Equity-Based Insurance Guarantees Conference November 18-19, 2013. Atlanta, GA

Equity-Based Insurance Guarantees Conference November 18-19, 2013 Atlanta, GA Equities/Rates Hybrid Derivatives: New Ways to Manage VA Risks and Opportunities in the Current Market Mohamed El-Hioum

Equities/Rates Hybrid Derivatives es New ways to manage VA risks and opportunities in the current market Mohamed El Hioum, CFA Director, Equities Structuring Group Deutsche Bank Securities Equity Based Insurance Guarantee Conference (Atlanta) 18 November 2013 (0925 1010 Hours) 1

Contents Rates-Equity Hybrids Market Overview New Products, New Risks Long-Term View on Rates-Equities Correlation Regimes Regimes Implication on Hedging and New Products 2 2 2

Rates-Equity Hybrids Market Overview 3 3 3

Rates-Equity Hybrids Market Overview Market Participants i and Transactions The hybrids market allows participants to efficiently express views or hedge exposure related to both equities and rates positions Transactions typically entail the purchase of conditional swaps, forwards or options, such as: Receiver swaps where notionals scale up as Equities fall SPX puts where notionals scale up as rates fall to hedge insurance liabilities SPX calls contingent on lower rates to express a risk-on mode supported by the Fed QE program SPX puts contingent on higher rates / payer swaptions contingent on lower SPX as tail risk protection The hybrids market has grown substantially since 2008, as asset classes have become more inter-related and attention to downside protection has increased. Market participants include: Insurance companies variable annuity hedging Asset managers multi-asset portfolio tail-risk protection Hedge funds leveraged market expressions, trading of correlation Pensions multi-asset risk factor allocations 4 4 4

Equities-Rates Correlation Market Historical i Rates / Equities Levels Historical i Equities / Rates Correlation SPX vs 10y Swap Rate Correlation Pricing Considerations Correl Swap Market Realized Correl Taking advantage of high correlations Expiry Bid Offer 1y 15 30 2y 18 33 3y 20 35 5y 22 37 10y 25 41 Term Correl 1m -35% 3m 6% 6m 23% Long-term correlation is quite elevated compared to recent realized volatility. Term structure of correlation is relatively steep, reflecting the cost of the premia Correlation skew As the correlation market gets more and more liquid the sensitivity to strike becomes more apparent 1y 40% Equity downside strikes would command higher h implied correlation than ATMs Source: Deutsche Bank Past performance, simulated or actual, is not a reliable indicator of future results 5 5 5

Rates Exposure in Equity Puts Equities Puts carry interest sensitivity through: Forward: Lower terminal interest rates lower the forward - e.g. a 1% decrease in interest rates increases the option premium by approximately Delta * Tenor * 1% Discounting : The higher the interest rate, the lower the premium paid the duration of the premium is equal to the tenor of the option Balance sheet and CSA considerations add additional rates and currencies correlation exposures to even the simplest put payoff CSA/Discount Eq/Ir Covar Rates Volatility Net Put Price Equity Volatility 6 6 6

Rates Slider Equity Put Current Environment We consider 10-year S&P at-the-money put options with a notional sliding from 0 if 10y USD swaps at maturity are at least 100bps greater than current 10y USD swaps to 100% if swaps at maturity are at least 100bps less than current 10y USD swaps Equity volatility has revisited pre-crisis lows, lowering prices for both vanilla and slider options USD rates duration premium has increased substantially recently, cheapening slider strikes that reference spot swap levels by pushing them further out-of-the-money This has lowered the ratio of the price of a slider option to the price of its underlying vanilla option 40% 35% Tenor Underlyings 10 years SPX Index 10 year USD Swap Rate (ISDAFIX 3) 30% Payoff Scaler x Max [0, ( 1 SPX Final / SPX Initial) ] SPX Initial 1765 25% Scaler Min [ Leverage, Max { 0, Leverage x (High Strike 10y USD swap rate at expiry) / (High Strike Low Strike) } ] 20% Leverage 200.0% 15% Vanilla Low Strike 1.72% High Strike 3.72% Slider 10% Jan 12 Apr 12 Jul 12 Oct 12 Jan 13 Apr 13 Jul 13 Indicative Offer 16.0% References SPX Index: 1765; Vanilla 1765 S&P Put: 23.7%; 10y USD swap: 2.72%; 10y forward 10y USD swap: 4.74% Historical pricing of an at-the-money S&P put option with notional sliding from 0 if 10-year USD swaps at maturity are at least100bps greater than spot 10- year USD swaps to 100% if 10-year USD swaps at maturity are at least 100bps less than spot 10-year USD swaps. The notional is linearly interpolated for intermediate swap levels. Pricing assumes a constant S&P-rates correlation. Source: DB. Historical pricing as of 05-Novermber-2013 7 7 7

Slider vs. Vanilla Ratio Ratio Sensitivity to Implied Volatility Sensitivities All else held constant, lower volatility increases the ratio with an inflexion point at about.75. Yet the ratio has been decreasing while volatility was dropping. 30% 25% 120% 100% 20% 80% 15% 60% 10% 40% 5% Slider/Vanilla Ratio 20% SPX 5y ATM Implied Vol 0% 0% Jan 12 Apr 12 Jul 12 Oct 12 Jan 13 Apr 13 Jul 13 Oct 13 S&P Delta 26% vs. 35% S&P Vega Rho Correlation Slider vs. Vanilla 59 bps vs. 89bps per 1 point increase in S&P implied volatility 8 bps vs. 5bps per 1 bp drop across the rates curve 7 bps per 1 point increase in SPX USD Rates Correlation Interest Rate Term Structure Term Structure Steepness vs. Ratio The recent decrease in the ratio between the slider and the vanilla has been the result of steepening term structure. 4.0 3.5 30 3.0 2.5 2.0 1.5 1.0 0.5 0.0 120% 3% 01 Nov 13 01 May 13 100% 2% 01 Nov 12 80% 2% 60% 1% 40% 20% Slider/Vanilla Ratio 1% Frwd Spot Spread 1y 5y 10y 20y 30y 0% 0% Jan 12 Apr 12 Jul 12 Oct 12 Jan 13 Apr 13 Jul 13 Oct 13 Source: Deutsche Bank Past performance, simulated or actual, is not a reliable indicator of future results 8 8 8 8

Hybrid Options - Pricing Considerations Assessing transaction size and risks Significant sizes for hybrid markets would be roughly 25% of significant sizes for the vanilla rates/equities markets The hybrid structure impacts liquidity in terms of pin risk, tail risk, replicating instruments and correlation sensitivity Pin risk, where the payout is either zero or one, becomes a concern if the asset trades near the strike close to expiry, consider using smoother payoffs The ease of replication increases the liquidity of the product; consider using zero coupon bonds payoffs vs. rates caps and floors or even swaps Correlation sensitivity limits the size to be traded, pure correlation swaps can not be traded in very large size Other ways to increase liquidity Limiting the maximum payout on the digital by trading option spreads rather than outright vanilla options helps cap the size of the digital and manage the pin risk Spreading the risk across several expiries is another way to mitigate pin risk and improve liquidity and pricing Correlation Market Correlation market transparency keeps improving; we started to see tighter pricing on correlation term structure and smile The improved transparency allows for competitive pricing both on the way in and on the way out 9 9 9

New Products, New Risks 10 10 10

Traditional Variable Annuities Products Rates and dequities ii Sensitivities ii ii Traditional Variable Annuity riders typically increase in value as rates and equities drop The sensitivity to rates depends on the rider elected and the level of the guarantee higher guaranteed income or roll ups increase that sensitivity The sensitivity to equities depends on the equity allocation, the minimum guarantees, roll ups and ratchets Guarantees Risks 0% 10% 10% 20% 20% 30% 30% 40% 40% 50% 50% 60% 60% 70% 70% 80% Guarantees Risks 0% 5% 5% 10% 10% 15% 15% 20% 20% 25% 25% 30% 30% 35% 35% 40% 40% 45% 45% 50% 80% 50% 45% 70% 40% 60% 35% 30% 50% 25% 40% 20% 15% 30% 10% 5% 20% 0% 10% 0% 5.00% 0.00% 5.00% Volatility 10.00% 40.0% 60.0% 80.0% 100.0% 120.0% 140.0% 160.0% 180.0% 200.0% 220.0% Equities 40.0% 70.0% 100.0% 130.0% Equities 160.0% 190.0% 220.0% 2.00% 1.00% 0.00% Rates 1.00% The charts above show the different forecasted values of policies with riders that include high roll ups and ratchets vs. basic policies with no riders Source: Deutsche Bank 11 11 11

Variable Annuities De-Risking New Products Features Since the financial crisis, insurers have had to raise fees, reduce benefits, and impose restrictions New products include many features that control for cost of hedging; such as volatility-controlled underlying funds, volatility indexed fees, treasury indexed benefits VA Guaranteed Benefits at Height of Arms Race Current Benefit Attributes Rider Type Base Growth Levels Fee Ranges Base Growth Levels Fee Ranges GMDB Annual, quarterly, monthly, daily ratchets, rollups of 5% to 7% 0.05% to 0.85% Most are now annual ratchets, only a few daily, quarterly; rollups are no more than 5% 0.05% to 1.15% GMWB Annual, 5 year, 3 year ratchets 0.40% to 0.85% Very few ratchets now. 0.10% to 1.20% GLWB Annual, quarterly, monthly, daily ratchets, rollups of 5% to 10% 0.30% to 1.25% Most rollups are 5%, just a few at 7%; limited daily ratchet 0.70% to 2.35% GMIB Annual, quarterly, monthly, daily ratchets, rollups of 5% to 7% 0.50% to 0.80% Most have been closed completely; rollups are 5% (Met recently went to 4%); some rollups tied to 10 year Treasury 0.50% to 1.10% GMAB Annual, 5 year, 3 year ratchets 0.25% to 0.85% Much fewer of these riders available and few ratchets. 0.45% to 1.15% Source: Soleares Research 12 12 12

Variable Annuities: Hedging the correlation risk Rates-Equities i Correlation The volatility control feature of many products reduced the vega and gamma costs of hedging these riders but still keeps the same cross correlation sensitivity, if not increased sensitivity to equities-rates correlation One way to source that correlation is through hybrid options on volatility controlled indices Tenor 5 years Underlyings SPXT10UE Index 10 year USD Swap Rate (ISDAFIX 3) Payoff Scaler x Max [0, ( 1 SPX Final / SPX Initial) ] SPX Initial 1755 Scaler Min [ Leverage, Max { 0, Leverage x (High Strike 10y USD swap rate at expiry) / (High Strike Low Strike) } ] Leverage 200.0% Low Strike 1.72% High Strike 3.72% Indicative Offer 9.0% References SPX Index: 1755; Vanilla 1755 S&P Put: 18.65%; 10y USD swap: 2.72%; 5y forward 10y USD swap: 4.35% Vanilla Vol Controlled S&P Delta 0.29 0.52 S&P Vega 59bps None DV01 12bps 7bps Correlation 7bps 4bps 13 13 13

Long-Term View on Rates- Equities Correlation Regimes 14 14 14

Volatility and Correlation Regimes: Framework The framework should be able to answer the following questions: What is the probability of being in a given regime currently? What was the probability of being in a given regime at a historical point (say, in July 2007), leading up to or after an event? What is the probability that an entire stream of observed returns was produced by a given volatility regime? A systematic regime-based strategy (hedging or asset-allocation scheme) will likely be based on a period of observations, not just a single day s snapshot of regime probabilities Model-fitting The calibration produces the model that would have generated the historical returns with the highest likelihood Assumptions 3 distributions 1 transition matrix Data S&P 500 daily totalreturns 62 13 10-year US Treasury rate changes 62-13 Maximum Likelihood Estimation Results 3 regime-specific ifi distributions 3 x 3 transition-probability matrix 15 15 15

Volatility and Correlation Regimes The resulting historical probabilities of being in either high-, low-, or medium-volatility regimes are shown below. high vol regime low vol regime SPX (log) Rates 1.000 0.900 0.800 0.700 0.600 500 0.500 0.400 0.300 0.200 0.100 0.000 50 Jan 62 Jan 65 Jan 68 Jan 71 Jan 74 Jan 77 Jan 80 Jan 83 Jan 86 Jan 89 Jan 92 Jan 95 Jan 98 Jan 01 Jan 04 Jan 07 Jan 10 Jan 13 16 16 16

Implied Volatility and Correlation Regimes Over a third of the time period since 1960 has seen the market in a low-volatility regime, where equities rally and long term rates trend mildly upward, while daily correlation is highly negative Over 50% of the period has experienced a medium-volatility regime, where equities tend to sell off mildly and rates stay relatively flat, with daily rates and equities returns staying negative 7% of the time has seen the volatility/correlation regime shift aggressively to a high-volatility regime where both equities and rates volatility realize negative trends and positive correlation Expected likelihood low medium high 34.87% 57.82% 7.32% Annualized Returns low medium high 20.95% 2.47% 15.79% 0.19% 0.06% 2.22% Covariance Matrices Low Medium High 7.43% 15.73% 42.84% 12.86% 0.40% 8.49% 1.11% 6.32% 2.83% 17 17 17

Implication For Hedgers And New Products 18 18 18

VA Hedging and EIA Products VA Hedging Volatility is contagious besides delta hedging, buy volatility to hedge against a high-volatility regime Use conditionality to target your hedge and cheapen downside protection Sell upside correlation to cheapen downside hedges Consider relative value strategies between different sources of risk Use rates, equities, credit and currencies for hedging EIA Products Buy volatility-controlled indices capped with vanilla calls 1Y, 1.5% premium, call spread: ATM call on SPXT5UE and cap call on SPX@110.2% cap strike 5Y, 6.0% premium, call spread: ATM call on SPXT5UE Consider upside through timer options 1y, 5% target vol budget 2.45% offer Buy equity upside conditional on rates staying within a range 50 to 60% discount on the vanilla prices Consider caps relative to interest rate levels 19 19 19

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