6/25/14 Structured Products Risk Management - FX Options - Confluence

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1 Structured Products Risk Management Added by Shawn Wang, last edited by Shawn Wang on Nov 29, 2013 In this tutorial I aim to go over the big picture of the kinds of TRFs that we deal with, laying out as simply as possible the important risk-and-p&laffecting concepts (highlighted in bold). While TRFs can be enormously complicated, it is usually the simple ones that are often the easiest to sell in the largest size and therefore pose the most urgent portfolio risk management issues. All examples provided below are from real-life cases where we have experienced notable risk management issues. Because this TRF vega supply from corporates usually dominates vega demand from hedge funds, these structures often drive both the structure of the vol surface as well as the day to day changes. To the extent that TRFs involve a directional view, the initial delta hedging and subsequent gamma trading also impact the spot market directly. Types of TRFs Target Redemption Forwards are best understood as alternatives to doing strips of forward sales (e.g. selling 100k of EURUSD every month to hedge some underlying business exposure). In order to improve the strike at which the forward sale is done, the client sells vanilla and exotic optionality (bank buys), which often lead to markedly improved strikes for the client (mostly Asian and Middle Eastern clients due to hedge accounting rules). To illustrate the amount of pickup involved, a recent GBPUSD TRF allowed our client to buy 1mio GBP per month for up to 12 months at while spot was at , with losses only occurring if spot fixing below Apart from the obvious details like currency, schedule, and notional, TRFs vary in three important ways: Payoff, Target Type, and KO Condition. Payoff There are just two main types of TRF payoff - linear and digital, analogous to payoffs for vanilla and digital options. Linear: Here is a simple 1x2 USDJPY buyer TRF from the bank point of view. This linear payoff looks like a forward plus a USD put. Notice it is a "buyer" TRF even though we are selling USDJPY at 95 because TRF terminology is always from client point of view (and the payoff charts can be either bank or client point of view). Digital: Here is a simple USDCNY AXKI TDP (with a digital payoff on the downside and linear payoff topside).this payoff looks like a two digitals plus a vanilla option. Notice the At expiry Knock-In on the linear payoff means that the bank does not profit until spot exceeds 6.5, giving more benefit to the client and decreasing the PV of this TDP. AXKOs are also possible but rare. Every TRF payoff is constructed out of these two basic building blocks. Linear or digital payoffs can be specified over any number of ranges in spot, leading to a wide array of possibilities, but in practice there are a few that stand out. In particular, when the client has a rangebound instead of directional view, they put on pivot TRFs and TDPs. Here is a 1x2 USDJPY pivot TRF with AXKI's at 85 and 115 for illustration. For clarity, this means that from 100 to 110, the client sells USDJPY to the bank at a rate of 110 (a profit for the client). Above 115, the client sells twice the notional amount also at a rate of 110 (a leveraged loss for the client). Between 110 and 115 nothing is done and neither party benefits. This logic is flipped for the spot scenarios below 100, the pivot strike of the TRF. Another popular variant demonstrating this idea is the collar TRF which also has a range where neither party benefits, but with no AXKI payoff discontinuity. 1/9

2 Target Type If varying payoffs were all there was to TRFs, they would be perfectly and statically replicable by first-generation european options. It is the possibility of premature knockout (or "redemption") of all remaining legs according to a preset target that make these products second-generation, and give TRFs their name. KO types boil down to a simple dichotomy: Big Figure vs Range Count. Big Figure Knockouts limit the total accumulated profit (or, less frequently, loss) of the client on a TRF. If we combine the above big fig KO with the first payoff in this tutorial, we have a basic TRF already in place: For each fixing in the schedule (say once a month over the next year) we will sell the notional amount of USDJPY at 95. If spot stays at 100, this means at each fixing the client will gain 5 big figures. This is tallied up by Middle Office and is referred to on the termsheet as Accumulated Intrinsic Value. Because we have limited the total profit to 15 big figures in the screenshot above, that means the First Exit Time of this trade is 3 months i.e. if spot goes nowhere this trade will be knocked out in 3 months and not finish its full 12 month schedule. Range Count (or ITM Count) Knockouts limit the total number of times fixings are In The Money for the client regardless of total accumulated profit. Because of this they are frequently used in conjunction with digital payoffs, however there is no a priori reason for this to be so. Here if spot fixes on three of the fixing dates outside the range from 97.2 and infinity (exclusive of 97.2) then the TRF knocks out. This is another way of saying the TRF KO's if spot fixes thrice between 0 and 97.2 inclusive - the statements are mathematically equivalent. The last thing to note here is that we can have dual KO structures with both Range Count and Big Figure knockouts, where the TRF knocks out due to one or both of them being hit. Worth noting here is that one of the more popular dual KO structures dealt in the bank involves only the bank's upside (client's downside) being knocked out if one of the KO conditions trigger, leaving only upside for the client. (the second KO condition kills the structure for both the client and the bank) KO Conditions Last and probably strangest are the rules governing what happens on the day the TRF knocks out. Exact/PartialStrike/PartialNotional: this is the most popular settlement method typically used in conjunction with big figure targets. In this scenario the amount the client gains on the last day is calculated to be just enough to make up the stated target. For a concrete example: in the 15 big figure USDJPY 95-strike TRF above, if spot fixed at 105 in the first month and then 105 again in the second month, the amount of profit paid out to the client in the second month is only 5 big figures' worth. If the TRF is cash settled this is referred to as an "Exact" payment where we simply hand over a cash payment, however if it is physically delivered then we either adjust the strike or the notional (less common) of the TRF in order for the total profit to work out to 5 big figures. Full: this is the second most popular method in which the client gets the full amount of the difference between spot and strike on the last day i.e. the TRF becomes like a full blown european option at some point with no hard cap on how much 2/9

3 the client can profit. In the above example, the amount of profit paid out to the client in the second month would be 10 big figures. However subsequent payments are still knocked out. Note that if spot declined to in the second month instead, then the client would essentially be long a free 100-strike USD call for the third month because the TRF did not knock out in the second month. In fact, the client is long better than a free vanilla call: if the call is not in the money in the third month, it renews to the fourth month, then the fifth, then the sixth, and so on until the defined end of the TRF or until it becomes in the money, whichever comes first. This evidently has much higher value than a vanilla call. KO: The exact opposite of Full - when the target condition is reached, the TRF knocks out and the client gets nothing. In the above example, the amount of profit paid out to the client in the second month would be zero. Worth observing here is that, broadly, the risk of a "KO" knockout < risk of an "Exact" knockout < risk of a "Full" knockout for selfevident reasons, and the PVs change accordingly. And One More Thing: Stepped Features Payoffs and Range Counts can be stepped (changed) over the lifetime of the TRF. This is a popular structure in AUDUSD TRFs: Here we see that the TRF strike is 0.98 for the first 3 months and 0.94 for the remaining 9. The bank is buying (client is selling) therefore the value for the bank is loaded in the back end and conversely the value of the target knockout feature is very high for the customer in the first three months (quantifiable as a knockout digital). TRF Risk Management Similarities. It is generally a good idea to compare TRFs to their vanilla counterparts and I have done my best to outline the similarities in my treatment above. Our complete understanding of the similarities and differences will define our ability to hedge the TRF book with first generation options. In general every discontinuity in payoff is a source of vega and gamma just as with vanilla options, therefore, for example, pivot TRFs are better hedged with vanilla strangles rather than straddles. Vega profile of pivot TRF looks like a strangle TRF fixings and strikes are always European (aka At Expiry) in nature - the only thing that matters is where the fix will be on the fixing day. This also makes TRFs easier to price than some first generation exotics under monte carlo methods. Cash settled TRFs have significant delta fixing bleeds. Because the cash settlement simulates the physically delivered forward, we have to buy or sell the delta at the fix to ensure we are fully hedged against fixing risk. We can chose to apply ramping on these digitals which decrease the payoff and PV against ourselves but also improve the risks seen when running simulations and hedging. This is similar to doing vanillla option spreads against European digitals and is pretty much the exact same philosophy. The similarity of Vega and Gamma under FET assumptions. For standard TRFs the relationship seems to hold that the TRF will have the same amount of gamma as its vega-equivalent vanilla option expiring at the FET. To clarify, if a 12-monthly TRF with an FET of 2 month 3/9

4 and 25k of vega is dealt, we know that that is roughly equivalent in vega to 15mio notional of 2month vanilla atm, which has a little more than 1 unit of gamma, which is also the amount of gamma that the TRF has. This is just a rule of thumb, with serious flaws explained below. Based on the above it would seem that the best vanilla hedge for a TRF would just be to hedge its vega amount at the FET, as that also takes care of the gamma. We will see that this is not exactly true. Differences. I have already introduced some unique TRF risk management concepts above but for convenience I will summarize the key differences in between vanilla portfolio and TRF portfolio management here: Because of the target redemption knockout feature, TRFs generally have less optionality than their equivalent first-generation counterparts (i.e. as asserted above, every TRF payoff is statically replicable with first gen options, however the second gen "contingent knockout" features of TRFs generally mean that TRFs have less option value than the static first gen portfolio). TRF fixings are often done alongside vanilla option fixings but usually off of a market standard fixing page like ASFH, TKFE, ECB, or WMR, due to the need for transparency with corporate clients, instead of in the direct vanilla market where we typically determine the fix internally or with our counterparty. This causes potential fixing risk as the options we use to hedge TRFs fix at different times and different rates than the TRFs themselves, however in practice this is never an issue as we hedge internally and roll out expiring hedges. The Deficiencies of FET as a rule of thumb. While the FET is a useful concept because it can be calculated by hand as an approximation, and the vega-gamma relationship noted above, it is important to know the problems with FET in order not to be tripped up. FET vs Vega Bucket: the FET will generally not be the biggest vega tenor sensitivity of the TRF. For example a standard 2mth FET TRF actually has 3mth and 6mth buckets that are 3 times as large as its 2mth bucket. This is generally due to the vega sensitivity of the downward monte carlo paths bleeding into the higher spot positions in subsequent months. Vega Buckets vs Vega Bleed: This introduces a dilemma - to hedge the vega bucket risk, we really need to sell 3mth and 6mth, however if the FET assumption proves correct, and spot does not move, the TRF redeems in 2 months, and upon redemption we are left with outright vanilla positions of 1-4mths in tenor. In short, the hedge deteriorates over time and TRF vega bleeds away faster than vanilla option vega, introducing the need to dynamically adjust the hedging portfolio. This difference in bleed speed extends to smile greeks like rega and sega. FET vs TRF lifespan: a simple 12-monthly fixing TRF with an FET of 1 month has different risks compared to a 52-weekly fixing TRF with an FET of 1 month, and very different risks compared to a 24-monthly fixing TRF with an FET of 1 month but with stepped down strikes from the second month on. Significant Vanna. Directional TRFs (the majority of non-pivot TRFs) are usually dealt at a markedly improved strike for the customer compared to the regular forward (this is often why they buy the TRF in the first place). For us this means that the "option strike" has a low delta and therefore introduces a vanna on top of the vega that we get given. Vega profile of a directional TRF: Weighted Vanna i.e. dweighted Vega dspot is markedly different than vanillas. Vanilla options do not change vega buckets dependent on spot, whereas TRFs do due to FETs changing over spot. So the buyer TRF is expected to live to 5 months if spot drops to 98 but only expected to survive 1 month if spot rises above 110 between the time the trade is dealt and its first fixing. Observe below how parallel vega increases when spot goes down and how it shifts backwards in buckets when spot goes down. 4/9

5 Digitals and Discontinuities There are broadly two kinds of digital risks related to TRFs: KO digitals and payoff digitals. These digitals are viewable in the Digital Report designed by Pascal available here: KO digitals revolve around the "KO Conditions" explained above. As they are usually some form of Exact KO and with a small notional per fix these digitals are usually small, however these KO digitals can be high when: there is a stepped payoff such as the AUDUSD TRF example above where the value for the bank is back-loaded and the upcoming fixing will determine whether or not we enter the "profit zone" for the bank there is a "full" payoff that is still live and is in the money. The payoff discontinuities occasionally make for sizable digital risks as well. These are most acutely felt when AXKI payoffs are applied on daily fixing structures (example below). While the KO digitals above are guaranteed to be one-time only, the AXKI digitals knock in and by definition live to see another day. In the example below we experience a daily digital where we want spot to fix above 85 (the pnl works out to be about 70k per day). 5/9

6 Smile Greeks vs Second Order Greeks Compared to vanilla options, TRFs have more acute second order greeks (e.g. vanna) than they do smile greeks (e.g. rega), due to the vega sensitivity to spot explained above. Part of this is a simple system issue - when running simulations the system simply bumps spot with all else constant and in doing so simply assumes that the implied vol surface will not perform, which does not realistically reflect the "true" risk of the position. However vol surfaces do not always perform, and TRFs really do have different smile greek - to - second order greek ratios. For illustration if we try to hedge the vega and vanna of a TRF we can do so reasonably successfully with some combination of atm and risk reversal hedges (probably a better idea to do a ratio risk reversal, but you get the point). The above chart shows the vega over spot of the TRF and various hedges. The net vega profile across TRF and hedges looks a little smoother over spot than the TRF itself. However, the TRF illustrated here has only -2k of rega and +0.5k of sega, while the vanilla hedge required to hedge this vanna adds +2.5k of rega and -0.6k of sega, causing the portfolio to be net long rega even though generally the portfolio vega decreases with increases in spot (vanna generally associated with a short rega position). The portfolio also becomes short wings despite the general design of TRFs to be long wings and tail events. Magnify these risk mismatches a thousandfold and this is representative of some of the biggest TRF portfolio management problems we have faced. 6/9

7 Here is an example portfolio that has negative vanna (shorter vega with higher spot): However this portfolio is long rega (which is normally higher vega higher spot): When we filter the portfolio to look at the TRF risk: 7/9

8 And compare this with the risks of the vanilla options used to hedge them: 8/9

9 The sega is not shown but the portfolio is also short sega from the vanilla hedges despite the TRFs being long sega and the TRF book generally being thought of as long sega. It is apparent that the differences in the ratio of second order greeks vs. smile greeks of TRFs as compared to vanillas has created a counterintuitive net portfolio position. If restricted to hedging TRFs with vanilla options (an incomplete market with respect to the greeks we are discussing), the portfolio manager must make a conscious choice between hedging the vega and smile greeks at present spot, or hedging the vega profile over spot at the cost of assuming significant smile greek positions. Note also how the above portfolio has option hedges in the 2y, 3y, and 4y buckets, while the TRF portion is completely clean of >2y risk.this is because those long dated TRFs that existed previously have bled away while the options hedging them have not yet been unwound. to be continued Structured Products Business Flow To be continued 9/9