical relevance, as short-time horizon esti-

mates might not be of great help if one has to liquidate a

large (and possibly illiquid) financial position.

Option market data can possibly overcome the afore-

mentioned problems. First, compared with historical

returns, option market data have a superior informative

power, especially as concerns the modelling of the under-

lying asset volatility.3Second, the implied moments of

option market data reflect investors' expectations, thus

being a naturally forward-looking indicator of agents'

beliefs. Third, at each observation date, option market

data have a matrix structure, the so-called option cross

section, which reflects the investors' future beliefs across

different strikes and times to maturity. Both dimensions,

strike prices and times to maturity, are important in risk

management. Through the different strike prices, it is pos-

sible to infer the desired future P&L distribution, without

the need of additional historical data. Through the dif-

ferent times to maturity, it is possible to naturally extract

option-implied risk forecasts with a time horizon equal to

the time to maturity of the options. All these properties

make the daily option cross section an interesting input to

use to infer the future P&L distribution.

Surprisingly, despite the increasing attention of aca-

demics and practitioners on the predictive content of

derivative securities, the use of option market data in risk

management is still widely unexplored. To the best of

our knowledge, only Äit-Sahalia and Lo (2000), Bali et al.

(2011), Samit (2012), Mitra (2015), Huggenberger et al.

(2018), and reference therein relate the topic.4

After presenting the option-implied methodology devel-

oped by Barone-Adesi (2016), this paper proposes an

extensive empirical analysis on the performances of the

option-implied risk measures and compares them with

the statistically based ones. Several backtesting results

show that the option-implied VaR and CVaRestimates are

accurate in the short (weekly) and long (monthly) term.

On a relative level, the option-implied methodology out-

performs the statistically based VaR and CVaR estimated

with an asymmetric GJR-GARCH model with nonpara-

metric innovations estimated with the filtered historical

simulated (FHS) approach of Barone-Adesi et al. (1999)

(henceforth denoted as GJR-GARCH-FHS). The choice

of the volatility model stems from Engle and Rosenberg

(2002), Barone-Adesi et al. (2008), Brownlees et al. (2011)

and Barone-Adesi et al. (2019) who show that, for the S&P

500, the asymmetric GJR-GARCH model of Glosten et al.

(1993) is the best performer among a big family of differ-

ent discrete volatility models.5The use of FHS innovations

is to better capture the nonparametric features of financial

markets.

Technicalities aside, the main difference between the

two approaches (option implied and statistically based) is

the type of information contained into the input data. Our

results show that inferring the risk measures from option

market data has both theoretical and practical advantages.

Results could be of interest for regulators, central banks,

and single companies. Regulators and central banks can

derive risk estimates of large companies without knowing

the precise composition of their portfolio. Large compa-

nies can compare the option-implied estimates with those

delivered by their internal models.

The remainder of the article is as follows: Section 2

reviews the concepts of VaR and CVaR. Section 3 intro-

duces and derives the option-implied VaR and CVaR,

showing how to link the risk measures presented in the

previous section to the option market data. In this section,

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