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Forward Vol Strategies - Quantitative Strategies

Long-dated USD callable bond issuance into Germany and Taiwan is continual, but this year's unprecedented demand from Taiwan has driven lower right vols lower. The recent jump was driven by regulatory changes. As this was an unintended consequence of regulatory loosening, we expect the window to close and callable issuance to decrease to more normal levels. In this report, we present and compare five forward vol strategies which all benefit from this effect.

Derivative Focus CROSS-ASSET Forward Volatility Strategies Global Markets Research 4 December 2014 Long-dated USD volatility opportunities Long-dated USD callable bond issuance into Germany and Taiwan is continual, but this year’s unprecedented demand from Taiwan has driven lower right vols lower. The recent jump was driven by regulatory changes. As this was an unintended consequence of regulatory loosening, we expect the window to close and callable issuance to decrease to more normal levels. In this report, we present and compare five forward vol strategies which all benefit from this effect. Large demand for USD callables While demand for callables is common in Germany and Taiwan with accounting leeway given for the call, i.e., they can receive the higher coupon without accounting for the call itself, there are distinct differences in most of the types and formats. Research analysts Quantitative Strategies Nick Firoozye - NIplc [email protected] +44 20 7102 1660 Qilong Zhang - NIHK [email protected] +852 2252 6191 Xiaowei Zheng - NIplc [email protected] +44 20 7102 8963 German insurers tend to prefer longer bonds with infrequent calls (or single calls), e.g., 30yNC10Y10Y, or 20YNC10Y10Y (i.e., a single call). Germans prefer both MTN formats and the non-mark-to-market Schuldscheine (for which issuance data are not readily available). Taiwanese insurers prefer frequent calls for their higher pick-up, e.g., 30YNC1Y1Y or 20YNC1Y1Y, and they have typically been prevented from doing more USD callables by regulators, aware that USD assets with TWD liabilities may result in mismatches. Formats have mostly included MTNs. But authorities in Taiwan wanting to resurrect a moribund Formosa bond market and attract foreign issuers, have relaxed rules on foreign investments. This has also had the unintended consequence of having TWD insurers load up on Formosa bonds (which do not count against a foreign asset limit) which are callable USD (and EUR) bonds issued by foreign companies. Fig. 1: Total figures from callable Formosa and callable MTNs Larger demand out of Taiwan Sum of Size (mm) Issue Month Total Jan-14 1,850.00 Feb-14 1,922.40 Mar-14 2,173.80 Apr-14 2,633.00 May-14 625 Jun-14 1,589.50 Jul-14 1,938.00 Aug-14 2,665.00 Sep-14 6,231.00 Oct-14 2,413.00 Nov-14 5,663.00 Dec-14 1,190.00 Grand Total 30,893.70 Source: GreTai, Nomura The recent concentration of zero-callable issuance is due to regulation change prior to this summer. The new regulation encourages foreign firms to list foreign currency denominated corporate bonds (called Formosa bonds) in the onshore OTC market. See Appendix A-1 for analyst certification, important disclosures and the status of non-US analysts. Nomura | Derivative Focus 4 December 2014 Investment in those bonds won‟t be counted as a part of foreign investment for lifers. Taiwanese lifers have 45% cap on their AUM for overseas investment. However, the majority of the Formosa bond issuance since then has been zero callable, which is not quite what the regulator was hoping for. Market participants are not very clear how long the regulatory leeway will last. Therefore, there has been a rush to invest in zero-callable Formosa bonds. This window is likely to close soon. The impact has been large, with long-dated vols especially in the lower right hand suffering significantly. We see the impact of Bermudan issuance in the vega profile (in the Appendix on Berm/Eur switch strategies) noting that 10y15y, 5y20y should all be under some downwards pressure from the recent glut in issuance. In particular, longerdated forward vol (e.g., 2y and 5y forwards), especially the lower right corner of the vol surface, have show significant carry (see Figure 2 in the black boxes for those vols which are significantly below spot). It is the larger vol carry in this region we would like to benefit from. Fig. 2: USD Forward volatility Lower right corner of the vol surface shows decent carry. Spot 1y 2y 3y 5y 7y 10y 15y 20y 30y 1y 49.0 69.0 78.4 81.8 80.2 77.1 73.1 72.3 69.5 2y 88.8 94.2 94.1 90.8 87.9 83.6 78.0 76.6 73.2 3y 102.3 99.7 97.5 92.9 89.8 85.4 79.1 77.0 73.3 5y 101.5 98.5 96.2 92.1 89.7 86.4 79.4 76.5 72.9 7y 97.3 94.9 92.9 89.1 86.9 83.7 76.3 73.0 69.8 10y 88.5 86.5 85.2 83.0 81.0 78.1 70.7 67.4 64.7 20y 64.3 61.8 61.0 60.1 59.6 58.8 53.2 51.6 48.3 30y 55.8 55.4 55.5 55.6 55.4 55.0 50.8 50.5 47.9 1y 1y 2y 3y 5y 7y 10y 15y 20y 30y 1y change 1y 2y 3y 5y 7y 10y 15y 20y 30y 1y 86.4 93.1 93.4 91.8 90.3 86.3 79.9 78.6 74.8 1y 37.4 24.1 15.0 10.0 10.1 9.2 6.8 6.3 5.3 2y 102.2 99.8 98.8 94.9 92.4 87.9 80.6 78.2 74.0 2y 13.4 5.6 4.7 4.1 4.5 4.3 2.6 1.6 0.8 3y 104.3 101.8 99.6 95.3 92.8 88.7 80.9 78.0 73.8 3y 2.0 2.1 2.1 2.4 3.0 3.3 1.8 1.0 0.5 5y 101.4 99.0 96.9 92.9 90.6 87.3 78.8 75.3 71.6 5y -0.1 0.5 0.7 0.8 0.9 0.9 -0.6 -1.2 -1.3 7y 96.5 94.3 92.5 88.9 86.7 83.2 74.9 71.2 67.9 7y -0.8 -0.6 -0.4 -0.2 -0.2 -0.5 -1.4 -1.8 -1.9 10y 86.5 84.3 83.2 81.2 79.2 76.2 68.4 65.1 62.2 10y -2.0 -2.2 -2.0 -1.8 -1.8 -1.9 -2.3 -2.3 -2.5 20y 63.1 60.5 59.8 59.0 58.5 57.9 52.1 50.5 47.1 20y -1.2 -1.3 -1.2 -1.1 -1.1 -0.9 -1.1 -1.1 -1.2 30y 55.3 54.9 54.9 55.1 54.9 54.4 50.0 49.7 30y -0.5 -0.5 -0.6 -0.5 -0.5 -0.6 -0.8 -0.8 2y 1y 2y 3y 5y 7y 10y 15y 20y 30y 2y change 1y 2y 3y 5y 7y 10y 15y 20y 1y 102.4 100.5 98.6 95.5 93.2 89.0 80.6 77.3 72.4 1y 53.4 31.5 20.2 13.7 13.0 11.9 7.5 5.0 2.9 2y 107.7 103.5 102.3 96.5 94.4 90.4 81.3 77.6 73.0 2y 18.9 9.3 8.2 5.7 6.5 6.8 3.3 1.0 -0.2 3y 105.9 103.3 100.3 95.6 93.8 90.5 81.0 77.1 72.7 3y 3.6 3.6 2.8 2.7 4.0 5.1 1.9 0.1 -0.6 5y 100.3 97.8 96.1 92.2 89.8 86.8 76.7 72.6 68.7 5y -1.2 -0.7 -0.1 0.1 0.1 0.4 -2.7 -3.9 -4.2 7y 94.2 92.3 90.7 87.5 85.5 81.8 72.4 68.3 64.9 7y -3.1 -2.6 -2.2 -1.6 -1.4 -1.9 -3.9 -4.7 -4.9 10y 83.3 80.9 80.0 78.6 76.5 73.6 65.2 62.0 58.8 10y -5.2 -5.6 -5.2 -4.4 -4.5 -4.5 -5.5 -5.4 -5.9 20y 61.5 59.1 58.4 57.6 57.2 57.0 50.9 49.3 45.6 20y -2.8 -2.7 -2.6 -2.5 -2.4 -1.8 -2.3 -2.3 -2.7 30y 54.4 54.0 54.1 54.2 54.0 53.6 48.9 48.6 30y -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.9 -1.9 30y 5y 1y 2y 3y 5y 7y 10y 15y 20y 30y 5y change 1y 2y 3y 5y 7y 10y 15y 20y 30y 1y 112.8 106.4 103.3 95.4 92.2 90.2 78.5 72.8 67.8 1y 63.8 37.4 24.9 13.6 12.0 13.1 5.4 0.5 -1.7 2y 105.9 102.7 101.2 93.1 90.3 88.7 76.6 70.7 65.9 2y 17.1 8.5 7.1 2.3 2.4 5.1 -1.4 -5.9 -7.3 3y 101.4 99.7 96.2 90.2 87.6 86.5 74.4 68.7 64.1 3y -0.9 0.0 -1.3 -2.7 -2.2 1.1 -4.7 -8.3 -9.2 5y 90.3 87.4 85.8 83.3 82.8 81.9 69.6 64.4 60.0 5y -11.2 -11.1 -10.4 -8.8 -6.9 -4.5 -9.8 -12.1 -12.9 7y 82.0 78.9 77.9 78.1 78.1 75.7 64.6 60.5 55.9 7y -15.3 -16.0 -15.0 -11.0 -8.8 -8.0 -11.7 -12.5 -13.9 10y 73.8 71.2 71.1 71.7 69.8 67.7 57.9 54.9 49.6 10y -14.7 -15.3 -14.1 -11.3 -11.2 -10.4 -12.8 -12.5 -15.1 20y 57.0 55.3 55.0 55.7 55.8 55.6 48.2 46.4 41.7 20y -7.3 -6.5 -6.0 -4.4 -3.8 -3.2 -5.0 -5.2 -6.6 30y 52.3 52.0 52.0 52.2 51.9 51.4 46.1 45.7 30y -3.5 -3.4 -3.5 -3.4 -3.5 -3.6 -4.7 -4.8 Source: Nomura Research Comparing forward volatility strategies There are several strategies we believe could capture depressed forward volatility. These include:    Berm/Eur 25yNC5y5y: long 25yNC5y5y straddles, short 5y20y straddles, both at 5y20y ATMF MCCS 5y5y20y: Long 10y20y payers, short 5y5y20y payers, struck at 5y20y rates Multi-strike MCCS 5y5y20y: Long 10y20y payers, short 5y5y20y payers, three pairs - each struck at ATM-50bp, ATM and ATM+50bp 2 Nomura | Derivative Focus  4 December 2014 Long 5y5y20y vol triangles: Long 5y5y straddles, short 5y25y straddles, long 10y20y straddles, all for equal notional and ATMF  Long FVA 5y5y20y: Enter into 5y5y20y forward vol agreement. In five years‟ time, exchange forward price for spot-settled 5y20y ATMF straddle We detail the pay-offs in five years‟ time and volatility dependence for each in the appendix, noting that many have quite similar pay-off profiles, with some crucial differences. The strategies are all long forward volatility (i.e., although they may have small vega initially, dVega/d time >0 and it grows over time, which we can see in the appendix, payoffs have a large vol dependence). They have differing rates sensitivities, and differing rehedging needs. As we see in Figure 3, there is significant directionality to a number of these trades, making it almost impossible to compare like with like. Fig. 3: Differing directionality – individual forward vol trades Berm/Eur, MCCS, Multi-MCCS and Vol Triangles show strong directionality. Rather, FVA has far less directionality. Berm/Eur Switch 25yNC5y5y 900 MCCS 5y5y20y 700 800 600 700 500 PV (cts) PV cts) 600 500 400 400 300 300 200 2009 to 2011 200 2009 to 2011 2012 to Present 100 100 0 2012 to Present 0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 2.5 3 3.5 5y20y Forward (%) Multi-strike MCCS 5y5y20y (ATM -50bp, +0, +50bp) 700 4 4.5 5 5.5 5 5.5 5y20y Forward (%) Vol Triangle 5y5y20y 1,800 1,600 600 1,400 500 PV (cts) PV (cts) 1,200 400 300 1,000 800 600 200 100 2009 to 2011 400 2012 to Present 200 2009 to 2011 0 2012 to Present 0 2.5 3 3.5 4 4.5 5 4.5 5 5.5 5y20y Forward (%) 2.5 3 3.5 4 5y20y Forward (%) 4.5 FVA 5y20y PV (cts) 2,000 1,500 1,000 2009 to 2011 2012 to Present 500 2.5 3 3.5 4 5.5 5y20y Forward (%) Source: Nomura Research Figure 3 also shows that the directionality for specific trades changes over time. As the trade ages and the underlying rates approach or moves above the strike, we see an initially positive duration (from 2009 to 2011) changing to a negative duration (from 2012 3 Nomura | Derivative Focus 4 December 2014 to expiry). This is true for all except the forward volatility, which appears to have a positive duration throughout, perhaps partly due to volatility-rates correlations. Figure 4 demonstrates the performance of these trades. It is not surprising that directional trades outperform in directional markets. MCCS, Multi-strike MCCS and FVA trades are better in terms of Calmar perhaps due to less dependence on rates. Fig. 4: Performance of all these trades for the past five years MCCS, Multi-MCCS and Berm/Eur switch appear to do best among them. But we are not comparing like with like. Max Gain Return to Term Return (p.a.) Std Dev (p.a.) Sharpe Ratio Max drawdown Calmar Ratio Berm/European Switch 25yNC5y5y 636% 295% 35% 38.3% 0.91 48.3% 0.72 MCCS 5y5y20y 566% 303% 36% 37.4% 0.95 39.5% 0.90 Multi-strike MCCS 5y5y20y 526% 320% 37% 42.0% 0.89 38.3% 0.98 Vol Triangle 5y5y20y 486% 167% 26% 35.4% 0.75 54.4% 0.48 FVA 5y5y20y 140% 131% 20% 23.4% 0.85 26.1% 0.76 Source: Nomura Research Reducing directionality and timing biases We create unhedged indices (to reduce timing bias) and hedged indices (to subsequently reduce directionality). The indices are computed by entering into trades monthly for FVA, MCCS, Multi-strike MCCS and Vol Triangle Strategies, and holding for one year. The Berm/Eur switch involves quarterly transactions, held for one year as well. The exotic trades have no transaction costs included. All revaluations of portfolios are done using weekly data. The delta-hedging is also done on a weekly basis following the method below:     Berm/Eur switch 25yNC5y5y (vs 5y20y European) is hedged against 5y20y; MCCS 5y5y20y and Multi-strike MCCS 5y5y20y are hedged against 10y20y1; Vol Triangle 5y5y20y is hedged against all three legs (i.e. 5y25y, 10y20y and 5y5y) for P&L stability in spite of maintenance challenges of hedging all three legs2; FVA 5y5y20y is hedged against 10y20y (in our study, FVA uses spot-settled swaptions which introduces delta from discounting and PV01). Except for the triangle hedge, all hedges assume parallel shifts, and more sophisticated hedging strategies have not been considered. All transactions are spot settled and EONIA discounting. Hedging costs are assumed at 0.3bp running (i.e., Rehedged Notional*Pv01*0.3bp for each rehedge). We see in Figure 5 that hedging improves the performance of MCCS, multi-strike MCCS and FVA trades. The Berm/Eur switch trade has a worse performance after hedging. The unhedged or hedged performance for the vol triangle is very similar. 1 The trades were chosen to some extent to try to attempt hedging with the same or similar instrument. Berm/Eur switch does not have the 10y20y as an underlying. We believe this is a small matter given its relative similarity to 5y20y. Moreover, the only Berm/Eur trades which would have 10y20y underlying (e.g., 30YNC10Y5Y vs 10y20Y have a natural maturity of 10 years rather than the 5-year maturity that is true of each of these trades. 2 We also considered hedging the vol triangle against a single instrument (10y20y), which led to a much worse hedging performance. Hence we only compare the hedging against all three legs for vol triangle here. 4 Nomura | Derivative Focus 4 December 2014 Fig. 5: Comparing latent directionality of the five hedged and unhedged indices (1y holding) Hedging is easy for some, harder for others, and there are gains from hedging for several strategies Berm/Eur switch 25yNC5y5y 120 6.0 5y20y Forward Rate (rhs) Hedged (lhs) Unhedged (lhs) 115 5.5 140 5.0 4.5 110 4.0 105 3.5 MCCS 5y5y20y 150 6.0 10y20y Forward Rate (rhs) Hedged (lhs) Unhedged (lhs) 5.5 5.0 130 4.5 4.0 120 3.5 110 3.0 3.0 100 2.5 95 Sep-09 Sep-10 Sep-11 Sep-12 Sep-13 Multi-strike MCCS 5y5y20y 160 10y20y Forward Rate (rhs) Hedged (lhs) Unhedged (lhs) 150 140 2.0 Sep-14 90 Sep-09 6.0 200 190 180 170 160 150 140 130 120 110 100 90 Sep-09 5.5 5.0 4.5 130 4.0 120 3.5 110 3.0 100 2.5 90 Sep-09 Sep-10 Sep-11 Sep-12 Sep-13 FVA 5y5y20y 300 240 2.0 Sep-14 2.5 Sep-10 Sep-11 Sep-12 Sep-13 Vol Triangle 5y5y20y 2.0 Sep-14 6.0 10y20y Forward Rate (rhs) Hedged (lhs) Unhedged (lhs) 5.5 5.0 4.5 4.0 3.5 3.0 2.5 Sep-10 Sep-11 Sep-12 Sep-13 2.0 Sep-14 6.0 10y20y Forward Rate (rhs) Hedged (lhs) Unhedged (lhs) 270 100 5.5 5.0 4.5 210 4.0 180 3.5 150 3.0 120 2.5 90 Sep-09 Sep-10 Sep-11 Sep-12 Sep-13 2.0 Sep-14 Source: Nomura Research We present the results for the hedged indices in Figure 6, highlighting Sharpe and Calmar ratios (since indices are not otherwise scaled to be easily compared). • Berm/Eur switch is clearly very directional and hedging reduces Sharpe ratio (although it increases Calmar). • The Vol triangle can have a very large delta. We initially hedged level alone but the performance of the “hedged” portfolio was so weak we decided against showing it. Our strategy of hedging all three legs appears to work reasonably. • The Single-Strike MCCS, Multi-strike MCCS and FVA perform better after hedging with large improvements in Sharpe and Calmar ratios.  • The hedged multi-strike MCCS outperforms hedged MCCS, suggesting that the lower negative gamma makes it easier to hedge, with greater efficacy in hedging. In general, the Multi-strike MCCS and FVA appear to be the superior strategies, have the best Sharpe and the best Calmar, with lower transaction costs. 5 Nomura | Derivative Focus 4 December 2014 Fig. 6: Performance of unhedged and hedged forward volatility Max Gain Return to Term Return (p.a.) Std Dev (p.a.) Sharpe Ratio Max Drawdown Calmar Ratio Total Hedged per Trade Initial Hedged Ratio B/E Switch 25yNC5y5y 16% 15% 2.6% 4.1% 0.65 6% 0.42 Unhedged Strategies MCCS Multi-strike Triangle 5y5y20y MCCS 5y5y20y 5y5y20y 32% 32% 87% 26% 26% 69% 4.8% 4.8% 11.9% 10.3% 10.2% 21.2% 0.47 0.48 0.56 14% 14% 30% 0.33 0.35 0.40 FVA 5y5y20y 148% 109% 21.2% 38.4% 0.55 49% 0.43 B/E Switch 25yNC5y5y 12% 12% 2.2% 3.8% 0.57 5% 0.42 Hedged Strategies MCCS Multi-strike Triangle 5y5y20y MCCS 5y5y20y 5y5y20y 39% 53% 78% 35% 46% 63% 6.1% 7.6% 11.1% 9.7% 10.0% 20.2% 0.62 0.75 0.55 12% 11% 26% 0.50 0.69 0.43 FVA 5y5y20y 188% 155% 23.2% 34.0% 0.68 43% 0.54 - - - - - 55.7% 20.6% 35.8% 244.2% 42.6% - - - - - 15.0% 18.7% 40.4% 11.3% 49.9% Source: Nomura Research In Figure 6, we also look at the hedging needs for all these trades. Two measures are calculated:   Total Hedged per Trade: the total hedged notional over the lifetime for each trade. The total hedged notional is calculated as the absolute value of initial hedged notional plus absolute value of subsequent notional change. Initial Hedged Ratio: the ratio of the absolute value of initial hedged notional to the total hedged notional over the lifetime. We note the following points: • In terms of total hedging requirement, the Triangle trade and Berm/Eur Switch strategy demand the most hedging amount for each trade. It appears the triangle hedging is not particularly good and it is more appropriate to consider hedging at least both level and slope in triangles. • The average rehedging in notional terms for the Single-Strike and Multi-Strike MCCS trade is around 20% to 40% of the notional of all legs for each trade, which is the least among all these trades. Also note that around 40% of total hedged notional for Multi-Strike MCCS trade can be done at the beginning of the trade. • The FVA trade has a relatively reasonable total hedging amount (~43% in terms of notional) for each trade, but almost half of the hedging can be done at the beginning of this trade (i.e., this is basically a static hedge). Conclusions Recent Taiwanese callable issuance has led to depressed long dated volatility in USD (and to a lesser extent in EUR). We have investigated five forward vol strategies in this report: Berm/Eur Switch 25yNC5y5y, single-strike MCCS 5y5y20y, multi-strike MCCS 5y5y20y, Vol Triangles 5y5y20y and FVA 5y5y20y. Clearly all strategies benefit from relatively depressed volatility in the lower right-hand side of the vol surface. All trades (including FVA) have an element of directionality. We have attempted to eliminate this. In the end, two strategies stand out as the best performers: Multi-strike MCCS which has the best Sharpe, best Calmar, and among the lowest rehedging costs, and FVA Strategy, which has low maintenance costs after the initial hedge and has a comparable Sharpe and Calmar. The performance of both hedged strategies exceeds that of any of the unhedged (but directional) strategies. 6 Nomura | Derivative Focus 4 December 2014 Appendix Bermudan/European Switch Bermudans/European is a strategy to go long forward volatility, with a good deal of directionality and some slope risk. Mostly regulatory and historical reasons lead investors in callables to choose differing tenors and call schedules. In general, the higher the call frequency, the larger the pick-up of callables to vanilla bonds. German investors tend to favour longer calls with less frequency or even structures with a single call, while Taiwanese investors tend to favour higher pick-up and will even consider annual call frequencies. The depressing impact on vega can be similarly spread out by a given issuance profile. Figure 7 shows that the Berm/Eur trade has a high dependence on the diagonal. The risk is concentrated on the Lower Right area. Fig. 7: 25yNC5y5y and 25yNC1y1y show varying degrees of risk spread across the diagonal Lower right is the primary area of influence NC5y5y 6M 1Y 2Y 3Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 1Y 0 0 0 0 0 0 0 0 0 0 0 2Y 0 0 0 0 0 0 0 0 0 0 0 3Y 0 0 0 0 0 0 0 0 0 0 0 5Y 0 0 0 0 0 0 0 0 0 1,578 0 7Y 0 0 0 0 0 0 0 0 0 0 0 10Y 15Y 20Y 25Y 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5,308 0 0 0 0 0 0 3,985 0 0 0 0 0 0 3,007 0 0 0 0 0 0 0 0 0 0 0 NC1y1y 6M 1Y 2Y 3Y 5Y 7Y 10Y 12Y 15Y 20Y 25Y 1Y 0 0 0 0 0 0 0 0 0 21 185 2Y 0 0 0 0 0 0 0 0 0 102 100 3Y 0 0 0 0 0 0 0 0 0 162 106 5Y 0 0 0 0 0 0 0 0 0 180 20 7Y 0 0 0 0 0 0 0 0 420 766 0 10Y 0 0 0 0 0 0 0 582 2,228 0 0 15Y 0 0 0 0 3 931 2,116 854 0 0 0 20Y 0 110 567 600 1,243 2,234 0 0 0 0 0 25Y 0 434 755 233 137 0 0 0 0 0 0 Source: Nomura Research. Both trades are receivers and struck at 3%. Like American Options, the Bermudan Option optimal exercise boundary is derived by backward induction on a recombining tree. Figure 8 demonstrates the optimal exercise boundary for 25yNC1y1y and 25yNC5y5y. The underlying forward has same final maturity (e.g., at annual intervals the forwards are 1y24y, 2y23y, 3y22y, etc up to 24y1y and 25y spot). Berms with more optionality require far more “in-the-moneyness” before early exercise. Rather, Berms with less optionality will have optimal exercise strikes closer to the underlying strike (3% in the example on the right). Unlike exercise boundaries in equities derivatives (e.g., for American Equity options), the choice of exercise vs continuation depends on the relative moneyness of a number of forwards on the curve, not just one underlying index. While Berms vs Europeans are a sort of forward vol trade, the slope dependence and vol slope dependence complicate the forward vol aspects. Fig. 8: Optimal exercise boundary Exercise boundary (shown for receivers) is far below strike initially, but converges at last exercise date 4.0% 3.5% 3.0% 2.5% 2.0% 1.5% Underlying Fwd Optimal Exercise (25yNC1y1y) Optimal Exercise (25yNC5y5y) Berm Strike: 3% 1.0% 0.5% 0.0% Nov 2015 Nov 2020 Nov 2025 Nov 2030 Nov 2035 Source: Nomura Research Figure 9 shows the payoff of a Bermudan/European Switch 25yNC5y5y trade, i.e. long $100mm 25yNC5y5y ATMF payers and $100mm 25yNC5y5y receivers vs short 7 Nomura | Derivative Focus 4 December 2014 $100mm 5y20y ATMF straddles. The strike is 3%. The pay-off can be divided into four regions:     If 20y rates < 3%, 20y rates > Optimal Berm receiver exercise (~2.4%) then European receiver is exercised and investor is long Berm (20yNC5y5y) Receiver + Berm (20yNC5y5y) Payer + Payer Swap (@3%) position. If 20y rates < Optimal Berm receiver exercise (~2.4%) both Vanilla receiver and Berm receiver are exercised (where the pink shaded area decreases to zero). The investor is long only the Berm payer. If 20y rates > 3%, but 20y rates < Optimal Berm payer exercise (~4.5%) then European payer is exercised and investor is long Berm Receiver + Berm Payer + Receiver Swap (@3%) position. If 20y rate > Optimal Berm payer exercise (~4.5%) then both Vanilla payer and Berm payer are exercised (where the grey shaded area decreases to zero). The investor is long only the Berm receiver. Figure 9 also shows a strong dependence of the Berm/Eur switch trade on forward volatility. Valuation depends on immediate call (i.e. 20y spot rate) but also on remaining forward calls and underlying vols (5y15y, 10y10y and 15y5y). There is also a dependence on slope and vol slope which leads to modest differences with other forward vol strategies in terms of hedging and performance. Fig. 9: Aged 5y pay-off of Bermudan/European 25yNC5y5y Forward vol exposure in 5y time 2000 Receiver Payer Straddle Vol -10bp Vol +10bp Pakcate payoff (cts) 1600 1200 800 400 0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 20y Swap (%) Source: Nomura Research Mid-Curve Calendar Spread (MCCS) Mid-Curve Calendar Spread (MCCS) is a strategy to go long forward vega, short gamma and long curve carry. The pay-off of a USD 5y5y20y MCCS trade is shown in Figure 10, which is to go long $100mm10y20y 4.5% receivers and short $100mm 5y5y20y mid-curve 4.5% receivers. In five years‟ time, the pay-off can be divided into two sections:   If the 5y20y rate > 4.5%, the Midcurve expires worthless and the resulting position, now 5y20y 4.5% Receivers remains. If the 5y20y rate < 4.5%, the Midcurve (physical settle) is exercised and becomes a Short Receiver Swap @ 4.5% (i.e., Long Payer Swap @ 4.5%). Using Put-Call Parity: Short 5y20y Receiver Swap @ 4.5% + Long 5y20y Receiver Swaption @ 4.5% = Long 5y20y Payer Swaption @ 4.5%. The pay-off profile is thus Long 5y20y Payer Swaptions at low rates and Long 5y20y Receiver Swaptions at high rates. Put call parity means it made no difference if it was implemented with receiver swaptions or with payer swaptions. 8 Nomura | Derivative Focus 4 December 2014 Fig. 10: Aged 5y pay-off of USD 5y5y20y MCCS trade 10% IRR level upper and lower range: [3.46, 5.33] and B/E level upper and lower range: [2.88, 5.87] 900 Payoff Current 5y20y Fwd % Strike 800 Terminal Value (cts) 700 600 500 10% IRR Level 400 300 B/E Level 200 100 0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 5y20y Fwd % Source: Nomura Research By combining the MCCS at several strikes, we widen the B/E range at the cost of some of the carry. In Figure 11, we show the payoff of Multi-Strike MCCS at 4%, 4.5% and 5% strikes for convenience. Fig. 11: Aged 5y pay-off of USD 5y5y20y Multi-strike MCCS 10% IRR level upper and lower range: [3.42, 5.37] and B/E level upper and lower range: [2.83, 5.91] 700 Strike 4.00% Strike 4.50% 600 Terminal Value (cts) Strike 5.00% 500 Package 400 10% IRR Level 300 B/E Level 200 100 0 0.5 1.5 2.5 3.5 4.5 5.5 Forward % 6.5 7.5 8.5 Source: Nomura Research Interestingly, the breakevens of the Multi-strike trade and the single strike trade are relatively similar. This is generally true at both higher and lower rates. This is part of the reason that the performance of the unhedged indices is similar, as we see in Figure 6. But the hedged indices perform quite differently and this can only be because hedging is effectively easier in the Multi-strike version, primarily because the gamma has been lowered considerably (we can see this primarily from the fact the pay-off has a flatter region rather than being peaked). Volatility Triangle A volatility triangle is another way to go long forward vega, short gamma and long curve carry, but with purely vanilla underlyings As vanilla approximations of MCCS trades, volatility triangles show decent carry to term. Figure 12 is the 5y P&L of USD 5y5y20y triangles, which is to go long $100mn 5y5y ATMF Straddles, long $100mn 10y20y ATMF Straddles and short $100mn 5y25y ATMF straddles for 548 cts (mid). The 5y P&L profile depends on both vol shifts and slope shifts. For USD 5y5y20y triangles, today‟s vega is 9ct/bp, which grows to approximately 20ct/bp at expiry. The sensitivity analysis on slopes shifts shows that it is a combined bull-steepener and bear-flattener. 9 Nomura | Derivative Focus 4 December 2014 Fig. 12: 5y P&L Profile of USD 5y5y20y Triangles Pay-off shows dependence of vol shifts and slope shifts 2,000 Base Vol - 10bp Base Vol Base Vol + 10bp 1,500 2,000 Slope - 10bp Constant Slope (25y-5y) Slope + 10bp 1,500 PnL(cts) 500 1,000 500 0 Parallel shifts of spot curve (bp) 200 180 160 140 120 80 100 60 40 20 0 -20 -40 -60 -80 200 180 160 140 120 80 100 60 40 0 20 -20 -40 -60 -80 -100 -120 -100 0 -500 -120 PnL(cts) 1,000 Shifts on fwd underlying the first leg (bp) Source: Nomura Research While vol triangles are similar to MCCS (i.e., the 5y5y and 5y20y options together are similar to shorting a5y5y20y midcurve), the pay-offs are in many ways much more diverse and depend on the different strikes and curve shape. We choose to only trade ATMF straddles in our vol triangles, only because this is more or less a market convention. But we can see many circumstances when, owing to changes in market correlation, butterflies will behave quite differently from an MCCS trade. Moreover, they have three separate underlying forward swaps and our experience shows we cannot use a single underlying to attempt a hedge. Forward Volatility Agreement (FVA) Forward Volatility Agreement has the simplest form of pay-offs among all these trades. It is long vega only. We consider the 5y5y20y FVA, an agreement whereby two counterparties agree to a 5y forward price to a 5y20y ATMF straddle. At exercise, the premium is exchanged for a physical settle straddle. We choose to make the straddle spot premium rather than forward premium and this induces some delta (through the PV01). The FVA trade provides a "pure" implied vol exposure. Forward vol exposure does not suffer time decay until the end of the forward period. It has no Black-Scholes delta nor gamma. Furthermore, a backwardised term-structure of forward vol yields positive carry. Fig. 13: Term structure of forward vol has been backwardised Forward vol position has positive carry. USD 5y20y spot bpvol USD 5y20y fwd bpvol 130 Basis Point Volatility 120 110 100 Positive carry 90 80 70 60 Jan-08 Jan-09 Jan-10 Jan-11 Jan-12 Jan-13 Jan-14 Jan-15 Jan-16 Jan-17 Jan-18 Jan-19 Source: Nomura Forward Volatility: What is it? Forward volatility is, as one would expect, the exposure to an asset‟s volatility at some point in the future. This exposure can be synthesised in a number of ways and, as we 10 Nomura | Derivative Focus 4 December 2014 mentioned above, it seems clear that many of our proposed forward vol products have very small vega at trade start but vega grows considerably through time. Forward vol itself can be synthesised through a combination of spot starting swaptions and midcurve swaptions of the same underlying at many different strikes. The intuition can be seen in Figure 14. Fig. 14: Forward Vol, Vanilla Vol and Midcurve Vol All three are linked Today 10 years Expiry of vanilla swaption, start of underlying swap Start of vanilla swaption Today Start of mid curve swaption 5 years Expiry of mid curve swaption Today 5 years Start of fwd strike swaption 30 years Maturity of underlying swap 10 years 30 years Start of underlying swap Maturity of underlying swap 10 years 30 years Expiry of fwd strike swaption, start of underlying swap  Maturity of underlying swap   Plain Vanilla Swaption (10y20y): Standard instrument where the strike is set at inception and the underlying swap starts on a spot basis from the option expiry date Forward Starting Swaption (Mid-curve swaption, 5y5y20y): The strike is set at inception but the underlying swap starts several years following the option expiry date Forward Strike Swaption (Forward vol agreement, 5y5y20y): The strike is only set after several years at the then ATM level, and the underlying swap starts on a spot basis from the option expiry date Source: Nomura Research Forward Volatility: Where does the carry come from? Rates forward volatility, unlike its counterparts in equities (and sometimes in FX), is generally a source of decent positive carry. In FX and Equities, forward vol is typically larger than spot vol, and in other words, a forward vol strategy would have negative carry. This effectively implies a non-stationarity to equities and FX underlyings, in line with much of historical experience. In rates, forward vol is often below spot vol. In other words, short-term spikes which may impact spot vol are effectively shrugged off by the forward vol market as being temporal. This is not true of all vols, since in the upper-left corner, the rates market prices in persistence or trending of short tenors and short forwards, and consequently the upper left (e.g., 1y, 2y tenors, 1y or 2y or shorter expiries) have negative carry. This is in line with historic experience where short rates are driven by trends in the economy and responsive policy rates, leading to, for all practical purposes, non-stationarity. Long-dated rates forward vol has positive carry. This implies that longer forward of short tenors (e.g., 5y1y, 5y2y, 5y5y) and longer tenors (5y10y, 10y10y,20y30y) have far more mean-reversion. In rates, much of the best forward vol carry is in long-tenor forward vol. Historically, long-tenor forwards (e.g., 5y20y, 10y10y) exhibit far more stability than other parts of the curve. The forward vol carry effectively prices in this historical phenomenon. 11 Nomura | Derivative Focus 4 December 2014 Appendix A-1 Analyst Certification We, Nick Firoozye, Qilong Zhang and Xiaowei Zheng, hereby certify (1) that the views expressed in this Research report accurately reflect our personal views about any or all of the subject securities or issuers referred to in this Research report, (2) no part of our compensation was, is or will be directly or indirectly related to the specific recommendations or views expressed in this Research report and (3) no part of our compensation is tied to any specific investment banking transactions performed by Nomura Securities International, Inc., Nomura International plc or any other Nomura Group company. Important Disclosures Online availability of research and conflict-of-interest disclosures Nomura research is available on www.nomuranow.com/research, Bloomberg, Capital IQ, Factset, MarkitHub, Reuters and ThomsonOne. Important disclosures may be read at http://go.nomuranow.com/research/globalresearchportal/pages/disclosures/disclosures.aspx or requested from Nomura Securities International, Inc., on 1-877-865-5752. If you have any difficulties with the website, please email [email protected] for help. The analysts responsible for preparing this report have received compensation based upon various factors including the firm's total revenues, a portion of which is generated by Investment Banking activities. Unless otherwise noted, the non-US analysts listed at the front of this report are not registered/qualified as research analysts under FINRA/NYSE rules, may not be associated persons of NSI, and may not be subject to FINRA Rule 2711 and NYSE Rule 472 restrictions on communications with covered companies, public appearances, and trading securities held by a research analyst account. Nomura Global Financial Products Inc. (“NGFP”) Nomura Derivative Products Inc. (“NDPI”) and Nomura International plc. (“NIplc”) are registered with the Commodities Futures Trading Commission and the National Futures Association (NFA) as swap dealers. NGFP, NDPI, and NIplc are generally engaged in the trading of swaps and other derivative products, any of which may be the subject of this report. ADDITIONAL DISCLOSURES REQUIRED IN THE U.S. Principal Trading: Nomura Securities International, Inc and its affiliates will usually trade as principal in the fixed income securities (or in related derivatives) that are the subject of this research report. Analyst Interactions with other Nomura Securities International, Inc. Personnel: The fixed income research analysts of Nomura Securities International, Inc and its affiliates regularly interact with sales and trading desk personnel in connection with obtaining liquidity and pricing information for their respective coverage universe. 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