RIDING THE SWAPTION CURVE
Johan Duyvesteyn Gerben de Zwart
TopQuants Autumn event Amsterdam – 18 November 2015 MOTIVATION
Volatility risk is priced in swaption markets
– Negative premium: realized volatility is lower than implied volatility
– Investors are willing to pay a compensation to volatility sellers
– Supported by various research methods and many authors
Term structure across the swaption maturity spectrum
– Higher volatility risk premium for low maturities
– Very little attention in the literature
2 LITERATURE OVERVIEW
Volatility risk premium Term structure VRP
Goodman & Ho (1997) Hedging Based tests THIS STUDY Duarte, Longstaff & Yu (2007)
Almeida & Vicente (2009) Fornari (2010) Model free tests Mueller, Vedolin & Yen (2011) Fornari (2010) Merener(2012) Trolle & Schwartz (2012)
3 HEDGING-BASED TEST
Straddle refresher • Combination of call and put option • Very sensitive to changes in volatility • Risk exposures measured by Greeks: delta, gamma, vega
Hedging-based test • Isolate movement in volatility and neutralize interference from directional movement in underlying instrument • The return on buying a straddle and dynamically delta-hedging is related to the volatility risk premium (Low & Zhang, 2005)
4 THIS STUDY
We develop a novel hedging-based test to empirically examine the presence of a term structure of the volatility risk premium in the swaption market
- Long-short combinations of two at-the-money swaption straddles with different maturities - Analyse the profit/loss to examine the difference in the VRP between maturities
Short: short term Long: longer term straddle straddle 3M 6M 9M 12M premium Volatility Risk Volatility Swaption maturity
5 DATA
Sample: Four largest and most liquid swap markets
– U.S., EMU, Japan, U.K.
– Daily pricing data (swap yields, ATM implied volatilities)
– April 1996 – 2011
Data source: Bloomberg
– Cross-validation with anonymous broker
– Swaption maturities: 3, 6, 9, 12 months
– 10 year swap tenor
Black pricing model
– Either Gamma or Vega neutral straddle combinations
6 EMPIRICAL RESULTS – MAIN RESULTS
1.20% Vega neutral Gamma neutral
1.00%
0.80%
0.60%
0.40% Annualized return Annualized
0.20%
0.00% 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 US UK EMU Japan
7 SUMMARY EMPIRICAL RESULTS
Observations
• Positive returns for all markets and maturity combinations
• Majority of returns significant
• Term structure visible
The empirical results indicate
• Existence of term structure in volatility risk premium across all 4 markets
• Incrementally decreasing term structure
8 ROBUSTNESS
Additional analysis to improve the intuition
• Macro economic announcements (Fornari, 2010; Andersen et al ,2007)
• Jump risk (Branger & Schlag, 2008)
• Volatility risk (Cremers et al. 2015)
• Discrete trading (Branger & Schlag, 2008)
9 DAY-OF-THE-MONTH EFFECT
0.9%
0.8%
0.7%
0.6%
0.5%
0.4%
0.3%
0.2%
Annualized equally weighted return 0.1% 3M vs 6M 6M vs 9M 9M vs 12M 0.0% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Working day of the month (1 = first day of the month)
10 JUMP RISK
1.20% Vega neutral Vega neutral ex Jumps Gamma neutral Gamma neutral ex jumps 1.00%
0.80%
0.60%
0.40% Annualized return Annualized
0.20%
0.00% 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 US UK EMU Japan
11 VOLATILITY RISK
Vega neutral Vega neutral excluding volatility Gamma neutral Gamma neutral excluding volatility 1.60%
1.40%
1.20%
1.00%
0.80%
0.60% Annualized return Annualized 0.40%
0.20%
0.00% 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 3 vs 6 6 vs 9 9 vs 12 US UK EMU Japan
12 DISCRETE TRADING – DELTA EXPOSURE
0.80 Straddle – 3 months US swaption
0.70
0.60
0.50
0.40 Delta 0.30
0.20
0.10
0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Day after opening the straddle
* 3 months US swaption
13 DISCRETE TRADING – DELTA EXPOSURE
Delta - Gamma neutral straddle combination* 0.80 0.70
0.60 0.50 0.40 Delta 0.30
0.20 0.10 0.00 -0.10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Day after opening the straddle
* 3 and 6 months US swaptions
14 DELTA RISK EXPOSURE - VEGA NEUTRAL
Delta - Vega neutral straddle combination* 0.80 0.70 0.60 0.50 0.40
Delta 0.30 0.20 0.10 0.00 -0.10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Day after opening the straddle
* 3 and 6 months US swaptions
15 STOCHASTIC MODELS
1.40% Vasicek Black SABR
1.20%
1.00%
0.80%
0.60%
0.40%
0.20%
0.00% 3 vs 6 6 vs 9 9 vs 12 3 vs 12 16 ECONOMIC IMPORTANCE
• Transaction costs are typically not included in related literature
• Our framework enables analyzing the economic importance
Break-even bid-ask spreads (3 vs 12)
0.70 Bid-offer in volatility points gamma neutral vega neutral 0.60 mix 50/50
0.50
0.40
0.30
0.20
0.10
0.00 17 USD EUR JPY GBP EQW ECONOMIC IMPORTANCE
• Strong diversification vega neutral and gamma neutral strategies 140 Vega neutral 135 Gamma neutral 130Break-even50/50 bid-ask combination spreads (3 vs 12) 125
120
115
110
105
100
95
90
18 SUMMARY AND CONCLUSION
• First paper to provide an hedging-based framework for testing the existence of a term structure in the volatility risk premium
• Our empirical results for the swaption market
– indicate a term structure in the volatility risk premium in all 4 major swaption markets
– suggest that the term structure is affected by both jump risk and volatility risk corroborating the equity market findings of Cremers et al. (2015)
– are robust for Jump Risk, Macro Economic Announcements and discrete trading biases
• Journal of Banking and Finance, Volume 59, October 2015, Pages 57–75 http://www.sciencedirect.com/science/article/pii/S0378426615001545 19