MANAGING POSITIONS PRE- AND POST-TRADE For educational purposes only. For professional and institutional clients only
Introduction GABRIEL MANCEAU Barclays, Volatility Trader ANTOINE DELGA Bloomberg, Equity Derivatives Application Specialist 2 3
Managing Positions Pre- and Post-Trade The Greeks Pre-Trade Post Trade Option Valuation & Risk Measures Vega Liquidity Volatility Trading Map Volatility Analysis and Trade Decisions Rich VS Cheap Volatility Volatility Trading Map Trading risks and challenges Convexity Trading Are Underlyings really lognormal?tail Risk Source: Barclays, Bloomberg You should not rely on historical or hypothetical historical information. Such historical and hypothetical historical information is not indicative of future performance 3
Option Valuation & Risk: Measures the Greeks Greeks Definition Vega Liquidity Delta and Realized Volatility
Introduction : What is Implied volatility? Strike Forward Maturity Implied vol Log Normal Diffusion Black and Scholes Option price Volatility surface for a given underlying by translating all options prices for all strikes and maturities Explain the price of options can calculate sensitivities to model inputs: no Model No Greeks! Simplify options prices to one variable common language for comparing any option price Exotics products: options prices Model taking inputs, trades specific portfolio price Any input variable can lead to a Greek 5
Greeks Direct Greeks Spot: Delta Gamma Volatility: Vega Time: Theta Change in price in for 1% move in spot -> P&L = spot return in % * delta Change in delta for 1% move in spot -> P&L = 50 * gamma * (spot return in % )^2 Rates (rho), repos (repo rho), dividends (dividend risk): forward determination Change in price in for 1 point change in implied vol (additive) -> P&L = vega * vol move Change in price in for 1 day move forward. Break-even ^2 = theta / (50 * gamma) Cross Greeks Vanna Absolute change in delta in for a 1 point additive move on the vol -> the skew greek Model Greeks From model inputs (exotics): model parameters sensitivities 6
Options Risk Measures the Greeks OVME <GO> Greeks profile for a call on euro stoxx : SX5E Dec 13 C2900 Index We can observe the profile of each greek of this call for a price variation at different dates:
How to trade vega? Example of a volatility strategy MARS <GO> Buying 4500 Straddle 2900 Sept 14 ` Our portfolio is worth 19.5 M and we have 5.17% in vega, equivalent to EUR 1 Million The Impact of a Volatility change as of now is linear 8
How to trade vega? Example of a volatility strategy MARS<GO> Buying 4500 Straddle 2900 Sept 14 ` The Impact of a Volatility change as is still linear but the drift weakens as time goes by 9
Greeks risk management for Volatility Portfolios Spot ladder on Greeks On a portfolio with various volatility strategies and assets Spot Greeks Shift P&L Change Delta Gamma Vega Rho Theta -20.00% (16,993,217) 51,735,140 8,220,296 1,363,975 (43,394) (143,455) -10.00% (6,634,572) 99,412,791 (4,436,269) 840,225 (22,293) (64,047) -8.00% (4,559,178) 88,357,043 (7,301,477) 626,217 (18,617) (49,533) -6.00% (2,824,505) 72,330,260 (8,879,257) 397,743 (15,175) (42,842) -4.00% (1,487,144) 54,627,604 (8,937,058) 174,869 (11,956) (41,856) -2.00% (540,331) 37,043,078 (9,475,732) (50,208) (8,938) (41,882) -1.00% (213,307) 27,058,775 (11,171,663) (164,252) (7,502) (34,281) 0.00% - 14,927,662 (13,670,430) (280,638) (6,113) (23,666) -1.00% (213,307) 27,058,775 (11,171,663) (164,252) (7,502) (34,281) 0.00% - 14,927,662 (13,670,430) (280,638) (6,113) (23,666) 1.00% 75,999 (125,065) (16,566,740) (394,063) (4,769) (10,243) 2.00% (11,276) (18,026,021) (19,056,298) (496,058) (3,462) 1,341 4.00% (724,290) (54,589,272) (16,342,166) (634,769) (898) 1,874 6.00% (1,998,915) (74,935,960) (2,642,287) (665,131) 1,733 (24,620) 4.00% (724,290) (54,589,272) (16,342,166) (634,769) (898) 1,874 6.00% (1,998,915) (74,935,960) (2,642,287) (665,131) 1,733 (24,620) 8.00% (3,365,551) (66,104,799) 13,790,487 (612,421) 4,562 (67,496) 10.00% (4,284,055) (29,904,304) 26,914,564 (517,109) 7,658 (98,198) 15.00% (1,987,823) 161,786,414 64,092,775 (23,615) 16,811 (166,326) 10
Greeks risk management for portfolios A more advanced Vega risk management Maturity TOTAL Strike Strike% July August September December March All Maturity 0 0.0% 4-28 346-204 552 669 143 5.0% -25 163-1,958 1,096-2,880-3,604 285 10.0% 41-257 3,042-1,686 4,128 5,267 713 25.0% -87 480-5,958-488 -27,121-33,174 1140 40.0% 486-1,709 14,739 1,104 9,724 24,343 1425 50.0% -965 10,680-78,125 46,225-12,843-35,028 1995 70.0% 521-31,621 30,812 153,319 41,128 194,160 2280 79.9% 8,321-76,021-30,169 101,920 14,353 18,403 2565 89.9% 13,711-328,278 523,492 243,061 76,810 528,797 2708 94.9% 28,491-213,970 151,962 53,749 12,475 32,708 2779 97.4% 26,149-116,902-113,579 10,276-16,000-210,055 2850 99.9% 87,993-5,323-69,799 38,532 1,356 52,759 2921 102.4% -29,748-117,137-405,265 2,652-12,977-562,475 2993 104.9% 5,055 97,600-322,165-23,136-45,489-288,135 3135 109.9% 5,587-34,307-40,942 49,303-12,590-32,949 3420 119.9% -354 5,983-10,848 30,307 6,993 32,081 3705 129.9% 105-1,119 5,123 9,687 4,479 18,275 3990 139.9% -30 306-1,507-1,851-1,147-4,228 4275 149.9% 8-79 385 432-156 590 4560 159.9% -2 15-74 -82-37 -180 5700 199.9% 0-0 2 2 0 4 11400 399.7% -0 0-0 -0-0 -0 42750 1498.9% 0-0 0 0 0 0 Total 145,261-811,523-350,487 714,219 40,758-261,771 WeightedTotal 506,682-2,214,875-763,084 1,052,746 48,385-1,370,147 11
Vega Liquidity in the world Avg daily Vega traded in M America EMEA Asia SPX/VIX > 150M 50M 10M APPL, Russel, Nasdaq, SX5E/V2X FTSE, DAX 5M Facebook, Google, EEM, PCLN,TSLA NKY 1M NFLX, MSFT,AMZN, C, LNKD, EFA, XLF, JPM FSTMIB, SMI, CAC, SX7E, AEX, TOP40 TPX, KOSPI, AXJO, HSCE, HSI 500k 12
SPX/VIX liquity 13
Delta and Realised Volatility options naked-delta and options delta-hedged is a completely different trading delta hedged trading: price based on the implied volatility (market sentiment), PL on the realised volatility: Realised volatility (RV) = a measure of the past fluctuations of the spot GV <GO> Realised volatility is linked to the Black Scholes theory: it is the best-guess for the volatility that should have been used in the option pricing formula. 3 Month realised vol for SPX, SX5E, FTSE, NKY 14
Pre-Trade : Volatility Analysis and Trading Decisions Rich VS Cheap Volatility Volatility Trading Map
Determining Rich vs Cheap implied volatility 1. Use a data analysis tool to calculate the realised volatility for multiple time periods 2. Compare realized volatility to the current implied volatility in the options 3. Repeat this procedure for similar underlying assets, then compare spreads of implied volatility to realized volatility 4. Consider any asset-specific catalysts (earnings, pending announcements or macroeconomic factors) that may justify the presence of a particular spread 16
Pre-Trade: Rich vs. Cheap Analysis Volatility Analysis VCA <GO> Comparing the implied with realized volatility for the main global indices Volatility is quite expensive around the globe 17
Pre-Trade: Rich vs. Cheap Analysis Volatility Analysis GV <GO> On the Euro Stoxx ATM 3 month VS 3month histo, a recent turn to rich after some hieratic cycles 18
Pre-Trade : finding the good entry point Historical evolution of the SX5E 1 year historical volatility GV <GO> Looking at the realized volatility over the last year. we are at the minimum! 19
Pre-Trade : finding the good entry point Historical evolution of the sx5e atm 1 year implied volatility GV <GO> Looking at the volatility over the last year. we are within the 9th percentile of the lowest volatility. This is a very low entry point 20
Pre-Trade : finding the good entry point Historical evolution of the 1 year volatility richness GV <GO> then we are now in a rich volatility regime 21
Pre-Trade : finding the good entry point Historical evolution of the 1 year volatility richness GV <GO> then we are now in a rich volatility regime 22
Pre-Trade : finding the good entry point SHOC <GO> Using historical analysis to determine best and worst entry for a long volatility trade: SX5E Straddle Looking at the best entry point study, we can see that the current vol is 18.88 The lowest implied volatility was at 17.86 (-1.02 compared to now) The average implied volatility was at 20.24 (+1.36 compared to now) The highest implied volatility was at 23.50 (+4.68 compared to now) Creating the relevant shocs 23
Pre-Trade : finding the good entry point Using historical analysis to determine best and worst cases MARS <GO> We can see how expensive or cheap becomes the Straddle according to the different Implied Volatility levels 24
Pre-Trade : Comparing Historical Volatility for Similar Underlying Assets Comparing Realized and Implied vol for the SX5e SPX spread GV <GO> 25
Case Study: Spread VSTOXX - VIX Analysing the Spread The spread has been very rarely negative 26
Case Study: Spread VSTOXX - VIX Looking at the term structure this days The Term Structure is pretty much constant around 3 27
Case Study: Spread VSTOXX - VIX Analysing the Spread However in the past like in end of 2011, there was better spreads opportunity Like a back-end future spread around 2.5 28
Pre-Trade : Comparing Historical Volatility for Similar Underlying Assets Analyzing richness of SX7E GV <GO> From a 13 low to highs spiking at 80: A clear Vol regime change on the EUR Banks Index 29
Pre-Trade : Impact of an Event on Volatility Historical evolution of the sx7e atm 1 year implied volatility GV <GO> Focusing on the Euro Stoxx EUR Bank index (SX7E Index), we observe a huge turn on volatility richness due to the concern on banks solvency raise in the context of the European Sovereign Crisis 30
Case Study: Variance Swap What is a Variance Swap? Payout = Vega traded 2 Strike (Realized Volatility 2 K 2 )) quadratic payout (K is the fair volatility) Constant gamma over life-time of the trade Theoretically replicable by a strip of options Delta resets everyday More expensive than straddle price for downside protection position: long 1M vega sep14 SX5E @ 22 31
Case Study: Variance Swap Example of a SX7E Var Swap OVME <GO> Buying a 12/30/11 SX7E Var Swap on 01/01/11: Locking a 35.30 Volatility on June,2 32
Case Study: Variance Swap Example of a SX7E Var Swap OVME <GO> Buying a 09/10/13 SX7E Var Swap on 06/02/13: We can see the money earned between end of August and November 33
Pre-Trade : Vol of Vol Trading Volatility Assets Comparative Forward variance: pays the square of realised volatility between 2 dates in the future Fair strike depends on the expectation of the future realised volatility No exposure to realised volatility until first date reach P&L only depend on implied vol until first date is reach Quadratic vega exposure (vega doubles when vol doubles) Vix / V2X future: Vix/V2X futures expires on the fair strike of a 30 days variance swap P&L linear in volatility Vega exposure constant cheaper than forward variance Both Implied volatility exposure, no gamma, but roll down/up theta Both No daily delta-hedge On Vix/V2x future expiry: VIX index = Future expiring = Fair strike of 30 day variance 34
Pre-Trade : Vol of Vol Trading Case Study: Forward Var / volatility futures Short 1M vega V2X nov13 future @ 19.8, Long Nov/Dec forward var @20.4 -> flat risk? 80,000,000 70,000,000 60,000,000 50,000,000 40,000,000 30,000,000 20,000,000 V2X Future Fwd Var Strategy p&l 10,000,000 - -10,000,000-10 20 30 40 50 60-20,000,000 Max down P&L: 600 000 at 20.4 expiry level Breakeven: under 15.5 and over 25.5 Example of P&L for a 40 Vol: 8.8 M V2X Expiry Level 35
Pre-Trade: Skew Trading Skew Historical Analysis Looking at the 1 month skew GV <GO> 36
Case Study : Risk Reversal Trading spot/vol dynamic OVME <GO> Based on negative correlation between spot and implied volatility Long Put Short Call dynamically delta hedged 5K dec13 2500/3200 rr, ref future = 2880 120M notional, 110K gamma, 22k vega, 16% delta -2.8M vanna but -5K theta Scenario Vol Up 1%, Spot Down 1% : New Delta -2.8 M Buy 2.8 M Delta Market back to flat: P&L = 23K on the day 37
Trading Risk : Skew Trade Looking at the skew differently : Sorting returns by Vol and Spot Trend How did this trade work in the last 2 years 2% 1% 1mth fixed strike vol move 2012 2.0% 1.5% 1mth fixed strike vol move 201 0% -1% spot move 1.0% 0.5% 0.0% spot move -2% -0.5% -3% -1.0% -4% -4% -3% -2% -1% 0% 1% 2% 3% 4% -1.5% -3% -2% -1% 0% 1% 2% 3% In 2012 In 2013 spot move vol move 2012 2013 + - 62% 67% - + 54% 65% 38
Post-Trade:Trading risks and challenges Pin risk Convexity Trading Tail Risk Exposure Are Underlyings really lognormal?
Summary of Volatility Assets exposure Property Options Variance Swaps Forward Variance Swaps VIX Futures Need to Delta-Hedge Gamma Exposure Theta Exposure Exposure to Realised Volatility Exposure to Implied Volatility Exposure to Interest Rates / Dividends Listed/OTC Listed OTC / Listed OTC / Listed Listed Convexity OTM / ATM Source: Barclays. You should not rely on historical or hypothetical historical information. Such historical and hypothetical historical information is not indicative of future performance 40
Theory limit with continuous : Pin Risk Short an option expiring in 15 days with implied volatility around 18, delta hedged Spot Deviation to the Strike (in %) Spot Deviation to the Strike (in %) 4 4 3 3 2 2 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-1 -1-2 Two equivalents spot realisation: One has a 4% move at the beginning of the period, the other at the end: Which one do you prefer?... -2 Applying this reasoning to a 9000 SX5E 2900 Sept 14 Long Call, one day before expiry, 1% below the strike with a vol around 18 and 12% Delta 41 Option Out of The Money still holding 150K premium to lose Max loss 460K if spot expires at 2900, break-even [-0.5%,+1.2%]
Convexity Trading Selling volatility performed well since 2008. Barclays short 1Month SPX variance swap systematic strategy 42
-10.0% -9.0% -8.0% -7.0% -6.0% -5.0% -4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% 11.0% 12.0% Convexity Trading S&P 20 years daily return probability comparison Historical distribution versus distribution implied by options prices and implied vol model 45.00% Probability 40.00% 35.00% 30.00% 25.00% 20.00% Historical Proba Predicted proba 15.00% 10.00% 5.00% 0.00% Daily return 43
Convexity Trading 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 Ratio Ratio 500.00 450.00 400.00 350.00 300.00 250.00 200.00 150.00 Ratio Ratio 2.00 100.00 1.00 - -7.0% -2.0% 3.0% 50.00 - -7.0% -2.0% 3.0% Tail risks are underestimated more than billion time 9,000,000,000,000.00 Ratio 7,000,000,000,000.00 5,000,000,000,000.00 3,000,000,000,000.00 Ratio 1,000,000,000,000.00-15.0% -10.0% (1,000,000,000,000.00) -5.0% 0.0% 5.0% 10.0% 15.0% 44
Post-trade : Tail Risk with Naked Put Let s remind us the profile of a Naked Short Put For a sole variation of the spot, shorting 40k dec 1900 Put gives us a EUR 400k gain. On the other side of the coin, we have an infinite potential loss, for example, a downside shift of -40% on the Euro Stoxx would cost us almost 60 m Sizeable losses when stress testing the strategy for the worst market conditions in recent years 45
Post-trade : Tail Risk with Short Call Strategy: sell 10M notional Nokia 1M atm call at 40% vol, 50% delta, 10K vega, 400K premium Expected P&L, 1.2M a year Stock up 50% 03/09 opening auction 2.5M loss Nokia realized volatility before the spike : 46
Theory Limit and trading behaviors How log normal an underlying is? beware of the underlying you are selling/buying Spot jumps while theory assumes continuous diffusion Beware of break-even thinking: portfolio with 5K theta, 1M gamma break-even = 5K 1M 50 = 1% (equivalent to 16% volatility) day1: +1%, day2: -1%, day3 :+1%, day4 :+1%, day5: -1% : 1% avg move, 16% realised volatility day1: 0%, day 2 : 0%, day3 : 0%, day4 : 0%, day5 :+5% : 1% avg move, 35% realised volatility Convexity rule: realised volatility >= volatility calculated from the average of the move Selling tail risk: high probability of a positive P&L, what about the expectation? Trader s dilemma: 2 losing strategies. Which one you may finally follow? Strategy 1: +15K 4 days / 5, -80K 1 day / 5-> P&L expectation: -1M a year Strategy 2: +10M 9 years /10, -100M 1 year /10 -> P&L expectation: -1M a year 47
Thanks for your attention! Any questions? GABRIEL MANCEAU Barclays, Volatility Trader ANTOINE DELGA Bloomberg, Equity Derivatives Application Specialist
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