detecting abnormal market behavior detecting abnormal market behavior using resampli using ...

50 Pages·2003·0.98 MB·English

Working Paper 03-13 Departamento de Economía de la Empresa
Business Economics Series 03 Universidad Carlos III de Madrid
March 2003 Calle Madrid, 126
28903, Getafe (Spain)
Fax [phone]

DDEETTEECCTTIINNGG AABBNNOORRMMAALL MMAARRKKEETT BBEEHHAAVVIIOORR
UUSSIINNGG RREESSAAMMPPLLIINNGG TTEECCHHNNIIQQUUEESS

Lucía Cuadro-Sáez(cid:244), J. Ignacio Peña‡ and Juan J. Romo‡

AAbbssttrraacctt

This article improves the assessment of market sentiment through risk neutral implicit density
functions estimates. The main finding is an indicator of “abnormal market behavior”, which
allows us to measure the degree to which the market is behaving normally and is not expecting
bad news. We test the results on two kind of events in four out of the five main crises in
emerging markets of the last decade: defaults on debt and devaluations or strong depreciations.
We find evidence that, in many cases, this new indicator could have anticipated the main
critical episodes of the crises shortly ahead. We use confidence intervals based on bootstrap
percentiles for the skewness and kurtosis of the implicit risk neutral density functions to detect
whether the market behaves normally or shows excessive risk aversion.

Keywords: Market sentiment, risk aversion, implicit risk neutral density function, bootstrap,
skewness and kurtosis.

JEL Codes: G14, G15, F34.

(cid:244) Banco de España and Universidad Carlos III de Madrid.
‡ Universidad Carlos III de Madrid.

We gratefully acknowledge Miguel de Las Casas for his help and suggestions. Also we thank Jose Maria Cuadro for interesting
discussions at early stages of preparing this paper; and Jose Manuel Campa, Daniel Navia and Alicia García-Herrero for useful
comments. All remaining errors are our own. The ideas expressed in the paper represent the personal opinion of the authors,
which do not necessarily coincide with those of Banco de España. Corresponding address: [email protected]
Abstract
This article improves the assessment of market sentiment through risk
neutralimplicit density functions estimates. The main …nding is anindica-
tor of “abnormal market behavior”, whichallows us to measure the degree
to which the market is behaving normally and is not expecting bad news.
Wetesttheresults ontwokindofeventsinfourout ofthe…vemaincrisesin
emerging markets of the last decade: defaults on debt and devaluations or
strong depreciations. We …nd evidence that, in many cases, this new indi-
cator couldhave anticipated the maincritical episodes of the crises shortly
ahead. We use con…dence intervals based on bootstrap percentiles for the
skewness andkurtosisof theimplicit riskneutraldensityfunctions todetect
whether the market behaves normally or shows excessive risk aversion.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Data and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.1 Implicit risk neutral density functions . . . . . . . . . . . . 12
3.2.2 The bootstrap method . . . . . . . . . . . . . . . . . . . . 19
4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
References . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 29
1. Introduction
Financial markets have experimented a deep transformation throughout the last
two decades. Financial development and new technologies allow for more trans-
parencyon tradingoperations, lowercostsandan greaterinformation availability.
Thereisnodoubtaboutthegrowingin‡uencethestockmarketexertson …nancial
3
development, not just in terms of size but also in terms of e¢ciency. Neverthe-
less, one should be aware of the drawbacks associated to this development since,
we have witnessed severe crashes on the stock markets during this period. Fi-
nancial market drops sometimes lead to market crashes or …nancial crises, which
may be dependent on market sentiment. “Self-ful…lling expectations” are critical
determinants of market crashes, specially when the country is dependent on for-
eign investment and therefore, vulnerable to external shocks1. This is the case of
emerging market economies, which have su¤ered more dramatically the impact
of …nancial crises, either due to problems within the country or caused by conta-
gion among countries. This paper contributes to the literature by examining the
role of expectations during crises events using an indicator of imminent negative
event. This new methodology aimed at predicting “abnormal market behavior”
lays on the implicit risk neutral density function (PDF), as a measure of market
expectations, on the skewness and kurtosis of the PDF, as indicators of the risk
aversion. Ourmain contribution, consistson theidenti…cation of therisk aversion
limits within “normal market behavior”. The idea is to determine the risk aver-
sion limit, at a given con…dence level, over which themarket behavesabnormally.
Therefore, we can detect the abnormality by examining thoseobservations out of
the con…dence intervals.
We test this new approach in four crises su¤ered by non industrial countries
1See García-Herrero (2001).
4
duringthenineties2: the Asian in 1997, theRussian in 1998, theBrazilian in 1999
and theArgentinean crisis in 2001. Theresults show that our indicator is able to
foresee “abnormal market behavior”.
The rest of the article is organized as follows: the next section presents a
literaturereviewon implicitrisk neutraldensityfunctions, thethird onedescribes
the data and the methodology used, the fourth section presents the results and
the last one concludes.
2. Literature Review
After the 1987 stock market Crash, the Black and Scholes model presents a de-
viation on the volatility curve, named as volatility smile. When comparing the
moneyness degreewith theimplicitvolatility, the function presentsasmile-shape,
pro…le indicating an excessive volatility of the very in the money options and of
the very out of the money options, with lower volatility for the at the money
options. The deviation from the constant volatility assumed by the Black and
Scholes model becomes signi…cant after the crash, and re‡ects a di¤erent pricing
rule: the market behavior seems to be risk averse3.
Another way of measuringthe same fact is to look at the implicit risk neutral
2See García-Herrero, A. (2001)
3Peña, Rubio and Serna (1999) …nd that time to expiration is a main determinant of the
volatility smile. Thisisconsistentwiththe ideathatthe implicitdistributionfunctionmay vary
with the time to expiration.
5
probability function,which alsopresents adeviation thatisinterpreted astherisk
averse behavior of the market. After the 1987 Crash, the implicit risk neutral
distributions became leptokurtic and left skewed4. This excessive skewness and
kurtosis are re‡ecting the risk averse behavior, provided that the left skewness
(for the call options) and the higher kurtosis are indicators of the probability
assigned to a market drop. The point is that before the Crash, the market did
not take intoaccountthepossibilityof acrash. However, ithappened,themarket
learned, includingthisknowledgeintheoption valuation weobservethereafter. In
the followingparagraphs we review the literature on implicit risk neutral density
functions.
The seminal paper on the implicit density functions is Breeden and Litzen-
berger(1978) wheretheystudytherelation between thepriceof an European call
option and the probability of gain when executing the contract. In other words,
they look for the relationship of the call option price and the probability of the
strike being lower than the price of the underlying asset at the expiration date.
This literature on implicit risk neutral probability functions can be classi…ed
intotworesearch trendsdependingon theparametricornon-parametricapproach.
The parametric vs. non-parametric distinction adopted in this paper is similar to
that presented in previous studies5. A parametric approach assumes that the
4See Jackwerth and Rubinstein (1996)
5 Ibid
6
distribution function of the PDF is well known and that its coe¢cients need to
be estimated. The non-parametric approach, does not assume any distribution
function, therefore it allows for the estimation of any probability function. There
is no consensus in the literature on the best method to be applied. Furthermore,
it seems that there is a proper method for each empirical study.
Withinthenon-parametricliterature,Rubinstein(1994)developsan optimiza-
tion criterion toextract the PDFs fromoptions prices. HeobtainsthePDFsfrom
a binomial tree, composed by the strikes of the options and their probability of
gain. In the same line, Jackwerth and Rubinstein (1996) base their investiga-
tion on the paper by Rubinstein (1994) and develop an alternative optimization
criterion that is tested it in the American S&P500 options market. They prove
that the PDFs look like a lognormal in the period prior to the Crash of 1987
and that it becomes leptokurtic, left skewed and sometimes multimodal, after it.
Finally, Manzano and Sanchez (1998) apply the results of Breeden and Litzen-
berger(1978)toderivetheimplicitriskneutralprobabilityfunctionof theSpanish
option market on interest rates.
By contrast, the other research trend applies parametricmethods to compute
the PDFs. This literature is represented by Melick and Thomas (1997) who
assumea mixtureof threelognormal distributions for the PDFs of oil prices, and
by Malz(1994), who obtains the probability of realignment of the exchange rates
during the European Monetary Crisis by assuming the lognormal shape for the
7
PDFs and a jump di¤usion process for the option prices. Bahra(1997) compares
some distributions proposed in the existing literature and selects the mixture of
two lognormal distributions to characterize the PDFs. Finally, Söderlind and
Svensson (1996)selecta mixture of n lognormal distributionsfor the shapeof the
PDFs.
This paper adopts a non-parametric approach, by computing the PDFs as
Jackwerth and Rubinstein (1996) propose. We go one step further transforming
the put options prices call option prices using the put-call parity. This transfor-
mation permits the observation of a wider range of moneyness given the limited
liquidity of the Spanish out of the money option market. Therefore, the range of
moneyness for which we compute the PDFs is wider than that we could obtain
by simply using the call options or the put options data.
3. Data and Methodology
3.1. Data
The empirical research presented in this paper is based on the data provided by
Mercado Español de Futuros Financieros de Renta Variable (MEFF RV) for the
European type options and futures on IBEX35 index, and by Mercado Continuo
de Bolsa de Madrid for the underlying index, IBEX 35. The database includes
daily closing prices from December 9th, 1996, to October 7th, 2002.
8
The PDFs are calculated using both call and put options so we can complete
the database including all the information available on option prices. No dis-
tinction is made on the type of option, since both put and call prices provide
information on the risk aversion considered by the market. Put option prices are
transformed into call option prices using the put-call parity:
c = p+S X(1+r) t
t ¡
¡
Where c isthe call option price, p is the put option price, S is the asset value
t
at t and X(1 +r) t is the actual value of the strike price.
¡
Weexcludeall thoseoptionspresentingnull volatilityortheirpricebeingequal
to zero or not satisfying the put-call parity.
3.2. Methodology
Theobjectiveofthepaperistheassessment of themarket feelingon theextremes.
Weidentify the point up towhich the market can be considered as behavingnor-
mally in terms of risk aversion. The graphs in Appendix 1 show the di¤erent
shapes of the PDF depending on the market sentiment that we catalog as “nor-
mal”,“rare” and “abnormal market behavior”. Theclassi…cation re‡ects thelevel
of excess risk aversion detected by our indicator: “normal” days do not present
any excess risk aversion, “rare” days do not have enough information to con…rm
the excess risk aversion, although we think that these are non- normal days; and
9
…nally an “abnormal market behavior” day, in which we can ensure at a 90%
con…dence level that there exist an excess of risk aversion in the market.
ThePDFis ameasureof market sentiment. This…eld hasbeen largely studied
and we use the approach of Jackwerth and Rubinstein (1996) to compute the
distributions. This is a non-parametric method in the sense that the resulting
PDF may adopt any shape, either lognormal or any other distribution function.
Oncewehave the assessed marketfeeling, weevaluateriskaversion by looking
to the deviation from the risk neutral assumption. Under a risk neutral behavior
the PDFs should not present any excess of skewness or kurtosis. The excess of
(left)skewnessobservedin thePDFsof the(call)optionpricesisinterpretedasthe
market’s consideration of the possibility of a large drop in the future (the option
expiration date). In other words, the greater drop considered by the market, the
higher left skewness, other things left equal. The excess kurtosis indicates the
probability mass assigned to the drop. This means not only that the market
considers the possibility of a drop, but that it may become extremely worrying
when the market assigns a high probability to a large size drop. “Self-ful…lling
expectations” constitute a key factor in determining whether a large drop in the
market may become a crisis.
At any point in time, we can have the skewness and kurtosis of the PDF,
but we need a benchmark to determine whether the observation responds to an
abnormal behavior or not. Indeed, we should have many PDFs on the same day
10