Special Techniques for Special Events

Transcription

1 Special Techniques for Special Events Bruno Dupire Head of Quantitative Research Bloomberg L.P. CFMAR UCSB Santa Barbara, May 20, 2017

2 The Problem Many market situations (earnings, pegged currencies, FDA approvals, acquisitions, elections, Brexit ) deviate from the usual regimes. How can the classical tools from derivatives space can be adapted to these extreme situations?

3 Outline I. Tools II. III. IV. Earnings Pegged Currencies Brexit V. US Elections

4 I. Tools

5 From market data to risk neutral densities

6 Option Market Data

7 FX Options Market Data (Risk Reversal and Butterfly in Deltas) Risk Reversal (RR) = Call -Put Butterfly (BF) = (Call + Put)/2 - ATM

8 FX Options Market Data (Call and Put in Deltas) Call = ATM + BF + RR/2 Put = ATM + BF - RR/2

9 Convert Delta To Strike

10 Implied Skew Delta Strike

11 Risk Neutral Density Φ K = 1 2 C(K) DF K 2

12 Implied Percentiles

13 From densities to skews

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16 FDA Approval Implied skew and risk neutral density of Sarepta Therapeutics Inc on 5/4/2016 Pending FDA approval Option Implied Prob of approval = 27% 16

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19 From variance to forward variance Apple Inc Earning Call 10/27/2015 5pm VS T i+1 2 T i+1 VS T i 2 T i T i+1 T i 19

20 II. Earnings

21 Earnings and Historical Volatility IBM often has more uncertainty on the day of an Earnings Announcement than the rest of the quarter

22 Earnings and Implied Volatility IBM 1M ATM Implied Volatility from Jan 2013 to May 2015 Implied Volatility exhibits significant drop on Earnings Dates

23 Earnings and Historical Volatility S&P 500: Percentage of Variance on Earnings Dates. Jan 13 May 15 Up to 48% of Variance is accounted for by just 10 of 600 days.

24 Earnings and Historical Volatility Sectors like Consumer Discretionary, Consumer Staples and Industrials have more Variance on Earnings Dates than Financials

25 Earnings and Historical Volatility More than 50% of stocks in the S&P 500 have more than 3 times the average variance on Earnings Dates

26 VS term structure 26

27 VS as a function of the as of date for 3 fixed maturities 27

28 Two ways to trade the realized variance Forward Variance: one as of date t, two maturities T1 and T2 t T1 Te T2 Drop in implied variance: one maturity T, two as of dates t1 and t2 t1 Te t2 T 28

29 3 related quantities A: Forward Variance for as of dates before earning day B: Realized Variance on the earning day C: Drop in variance on earning day for further maturities 29

30 EARNINGS 30

31 III. Pegged currencies

32 A brief history of pegged currencies

33 On 16 September 1992, Black Wednesday, the British pound was forced out of the European Exchange Rate Mechanism which had required the maintenance of a floor of on the GBPDEM exchange rate

34 In the Peso crisis of December 1994, an attempt to devalue the rate at which the Mexican peso was pegged to the US dollar triggered large-scale capital flight which quickly forced a floatation

35 The Hong Kong dollar has been pegged to the US dollar since 1983

36 The Argentine currency board which had pegged the peso to the US dollar at a 1-to-1 exchange rate was abandoned in December 2001 with the imposition of capital controls, discrete devaluations and the forced pesification of dollar deposits, ultimately ending with a float

37 Venezuelian Bolivar VEBUSD Spot Exchange rate Price of 100 VEB in USD 37

38 In September 2011, the Swiss National Bank imposed a floor of 1.2 on the EURCHF exchange rate to prevent excessive strengthening of the Swiss franc which was seen as a safe haven currency during the eurozone crisis. This peg was terminated on 15 January 2015

39 Possible trades

40 EURCHF Floor Break

41 Option prices on the eve of the termination of the EURCHF floor reflected attractive short-term profit opportunities if one believed that there was some possibility that the peg would be terminated within a month and that the EURCHF spot rate would gap down with a large jump in such an event

42 The opportunity was much better on the eve of de-pegging than it had been in mid-2012 when the peg had been tested by the market

43 IV. Brexit

44 Excess Forward Variance Good indicator of the market expectation on the uncertainties caused by Brexit 44

45 Currency option markets The currency option markets have seen dramatic changes in the past few months due to the UK s EU referendum As a complement to what the polls say, we can listen to the currency option market to understand what market participants are thinking. 45

46 Risk neutral density Risk neutral probabilities are probabilities of future values of the underlying asset in the risk-neutral measure Risk neutral probabilities can be extracted from the market prices of options 46

47 Extrapolation Plain vanilla options are usually quoted for standard tenors, 1W, 2W, 1M, Extrapolate from nearby market expiries to the referendum date 47

48 Pre and post referendum Dramatic change of implied skew before and after the referendum As of May 18, 2016, what was expected to happen on June 23, 2016? 48

49 Binary outcome Brexit EURGBP expected to increase More volatile Binary Outcome Bremain EURGBP expected to drop Less volatile 49

50 Calibration The parameters of the bimodal Gaussian distribution are calibrated to be consistent with the market observations of pre- and post-referendum densities The probabilities of Brexit/Bremain, the expected changes of the exchange rates upon Brexit/Bremain are derived in a consistent manner + = 50

51 What does + mean At time T, S T jumps to S T + = JS T, where the jump size J follows a distribution with density function φ J. J is assumed to be independent from the spot process S t or Call K, T + = Call K x, T xφ J x dx φ log ST φ log J = φ log ST + Discontinuous implied volatility surface, σ K, T σ K, T + 51

52 Simulated paths As of May 11, 2016, Probability of Brexit = 20.2%, Expected Move of USDGBP in case of Brexit = 8.42% Solid line: Brexit Dashed line: Bremain The exchange rate USDGBP follows local volatility dynamics calibrated to the market, except at June 23, 2016, the rate will experience a jump. The jump distribution follows bimodal Gaussian model 52

53 Brexit impact on other currencies Expected moves of other currencies in case of Brexit can be implied from the respective option markets 53

54 Excess Forward Variance Good indicator of the market expectation on the uncertainties caused by Brexit 54

55 V. US ELECTION

56 US ELECTION 2016 USDMXN Implied Vol Surface as of Oct 13,

57 US ELECTION 2016 Excess forward variance observed in the period containing the election day USDMXN Implied Vol Surface as of Oct 13,

58 US ELECTION 2016 Time series of excess forward variance on the election day and Clinton/Trump spread (RCP Poll Average) 58

59 US ELECTION 2016 As of Date: Oct 13, % chance of Clinton victory v.s. 42% Trump victory 59

60 US ELECTION 2016 As of Date: Oct 13,

61 VI. FRENCH ELECTION

62 French Election 2017 Ticker: CAC Index As of Date: Mar 8,

63 French Election

64 French Election 2017 Ticker: CAC Index As of Date: Mar 8,

65 French Election 2017 Risk-neutral densities immediately before and after the election (from interpolation) 65

66 French Election

67 French Election

68 Cac index

69 Cac index Bimodal Gaussian 69

70 Eurusd

71 Eurusd Bimodal Gaussian 71

72 Conclusion Option data gives the risk neutral densities and forward variance Many market situations deviate from the usual regimes Requires adjusting of classical methods Conditional behavior read from the market can be monetized

73 Thank You