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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
3
Managing Positions Pre- and 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
The Greeks
Pre-Trade
Post Trade
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
Option Valuation & Risk: Measures – the “Greeks”
Greeks Definition
Vega Liquidity
Delta and Realized Volatility
5
Introduction : What is Implied volatility?
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
Log Normal
Diffusion
Black and Scholes
Implied vol
Forward
Strike
Maturity
Option price
6
Greeks
Spot:
Direct Greeks
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)
Absolute change in delta in £ for a 1 point additive move on the vol -> the skew
greek
From model inputs (exotics): model parameters sensitivities
Delta
Gamma
Vega
Volatility:
Time:
Theta
Cross Greeks
Vanna
Model Greeks
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:
OVME <GO> Options Risk Measures – “the Greeks”
8
Buying 4500 Straddle 2900 Sept 14 `
MARS <GO>
Example of a volatility strategy
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
How to trade vega?
9
Buying 4500 Straddle 2900 Sept 14 `
MARS<GO> Example of a volatility strategy
The Impact of a Volatility change as is still linear but the drift weakens as time goes by
How to trade vega?
10
Spot ladder on Greeks
On a portfolio with various volatility strategies and assets
Greeks risk management for Volatility Portfolios
Spot
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)
Greeks
11
A more advanced Vega risk management
Greeks risk management for portfolios
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
Vega Liquidity in the world
America EMEA Asia
SPX/VIX > 150M
SX5E/V2X
APPL, Russel, Nasdaq, FTSE, DAX
Facebook, Google,
EEM, PCLN,TSLA
NKY
NFLX, MSFT,AMZN, C,
LNKD, EFA, XLF, JPM
FSTMIB, SMI, CAC,
SX7E, AEX, TOP40
TPX, KOSPI, AXJO,
HSCE, HSI
12
50M
10M
5M
1M
500k
Avg daily
Vega traded
in M
13
SPX/VIX liquity
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
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.
14
3 Month realised vol for SPX, SX5E, FTSE, NKY
GV <GO>
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
17
Comparing the implied with realized volatility for the main global indices
VCA <GO>
Volatility Analysis
Volatility is quite expensive around the globe
Pre-Trade: Rich vs. Cheap Analysis
18
On the Euro Stoxx ATM 3 month VS 3month histo, a recent turn to rich
after some hieratic cycles
GV <GO>
Volatility Analysis
Pre-Trade: Rich vs. Cheap Analysis
19
GV <GO>
Historical evolution of the SX5E 1 year historical volatility
Pre-Trade : finding the good entry point
Looking at the realized volatility over the last year. we are at the minimum!
20
GV <GO>
Historical evolution of the sx5e atm 1 year implied volatility
Pre-Trade : finding the good entry point
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
21
GV <GO>
Historical evolution of the 1 year volatility richness
Pre-Trade : finding the good entry point
… then we are now in a rich volatility regime
22
GV <GO>
Historical evolution of the 1 year volatility richness
Pre-Trade : finding the good entry point
… then we are now in a rich volatility regime
23
SHOC <GO>
Using historical analysis to determine best and worst entry for a long volatility
trade: SX5E Straddle
Pre-Trade : finding the good entry point
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
24
MARS <GO>
Using historical analysis to determine best and worst cases
Pre-Trade : finding the good entry point
We can see how expensive or cheap becomes the Straddle according to the
different Implied Volatility levels
Pre-Trade : Comparing Historical Volatility for Similar Underlying Assets
25
GV <GO>
Comparing Realized and Implied vol for the SX5e – SPX spread
Case Study: Spread VSTOXX - VIX
26
Analysing the Spread
The spread has been very rarely negative
Case Study: Spread VSTOXX - VIX
The Term Structure is pretty much constant around 3
27
Looking at the term structure this days
Case Study: Spread VSTOXX - VIX
However in the past like in end of 2011, there was better spreads opportunity…
… Like a back-end future spread around 2.5
28
Analysing the Spread
Pre-Trade : Comparing Historical Volatility for Similar Underlying Assets
29
GV <GO>
Analyzing richness of SX7E
From a 13 low to highs spiking at 80: A clear Vol regime change on the EUR
Banks Index
30
GV <GO>
Historical evolution of the sx7e atm 1 year implied volatility
Pre-Trade : Impact of an Event on Volatility
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
Case Study: Variance Swap
Payout = 𝑉𝑒𝑔𝑎 𝑡𝑟𝑎𝑑𝑒𝑑
2∗𝑆𝑡𝑟𝑖𝑘𝑒× (𝑅𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦2−𝐾2))
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
What is a Variance Swap?
32
OVME <GO>
Buying a 12/30/11 SX7E Var Swap on 01/01/11:
Locking a 35.30 Volatility on June,2…
Case Study: Variance Swap
Example of a SX7E Var Swap
33
OVME <GO>
Example of a SX7E Var Swap
Buying a 09/10/13 SX7E Var Swap on 06/02/13:
We can see the money earned between end of August and November
Case Study: Variance Swap
Pre-Trade : Vol of Vol Trading
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
Volatility Assets Comparative
-20,000,000
-10,000,000
-
10,000,000
20,000,000
30,000,000
40,000,000
50,000,000
60,000,000
70,000,000
80,000,000
- 10 20 30 40 50 60
V2X Future
Fwd Var
Strategy p&l
Short 1M vega V2X nov13 future @ 19.8, Long Nov/Dec forward var @20.4 -> flat risk ?
35
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
Pre-Trade : Vol of Vol Trading
Case Study: Forward Var / volatility futures
Pre-Trade: Skew Trading
36
GV <GO>
Looking at the 1 month skew
Skew Historical Analysis
Case Study : Risk Reversal
37
OVME <GO>
Based on negative correlation between spot and implied volatility
Trading spot/vol dynamic
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
38
How did this trade work in the last 2 years
-4%
-3%
-2%
-1%
0%
1%
2%
-4% -3% -2% -1% 0% 1% 2% 3% 4%
1mth fixed strike vol move
spot move
2012
-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
-3% -2% -1% 0% 1% 2% 3%
1mth fixed strike vol move
spot move
201
Trading Risk : Skew Trade
Looking at the skew differently : Sorting returns by Vol and Spot Trend
In 2013
spot move vol move 2012 2013
+ - 62% 67%
- + 54% 65%
In 2012
Post-Trade:Trading risks and challenges
Pin risk
Convexity Trading
Tail Risk Exposure
Are Underlyings really lognormal?
40 40
Summary of Volatility Assets exposure
You should not rely on historical or hypothetical historical information. Such historical and hypothetical historical information is not indicative of future performance
Source: Barclays.
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
-2
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Spot Deviation to the Strike (in %)
41
Short an option expiring in 15 days with implied volatility around 18, delta hedged
Theory limit with continuous : Pin Risk
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
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Spot Deviation to the Strike (in %)
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
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.
42
Barclays short 1Month SPX variance swap systematic strategy
43
S&P 20 years daily return probability comparison
Historical distribution versus distribution implied by options prices and implied vol
model
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
-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%
Historical Proba
Predicted proba
Daily return
Probability
Convexity Trading
44
-
50.00
100.00
150.00
200.00
250.00
300.00
350.00
400.00
450.00
500.00
-7.0% -2.0% 3.0%
Ratio
Ratio
-
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
-7.0% -2.0% 3.0%
Ratio
Ratio
(1,000,000,000,000.00)
1,000,000,000,000.00
3,000,000,000,000.00
5,000,000,000,000.00
7,000,000,000,000.00
9,000,000,000,000.00
-15.0% -10.0% -5.0% 0.0% 5.0% 10.0% 15.0%
Ratio
Ratio
Tail risks are underestimated more than billion time…
Convexity Trading
Post-trade : Tail Risk with Naked Put
Let’s remind us the profile of a Naked Short Put
45
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
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
49
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not take account of dividends and other corporate actions and may deduct fees and commissions. An investment in an index
may be taxed differently to a direct investment in the components of the index.
SPONSOR ACTION THE INDEX SPONSOR MAY CHANGE THE INDEX. It may adjust the composition or calculation methodology and may
suspend or cancel the index. This will affect the performance of the Product.
INDEX SUBSTITUTION THE INDEX MAY BE SUBSTITUTED IN CERTAIN CIRCUMSTANCES. Such action may negatively affect the value and
performance of the Product.
Risk Factors
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