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.
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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
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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.
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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.
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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
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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.
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Nomura | Derivative Focus
4 December 2014
Appendix A-1
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Nomura Securities International, Inc., Nomura International plc or any other Nomura Group company.
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