Hedg dgin ing g of aut utoc oca alllla abl ble es Benoit Rauly, UBS, Global Head, Complex Equity and Hybrid Trading 04/04/2013
ESCP ESCP Eur Europ ope e
Introduction z
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Au A u t o c all al l abl ab l e : a range of payoffs which can mature prior to the scheduled maturity date if certain predetermined market conditions are achieved It has become very popular across a wide range of clients (retail, private banks, institutions) across th e globe glob e (Japan, Korea, Europe, US) Over USD 25bn is being traded every year in any type of wrapper (note, swap, structured fund etc...) This payoff offers an interesting alternative to traditional equity investments as they generate attractive yields and allow the investor to express a specific view with flexible features The high volume of trade can lead to concentrated concentrated risk s on the books of hedge providers Some of the second order risks can lead to significant P&L volatility for the investment banks in certain market environments
Exa xampl mple e : Auto A utoca callable llable on Eme mergi rging ng Markets Inde Index x Rationale z
I am an investor who has a preference for emerging markets (EM) equities
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I am looking for a product which would offer z z z z
An opportunity to gain from any positiv e performance of these markets A product with high coupons A product with limited downside risk but without fu ll capital capital pr otection otection A product with an early redemption feature
Bank A issues a Step-D Step-Down own Autoc all on Emerging Markets arkets (MSCI (MSCI EM Index) Index) in n ote format
Let’s take a co conc ncrete rete exampl xample e
Indicative Indic ative Terms Terms Currency Underlyings Maturity Au to c all Bar ri er Au to c all co u po n
USD MSCI EM Index 3 years 100% 10% after 1 year, 20% after 2 years, 30% after 3 years
Kick-In Barrier (Maturity)
50%
Redemption Redemption on A utocall Redemption Redemption at maturity
100% + Step-Up coupon 1) If MSCI EM Index > 100% the structure redeems at 130% x Notional 2) if MSCI EM Index < 100% and a) No Kick-In occurred, the structure redeems at 100% x Notional b) A Kick-In occurred, the structure redeems at MSCI EM Index x Notional
What are th the e sc sce enario narios s? MSCI Emerging Markets Index
Scenario Scenario A : auto-called in year 1
130%
Payoff = 100% + 10% coupon
C 120% 110%
Scenario Scenario B : auto-called in year 2 A
B
Payoff = 100% + 20% coupon
T 100%
Obs 1
Obs 2
Obs 3
Scenario Scenario C : redemption at maturity / No Kick-In occured Payoff = 100% + 30% coupon
Scenario Scenario D : redemption at maturity / A Ki c k -In oc c u r ed Payoff = MSCI EM Index * 100%
50% 45%
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At A t T=0 I pay p ay 100% to t o Ban k A
Sensitiv nsitivity ity to vol and skew skew z
3 years Bank A bond pays a fixed coupon of 10% of 10% How can I get such suc h a coupon cou pon with wit h the autocallable autocallabl e when 3 year year US swap rates are
0.5% 0.5%
? 1. The coupon is financed by an ATM put with a down and in barrier at 50% 2. Hence, the investor sells the down and a nd in put to Bank A z
As a result : z
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Bank A is long vol (if vol increases, so does the probability of the put hitting KI barrier, which reduces the product value) Bank A is long skew (if skew increases, so does the probability of the put hitting KI barrier, which reduces the product value) In the above example, example, Vega = -0.60% (as a comparison, comparison, a 3Y atm atm put vega vega is 0.60%), 0.60%), i.e. the the client client who bought the product is short vol, Bank A is long
Assuming we had a flat flat vol, we would only be able to offer a coupon of 6.5% p.a. (instead (instead of the 10% p.a.). Given this is skew sensiti sensitive ve,, the bank cannot price the product with a flat vol Bank A will use a local vol model to price and hedge the autocall.
Delt lta a he hedgi dging ng th the e st stru ruct cture ure z
If the forward increases, then the probability of hitting hitting the KI decreases and the product value increases. increases. In other words, once I have bought the underlying to hedge the delta, I will expect a certain amount of dividend in the futures that will help deliver the coupon. As a result, z z
the autoca autocall ll is long forward forward,, so Bank A is short spot and long dividends Bank A needs to buy the underlying index to hedge the spot
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In our example, the initial delta is quite high = 60%
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The Bank still needs to hedge the long divi dend exposur exposur e later…
Gamm mma a he hedg dgin ing g the t he st stru ruct ctur ure e z
At day 1, Bank A is long g amma Bank A short s a put D&I Æ Bank A is short theta and long gamma
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If spot goes down, Bank A becomes longer gamma longer gamma
Gamma profile
Spot
100%
Hedging of vol and skew skew on day day 1 z
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Given Bank A is long vol vol and long ske skew w, both of these need to be sold to be flat sells sells vega vega and skew skew by by sellin g OTM OTM puts put s on each of the 3 underlyings Which maturity has to be used for the hedge ? z z
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Bank A can choose to do everythin everythin g to the expected life of the trade from the model if it is a small trade Else Bank A might do a portfolio of hedges with a portfo lio of o f OTM OTM puts to each probability of KI
In this example, if the bank hedges, the expected maturity is 2Y
Bank A will for instance sell 50% put with maturity 2Y
Wha hatt do d o I do wit w ith h my m y divi di vide dend nd exposure exposu re ? z
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As seen before, Bank A needs to sell dividends to hedge the exposure coming from the short autocallable Meanwhile, Bank A has sold puts to hedge skew/vol. This actually is a hedge as it gives it the opposite position. However, there is more delta on the autocallable autocallable than the OTM OTM put, put, so this in not enough… Bank A can hedge the rest with a synthetic forward
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How does it work/get quoted ? Bank A buys buy s Dec Dec ATM cal c alll / sells Dec Dec ATM Put Pu t , cross with the nearest to deliver future Note : this is a static hedge which need to be updated through the life with relative and absolute performance of the underlying
Hedgi dging ng rho r ho and and fund f undin ing g rho rh o z
At Day 1, Bank A is long funding rho Bank A enters a swap rate of maturity “expected maturity ”
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At Day 1, Bank A is long rho Bank A deposits c ash to t he Bank’s Bank’s Treasury Treasury for “expected maturity ”
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But what is the “expected maturity ” ? Expected maturit y can be defined as : (probability to exit in year i)
Near ly al l do done ne ? z
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A bit of effort, but spot, dividends, vol, and skew exposure are now hedged. I need to rebalance delta based based on gamma.
So after that, can Bank A just get done with i t and wait until expiry except for a bit o f delta/gamma delta/gamma hedging ?
Unfortunately, this is just the beginning and all these hedges need active rebalancing rebalancing !
Equ quit ity/R y/Ra ates and and Equ quit ity/ y/F Fun undi ding ng co corr rre elation z
If the underlying is up, up , then the autocall probability increases, meaning that the expected maturity reduces. Bank A needs to borrow back some of its long dated deposits deposits to redepo redepo it to shorter term shorter term
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If we assume positive equity/rate correlation, then with underlying up, rates rates should sho uld also be up, up, i.e a bond is down. down . z Negati Ne gative ve P&L due to this correlation z If the autocallable autocallable is longer dated, dated, this effect effect gets bigger as bigger as duration increases increases z Use stochastic rates/local equity vol model to capture this effect z Sensitivity to rates volatility This negative effect is compensated by the Equity quit y / fundi ng corr elation elation : z When the underlying is up, it most likely correlates with the funding rate being be ing down, which is the opposite oppo site effect effect to the above. z Likewise, when markets fall, fall , Bank A becomes long dated dated cash when it needs it the most (mitigation of losses in 08 with banks CDS significantly up)
Equ quit ity/ y/D Div ivid ide ends co corr rre ela lati tion on z
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If the underlying is down, down , the duration increases. In the mean time, the delta increases. z The dividend sensitivity increases significantly as the bank is expected to hold the delta for a longer period z Bank A becomes longer dividends z Most often, dividend is correlated with spot, so dividends are down P&L loss los s ! Note that sensitivity is to implied dividend yield, not realised. There is concentrated position in the market : z Everyone is long at the same time and dividends are very illiquid z The fall is exacerbated P&L loss lo ss i s exacerbated.. exacerbated.... To take this effect into account, Bank A needs to use proportional dividend model Ex : rather than assuming that Index will pay 100 USD of dividends, assume that it will pay 50 USD + 50 USD * (spot/spot initial) (equivalent to 50% correlation ish)
DEDZ3 Index - Eurostoxx Eurostoxx Dividend Dividend Future Future Decembe Decemberr 13 expiry expiry since since June June 2008 2008 (gross cash dividend dividend announced and paid by the constituents of the Euro Stoxx 50 Index for the calendar year 2013)
Loss expected in the market from this effect alone > $500m
Vega conv co nve exi xity ty z
When the underlying falls, falls, Bank A becomes longer longer vol and skew skew (as KI probability increases). And vice versa, versa, i.e when spot is up (probabil (probability ity of KO increases increases), ), Bank A becomes becomes shorter shorter vol and skew z z
Very dynamic exposure to vol, which is supposed to follow the skew skew curve (i.e. vol down with spot up) Short convexity This can lead to significant P&L if the vol does not follow the the skew curve, in particular when the street is dominated by this kind of product.
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Given significant size are issued, it is highly likely the risk gets concentrated. concentrated . In addition, there is a v o l cliff just just above KI, i.e. i.e. : z z
The closer to KI, the higher t he vega vega BUT when KI is hit, there is no more mo re vega vega in the product whilst hedges remain Bank A becomes short vol at the worst wor st time, ti me, i.e. i.e. when markets cr ash and so they all need to buy vol at the the worst worst time time
Vega conv co nve exi xity ty examples A) A ) 2008 Fin Fi n anc an c i al c r i s i s In 2008, there was high concentration in market and very violent spot move towards lower KI barriers : z Vol did not pay above the barrier as everyone gets longer at the same same time and no liquidity was available z Opposite after everything everything KI through large moves, i.e. i.e. vol goes up significantly after KI events when everyone is short significant losses across banks at the same time
B) 2012, Japan Most products had no KI or KO for a while. As a result, concentration increased as position did not reduce. dVega/dSpot was around USD 4m per 1% move move estimated in the the market There was little liquidity from other flows, low implied, call buyers to buy Japan story. As a result z
NKY vol vol up with spot spot up, i.e. invert inverted ed skews skews significant losses in market also if no other hedge
Varia riant nt : Auto Autoca calla llable ble on Eme mergi rging ng Marke rkets ts Rationale z I am an investor with a strong conviction for emerging market market (EM) equities. I am bullish on all those 3 markets Russia, Brazil and China. z
I am looking for a product which would offer z
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An opportunity to gain from a positi ve perfor performance mance of my 3 preferred markets (and not from the other emerging markets) A products with high coupons but not necessarily necessarily fu ll capital protection A product with an early redemption feature
Bank Bank A issues issues for me a “ worst of” Autocall Autocall on Eme Emerging Ma Markets rkets in note forma formatt
Exa xampl mple e : Wors Worstt of Aut Autoca ocallable llable on Eme Emergi rging ng Ma Marke rkets ts
Indicative Indic ative Terms Terms Currency Underlyings Maturity Au to c all Bar ri er Au to c all co u po n Kick-In Barrier (At maturity) Redemption Redemption on A utocall Redemption Redemption at maturity
Reoffer
USD RDXUSD Index (Russia), EWZ US Equity (Brazil), HSCEI Index (China)
3 years 100% 18% after 1 year, 36% after 2 years, 54% after 3 years 50% 100% + Step-Up coupon 1) If WO If WO > 100% the structure redeems at 154% x Notional 2) if WO if WO < 100% and a) No Kick-In occurred, the structure redeems at 100% x Notional b) A Kick-In occurred, the structure redeems at WO x Notional 100% “WO” stands for the level of the worst performing stock as a percentage percentage of its level at the strike date
Why does corre cor rela lati tion on ma matt tte ers ? z
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Bank A is short correlation, correlation , i.e. if correlation is low, the likehood to hit the KI is higher, which reduces the product value, i.e. Bank A makes money How much is this effect worth ? Quite a lot ! As we see, in the first example, we could offer a coupon of 10% 1 0% p.a. to client. With this worst of feature, we are now able to deliver a coupon of 18% p.a. : coupon jumps from 10% p.a. to 18% p.a.
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Implied correlation matrix between between the the 3 underlyings underlyings :
Russia
Brazil
China
Russia
100.00%
78.98%
80.81%
Brazil
78.98%
100.00%
77.99%
China
80.81%
77.99%
100.00%
How ca can n we w e he hedg dge e co corr rre elatio lation? n? z
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Daily impact : cross-gammas (if index 1 is up +2%, this generate a negative delta of on index 2 and index 3. If index 2 and index 3 are up as well, I will lose money from the cross-gamma effect) P&L based on their moves It is very difficult to hedge this correlation as most products in the market are giving the same exposu exposure re,, so the market is mainly one way If anything Bank A can hedge it with : a) IDB IDB market m arket : call call vs call call 50% call A + 50% 50% call B – call basket basket (50% (50% A, 50% B) Long correlation Æ vega hedge hedge / delta hedge / correlation correlation exposure exposure
b) trading other products giving the opposite exposure z
Best-of (but very expensive) products
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Call on dispersion dispersion ( perf(A) perf(A) – (perf(A) (perf(A) + perf(B))/2 perf(B))/2 + perf(B) perf(B) – (perf(A) (perf(A) + perf(B))/2 perf(B))/2 - K )+
Now ge g etti tting ng on wit with h the th e digi digita tals… ls… Bank A will have to manage a digital option to be able able to offer the coupon Digital call options are all-or-nothing options that settle at 100 if ITM, or at 0 if OTM
Delta tends to infinity as time to expiry (T) approaches zero
Gamma can soar and and plun ge as time to infinity as time to expiry (T) approaches zero
Call sp spre rea ad he h edg dgin ing g of o f dig d igit ita als z
A digital option is almost always hedged as a call sp read. read. By doing this, the bank achieves a chieves a smoother set of gr eeks eeks especially the delta. long position position on a call call with "strike "strike = strike strike of the the digital digital - overhedge overhedge amount" amount" and a short position on a call with "strike = strike of the digital" with each with a quantity = "the digital payoff/overhedge".
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Note that the call spread is structured that it is more expensive than the original binary option and as a result the bank will quote prices for a call spread. The maximum delta for the call spread will be “ Digital payoff/ payoff/O Overhedge verhedge amount”
Call spr spre ead he h edgi dging ng of dig digit ita als example z
Let’s take the following example :
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$10m digital notional 98-100 CS (Æ 2% overhedge)
Maximum delta = 10m / 2% = $500m !!!
We need to ensure we’ll have sufficient liquidity to trade that delta in the market. For Eurostoxx, SPX or Nikkei, this size is fine but for a stock like Peugeot for example, it would take several days to trade such a delta without moving the market…
Barr Ba rrie ierr shift shi ft z
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The barrier shift is the amount by which t he bank bank shift s the barrier barrier whil e prici ng so that in fact they are really pricing a new digital whose replicating call spread is the hedge of the actual binary option. The barrier shift is chosen so that the resulting shifted payoff over-replicates payoff over-replicates the payoff of the binary by the least amount, but such that the Greeks Greeks of the t he new payoff are managea manageable ble near the barrier. The size of the shift chosen by the bank depends on different factors : z z z
Discontinuity size Liquidity of the underlying (daily volume of the t he hedging instrument) Volatility of the underlying
Let’ Le t’s s go ba back ck to t o our ou r prim pr ima ary ca c ase se… … z
Assumptions : z Daily volume of the underlying : $500m z maximal volume that Bank A can trade : 30% z Autocollable notional : $100m z Remember : coupon year 1 = 10%, 10%, coupon year 2 = 20%, coupon year 3 = 30% barrier = 50%
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“Maximum “Maximum delta” delta” = $150m (=30%*$ (=30%*$500m) 500m)
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Payoff Payoff / overhedge overhedge size (%) = delta delta max ≤ “Maximum delta” Æ z z z z
overhedge overhedge size (%) = Payoff Payoff / “Maximum delta” delta” overhedge size (%) (%) = ($100m * 10%) 10%) / $150m $150m = 6.67% Aut A ut oc all al l Year 1 : overhedge Aut A ut oc all al l Year 2 : overhedge overhedge size (%) (%) = ($100m * 20%) 20%) / $150m $150m = 13.33% overhedge size (%) (%) = ($100m * 30%) 30%) / $150m $150m = 20% Aut A ut oc all al l Year 3 : overhedge overhedge size (%) = ($100m ($100m * 50%) / $150m = 33.33% Put Year 3 : overhedge
Conclusion z
We didn’t get into vol vol of vol vol or qua or quanto nto covaria covariance nce.. Maybe next year.
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Not such an easy life being a trader... Sales and structurers structurers do not get fired when the the product goes wrong
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Always beware of crowd of crowd ed trades trades. Liquidity is never there when you need it the most Having the right model to value all your risks is very important, but you cannot replace experience and a deep knowl edge of your market market These products are very dynamic so they require constant r ebalancing ebalancing.. Hedging costs can add up very quickly so you need to have a macro view