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.