Measuring Market Fear

Transcription

1 Measuring Market Fear Wim Schoutens London, CASS 20 th of October

2 Joint Work with Jan Dhaene Daniel Linders Monika Forys Julia Dony 2

3 CONTENT Measuring market fear on the basis of option data. Market Fear Components Volatility Liquidity Herd-behavior Counterparty Risk Volatility measuring by VIX Liquidity measuring by implied liquidity & conic finance Herd-behavior measuring by comonotonicity ratios Introducing the market overall fear index 3

4 MARKET FEAR What do people watch at in case of fear? GOLD 4

5 MARKET FEAR What is a good sovereign debt fear indicator? SOVX 5

6 MARKET FEAR A measure of trust between bank : EURIBOR-OIS SPREAD 6

7 MARKET FEAR How much can markets swing around? VIX 7

8 MARKET FEAR VIX, what does it mean? Volatility is the annualized standard deviation of asset Implied volatility: The volatility that makes the output of an option pricing model equal to the market value Historical volatility: Annualized standard deviation of observed asset returns QUESTION : If a stock has a volatility of 16% how much is it likely to move in one day? If the one year return is normally distributed the stock has 68% probability of moving by 16% or less up or down. 16% Over one day the standard deviation will be: Days ina year Use 256 trading days so daily vol. is 1% ; Really 252 trading days in a year, but 256 is a good and easy approximation 8

9 MARKET FEAR COMPONENTS There are a variety of market fear factors. We have market risk and nervousness. The higher the volatility the more market uncertainty there is and the wider swings in the market can occur. We have liquidity risk. The bid and ask spread widens in periods of high uncertainty. We have herd-behavior. In a systemic crisis, all assets move into the same direction. The more comonotone behavior we have the more assets move together and the more systemic risk there is. 9

10 MARKET FEAR COMPONENTS The aim is to measure the market fear factors on the basis of market option data in a single intuitive number. The measure will be more precisely based on vanilla index options and individual stock options. By making use of option data and not of historical data we have a forward looking measure indicating markets expectations for the near future. The classical example of using of option data is the measurement of market volatility by the VIX methodology. We will measure volatility, herd-behavior and liquidity in a similar manner and hence will be able of exactly decomposing the overall market fear into its components. 10

11 VIX The VIX index is often referred to as the fear index or fear gauge. It is a key measure of market expectations of near-term volatility conveyed by SP 500 stock index option prices. Since its introduction in 1993, the VIX has been considered by many to be a good barometer of investor sentiment and market volatility. It is a weighted blend of prices for a range of options on the SP500 index. The formula uses as inputs the current market prices for all out-ofthe-money calls and puts for the front month and second month expirations. The goal is to estimate the implied volatility of the SP500 index over the next 30 days. 11

12 VIX The VIX calculation is very related to the implementation of a Variance Swap (cfr. work by P. Carr, D. Madan, A. Neuberger and others) On March 26, 2004, the first-ever trading in futures on the VIX Index began on CBOE Futures Exchange (CFE). As of February 24, 2006, it became possible to trade VIX options contracts. The VIX methodology has been applied on many other indices. On the January 5, 2011, CBOE announced to also VIX-ify individual stocks like (APPL, IBM, GS, GOOG, ). 12

13 VIX The magic VIX formula is : VIX = σ x 100 T is time to maturity F is forward index level K i are strikes R is interest rate and Q(.) are mid prices 13

14 VIX The formula is applied to the front month (with T > 1 week) and the next month and is finally obtained by inter/extrapolation on the 30 days point: 14

15 MEASURING LIQUIDITY How to measure and quantify in an isolated manner liquidity? Bid-ask spread are a good indication but can be misleading. Example: Which European Call Option is the most liquid? EC1 on Stock1 Maturity = 1y EC2 on Stock2 Maturity = 1y A) EC1 B) EC2 C) Both D) Can t say Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR 15

16 MEASURING LIQUIDITY How to measure and quantify in an isolated manner liquidity? Bid-ask spread are a good indication but can be misleading. Example: Which European Call Option is the most liquid? EC1 on Stock1 Maturity = 1y r=0%; q=0% S1=100 K=100 EC2 on Stock2 Maturity = 1y r=0%; q=0% S2=20 K=10 A) EC1 B) EC2 C) Both D) Can t say Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR 16

17 MEASURING LIQUIDITY How to measure and quantify in an isolated manner liquidity? Bid-ask spread are a good indication but can be misleading. Example: Which European Call Option is the most liquid? EC1 on Stock1 Maturity = 1y r=0%; q=0% S1=100 K=100 Vol=25.13% Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR EC2 on Stock2 Maturity = 1y r=0%; q=0% S2=20 K=10 Vol=1.0% Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR A) EC1 B) EC2 C) Both D) Can t say Probability that Stock2 after one year will trade above 19.0 EUR is (5 sigma event). And hence option will always payout more than 9 EUR. 17

18 MEASURING LIQUIDITY It is very difficult to measure liquidity in an isolate manner. Bid and ask spreads can move around in a non-linear manner if spot, vol, or other market parameters move, without a change in liquidity. The concept of implied liquidity in a unique and fundamental founded way isolates and quantifies the liquidity risk in financial markets. This makes comparison over times, products and asset classes possible. The underlying fundamental theory is based on new concepts of the two-ways price theory of conic finance. These investigations open the door to stochastic liquidity modeling, liquidity derivatives and liquidity trading. 18

19 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6 0,65 0,7 0,75 0,8 0,85 0,9 0,95 1 CONIC FINANCE We will make use of the minmaxvar distortion function: 1,2 1 0,8 0,6 0,4 uniform minmaxvar2 0,2 0 19

20 CONIC FINANCE We use distorted expectation to calculate (bid and ask) prices. The distorted expectation of a random variable with distribution function F(x) is defined 0,25 0,2 0,15 norm 0,1 minmaxvar2 0, ,5-3 -2,5-2 -1,5-1 -0,5 0 0,5 1 1,5 2 2,5 3 3,

21 CONIC FINANCE The ask price of payoff X is determined as 0,3000 0,2500 0,2000 0,1500 0,1000 probabilities distorted probabilities The bid price of payoff X is determined as 0,0500 0, cash flow (sorted) probabilities 0,2000 0,2000 0,2000 0,2000 0,2000 cumulative probabilities 0,2000 0,4000 0,6000 0,8000 1,0000 distorted cum probs 0,2515 0,4661 0,6635 0,8450 1,0000 distorted probabilities 0,2515 0,2146 0,1975 0,1815 0,1550 sorted neg. CF probabilities 0,2000 0,2000 0,2000 0,2000 0,2000 cumulative probabilities 0,2000 0,4000 0,6000 0,8000 1,0000 distorted cum probs 0,2515 0,4661 0,6635 0,8450 1,0000 distorted probabilities 0,2515 0,2146 0,1975 0,1815 0,1550 rn average cash flow 6,00 bid distored avearge CF 5,40 ask negative distorted average neg CF 6,59 mid mid of bid and ask price 5,99 21

22 CONIC FINANCE These formulas are derived by noting that the cash-flow of selling X at its ask price and buying X at its bid price is acceptable in the relevant market. We say that a risk X is acceptable if M is a set of test-measures under which cash-flows need to have positive expectation. Operational cones were defined by Cherney and Madan and depend solely on the distribution function G(x) of X and a distortion function. To have acceptability we need to have that the distorted expectation is positive: 22

23 CONIC FINANCE For a EC (K,T), we have 23

24 IMPLIED LIQUIDITY We will call the parameter, fitting the bid-ask around the mid price, the implied liquidity parameter. Hence for the EC(K,T) with given market bid, b, and ask, a, prices, the implied liquidity parameter is the specific λ >0, such that: Calculation is straightforward: we have a close formula for G(x) and have to find via a simple inversing using the previous graph the corresponding implied liquidity 24

25 MEASURING LIQUIDITY How to measure and quantify in an isolated manner liquidity? Bid-ask spread are a good indication but can be misleading. Example: Which European Call Option is the most liquid? EC1 on Stock1 Maturity = 1y r=0%; q=0% S1=100 K=100 Vol=25.13% Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR λ = 626 bp EC2 on Stock2 Maturity = 1y r=0%; q=0% S2=20 K=10 Vol=1.0% Bid = 9 EUR Mid = 10 EUR Ask = 11 EUR λ = bp A) EC1 B) EC2 C) Both D) Can t say 25

26 3/01/2007 3/02/2007 3/03/2007 3/04/2007 3/05/2007 3/06/2007 3/07/2007 3/08/2007 3/09/2007 3/10/2007 3/11/2007 3/12/2007 3/01/2008 3/02/2008 3/03/2008 3/04/2008 3/05/2008 3/06/2008 3/07/2008 3/08/2008 3/09/2008 3/10/2008 3/11/2008 3/12/2008 3/01/2009 3/02/2009 3/03/2009 3/04/2009 3/05/2009 3/06/2009 3/07/2009 3/08/2009 3/09/2009 3/10/2009 IMPLIED LIQUIDITY EVOLUTION OVER TIME We clearly see that ATM liquidity is non constant over time and exhibits a mean-reverting behavior. The long run average of the implied liquidity of the data set and over the period of the investigation this equals 412 bp. The highest value for the implied liquidity parameter was 1260 bp on the 24th of October Around that day (and the week-end before) several European banks were rescued by government interventions. 0, , , , , , , , LIQ CREDIT CRISES 26

27 HERD BEHAVIOR AND COMONOTONICITY Comonotonicity measures herd behavior. A random vector is comonotonic if where U is a Uniform(0,1) random variable and A comonotonic vector is driven by just one single factor (systemic risk) Given a vector we call the comonotonic counterpart of X the vector 27

28 HERD BEHAVIOR AND COMONOTONICITY Dow Jones, SP500 and any other indices are a weighted basket: We will denote by where is the comonontonic counterpart of The comonotonic version incorporates perfect herd behavior. Intuitively, call options under perfect herd-behavior are more expensive, since each component moves in the same direction. 28

29 HERD BEHAVIOR AND COMONOTONICITY We will derive a bound for call options on the Index in terms of options in individual stocks. Comonotonic theory tells us that where is a specially optimal strike and is the closest lower market traded strike. 29

30 3/01/2007 3/02/2007 3/03/2007 3/04/2007 3/05/2007 3/06/2007 3/07/2007 3/08/2007 3/09/2007 3/10/2007 3/11/2007 3/12/2007 3/01/2008 3/02/2008 3/03/2008 3/04/2008 3/05/2008 3/06/2008 3/07/2008 3/08/2008 3/09/2008 3/10/2008 3/11/2008 3/12/2008 3/01/2009 3/02/2009 3/03/2009 3/04/2009 3/05/2009 3/06/2009 3/07/2009 3/08/2009 3/09/2009 3/10/2009 HERD BEHAVIOR AND COMONOTONICITY It is well know that the cdf of the stocks can be extracted out option info: We hence have an upper bound for each traded vanilla index options in terms of the traded component options. CALL COMONTONIC RATIO : 1, , , , , , , , COM on calls CREDIT CRISES 30

31 3/01/2007 3/02/2007 3/03/2007 3/04/2007 3/05/2007 3/06/2007 3/07/2007 3/08/2007 3/09/2007 3/10/2007 3/11/2007 3/12/2007 3/01/2008 3/02/2008 3/03/2008 3/04/2008 3/05/2008 3/06/2008 3/07/2008 3/08/2008 3/09/2008 3/10/2008 3/11/2008 3/12/2008 3/01/2009 3/02/2009 3/03/2009 3/04/2009 3/05/2009 3/06/2009 3/07/2009 3/08/2009 3/09/2009 3/10/2009 HERD BEHAVIOR AND COMONOTONICITY Replace by Comonotonic upperbound A similar expression exists for put options. We repeat this for each option in the market and come (cfr. VIX) to a VIXified 30 days herd-behavior measure. Note that we have derived now a market implied upperbound for VIX! 100,00 90,00 80,00 70,00 60,00 50,00 40,00 30,00 20,00 10,00 0,00 VIX VIX COM CREDIT CRISIS 31

32 HERD BEHAVIOR AND COMONOTONICITY We call the quantities the comonotonicity ratios. The closer this number is to 1, the closer we are to the comonotonic situation; If the ratio equals 1, we hence have perfect herd behavior. In conclusion, the above gives us a way to compute how much forward looking herd behavior there is on the basis of option surfaces. Furthermore, the gap between fully comonotonic and the current market situation can be monetized via a long-short position in options. 32

33 3/01/2007 3/02/2007 3/03/2007 3/04/2007 3/05/2007 3/06/2007 3/07/2007 3/08/2007 3/09/2007 3/10/2007 3/11/2007 3/12/2007 3/01/2008 3/02/2008 3/03/2008 3/04/2008 3/05/2008 3/06/2008 3/07/2008 3/08/2008 3/09/2008 3/10/2008 3/11/2008 3/12/2008 3/01/2009 3/02/2009 3/03/2009 3/04/2009 3/05/2009 3/06/2009 3/07/2009 3/08/2009 3/09/2009 3/10/2009 HERD BEHAVIOR AND COMONOTONICITY JUNE, 7, 2007 :Bear Stearns informs investors in two of its CDO hedge funds, it was halting redemptions 100,00% 90,00% AUG, 6, 2007 : American Home Mortgage Investment Corporation files Chapter 11 bankruptcy. AUG 7, 2007: Numerous quantitative long/short equity hedge funds suddenly begin experiencing unprecedented losses. AUG 9, 2007: BNP Paribas suspends three investment funds that invested in subprime mortgage debt. AUG, 10, 2007: Central banks coordinate efforts to increase liquidity. VIX RATIO CREDIT CRISES 80,00% 70,00% 60,00% 50,00% 40,00% 30,00% 20,00% 10,00% 0,00% 33

34 3/01/20 3/02/20 3/03/20 3/04/20 3/05/20 3/06/20 3/07/20 3/08/20 3/09/20 3/10/20 3/11/20 3/12/20 3/01/20 3/02/20 3/03/20 3/04/20 3/05/20 3/06/20 3/07/20 3/08/20 3/09/20 3/10/20 3/11/20 3/12/20 3/01/20 3/02/20 3/03/20 3/04/20 3/05/20 3/06/20 3/07/20 3/08/20 3/09/20 3/10/20 THE MARKET FEAR COMPONENTS : THE FEAR INDEX Weighted sum of VIX, LIQ and COMVIX Average level = 100; Level > 100 = Stress ; Level < 100 : no-stress 300 LIQF COMF VIXF

35 9/01/2007 9/02/2007 9/03/2007 9/04/2007 9/05/2007 9/06/2007 9/07/2007 9/08/2007 9/09/2007 9/10/2007 9/11/2007 9/12/2007 9/01/2008 9/02/2008 9/03/2008 9/04/2008 9/05/2008 9/06/2008 9/07/2008 9/08/2008 9/09/2008 9/10/2008 9/11/2008 9/12/2008 9/01/2009 9/02/2009 9/03/2009 9/04/2009 9/05/2009 9/06/2009 9/07/2009 9/08/2009 9/09/2009 9/10/2009 FEAR TRADING Go LONG the market if FEAR INDEX < 90. Go SHORT the market if FEAR INDEX > 140. Be NEUTRAL else INDEX FEAR TRADING FIX

36 CONCLUSION There are a variety of market fear factors. We have market risk and nervousness. The higher the volatility the more market uncertainty there is and the wider swings in the market can occur. We have liquidity risk. The bid and ask spread widens in periods of high uncertainty. We have herd-behavior. In a systemic crises, all assets move into the same direction. The more comonotonic behavior we have the more assets move together and the higher the systemic risk there is. The aim is to measure the market fear factors on the basis of market option data in a single intuitive number. We have presented the market overall fear index. The calculations are solely based on vanilla index options and individual stock options. 36

37 CONCLUSION CONTACT: Wim Schoutens More info on: 37