Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion The impact of counterparty risk and collateralization on longevity swaps Enrico Biffis Imperial College London & Pensions Institute David Blake Cass Business School & Pensions Institute Lorenzo Pitotti Imperial College London & Algorithmics Ariel Sun Risk Management Solutions Paris - February 3, 2011 1/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Agenda 1 Motivation 2 Counterparty risk 3 Bilateral default risk 4 Collateralization 5 Examples 6 Conclusion 2/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Agenda 1 Motivation 2 Counterparty risk 3 Bilateral default risk 4 Collateralization 5 Examples 6 Conclusion 3/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Recent transactions Date Hedger Size Term (yrs) Type Interm./supplier Jan 08 Lucida Not disclosed 10 indexed JPM ILS funds Jul 2008 Canada Life GBP 500m 40 indemnity JPM ILS funds Feb 2009 Abbey Life GBP 1.5bn run-off indemnity DB ILS funds Partner Re Mar 2009 Aviva GBP 475m 10 indemnity RBS Jun 2009 Babcock GBP 750m 50 indemnity Credit Suisse International Pacific Life Re Jul 2009 RSA GBP 1.9bn run-off indemnity GS (Rothesay Life) Dec 2009 Berkshire GBP 750m run-off indemnity Swiss Re Council Feb 2010 BMW UK GBP 3bn run-off indemnity DB Paternoster Dec 2010 Swiss Re US 50m 8 indexed ILS funds (Kortis bond) Feb 2011 Pall GBP 70m 10 indexed JPM Pension Fund 4/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Motivation Hedgers’ concerns • longevity swaps introduce credit risk to a counterparty • Global Financial Crisis and tighter regulation of OTC transactions Other markets: interest-rate swaps (IRSs) for example • almost every swap bilaterally collateralized • cash collateral in over 90% of the cases • collateral thresholds based on credit ratings, CDS spreads, etc. Questions • insurance ( indemnity ) vs. capital markets ( value ) paradigm • to what extent does collateralization reduce pooling/diversification benefits traditionally used as substitute for credit enhancement? • how does impact of collateral costs compare with interest-rate swaps? • longevity swap pricing with bilateral default risk and collateral 5/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Indemnity-based longevity swaps Stylized example: single payment at time T • notional n , fixed payment p • variable payment S T (realized survival rate) n × p Party A Party B (hedger) (hedge supplier) n × S T 6/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Indemnity-based longevity swaps Stylized example: single payment at time T • notional n , fixed payment p • variable payment S T (realized survival rate) n × p Party A Party B (hedger) (hedge supplier) n × S T Swap value (hedger’s viewpoint) � T � � � � V 0 = nE Q exp − r t d t ( S T − p ) 0 6/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Indemnity-based longevity swaps Stylized example: single payment at time T • notional n , fixed payment p • variable payment S T (realized survival rate) n × p Party A Party B (hedger) (hedge supplier) n × S T Longevity swap rate � T Cov Q � � � � exp − 0 r t d t , S T p = E Q [ S T ] + � T � � �� E Q exp 0 r t d t − 6/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Indemnity-based longevity swaps Stylized example: single payment at time T • notional n , fixed payment p • variable payment S T (realized survival rate) n × p Party A Party B (hedger) (hedge supplier) n × S T Longevity swap rate p = E Q [ S T ] + 0 6/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Indemnity-based longevity swaps Stylized example: single payment at time T • notional n , fixed payment p • variable payment S T (realized survival rate) n × p Party A Party B (hedger) (hedge supplier) n × S T Longevity swap rate p = E Q [ S T ] + 0 We focus on baseline swap rate p = E P [ S T ] . 6/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Agenda 1 Motivation 2 Counterparty risk 3 Bilateral default risk 4 Collateralization 5 Examples 6 Conclusion 7/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Case study UK-based hedger • 10,000 individuals (England & Wales) aged 65 in 1980 • indemnity-based solution over 1980 − 2005 • interest risk hedged away Realized cashflows • population evolves as in Human Mortality Database (HMD) � � � � • cashflow hedge in operation: realized rate − swap rate Marking to market (MTM) • assume swap rates coincide with Lee-Carter forecasts based on most recent HMD information available • allow for mortality experience/counterparty risk 8/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Cashflows and marking-to-market 1200 CFs MTM 1000 800 GBP 600 400 200 0 1980 1985 1990 1995 2000 2005 year 9/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Longevity swap rates 1 0.98 0.96 0.94 0.92 LC forecast 0.9 0.88 0.86 0.84 0.82 0.8 1980 1985 1990 1995 2000 2005 year 10/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Hedge supplier’s credit deterioration 1000 500 0 −500 GBP −1000 −1500 CFs MTM −2000 MTM + 50bps MTM + 25bps −2500 1980 1985 1990 1995 2000 2005 year 11/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Agenda 1 Motivation 2 Counterparty risk 3 Bilateral default risk 4 Collateralization 5 Examples 6 Conclusion 12/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Bilateral default risk Counterparty risk is bilateral • if the hedger is a pension plan... ⋆ sponsor’s covenant (“ability and willingness of the sponsor to pay sufficient advance contributions to ensure that the scheme’s benefits can be paid as they fall due”) in the UK ⋆ use/extrapolate spreads in credit/CDS market ⋆ analyze funding level/strategy of the scheme Need to allow for credit enhancement tools • termination rights (credit puts, break clauses, etc.) • collateralization (posting of cash/securities) Need to allow for MTM and costs accruing from MTM procedure 13/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Valuation • hedger’s viewpoint, unitary notional ( n = 1 ) • default intensities ( λ A t ) t ≥ 0 , ( λ B t ) t ≥ 0 • ψ A , ψ B ∈ [0 , 1] recovery rates upon default of the counterparty • swap’s market value (e.g., Duffie/Huang, 1996) � T � � � � S T − p d �� V 0 = E Q exp − ( r t + Λ t ) d t 0 Λ t := 1 { V t < 0 } (1 − ψ A ) λ A t + 1 { V t ≥ 0 } (1 − ψ B ) λ B t . 14/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Valuation • hedger’s viewpoint, unitary notional ( n = 1 ) • default intensities ( λ A t ) t ≥ 0 , ( λ B t ) t ≥ 0 • ψ A , ψ B ∈ [0 , 1] recovery rates upon default of the counterparty • swap’s market value (e.g., Duffie/Huang, 1996) � T � � � � S T − p d �� V 0 = E Q exp − ( r t + Λ t ) d t 0 Λ t := 1 { V t < 0 } (1 − ψ A ) λ A t + 1 { V t ≥ 0 } (1 − ψ B ) λ B t . • swap rate � T Cov Q � � � � exp − 0 ( r t + Λ t ) d t , S T p d = E P [ S T ] + ≤ E P [ S T ] � T � � �� E Q exp − 0 ( r t + Λ t ) d t 14/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Valuation • hedger’s viewpoint, unitary notional ( n = 1 ) • full recovery: ψ A = ψ B = 1 • swap’s market value � T � � � � P − p d �� V 0 = E Q exp − r t d t 0 • swap rate � T Cov Q � � � � exp − 0 r t d t , S T p d = E P [ S T ] + ≤ E P [ S T ] � T � � �� E Q exp − 0 r t d t 15/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Valuation • hedger’s viewpoint, unitary notional ( n = 1 ) • full recovery: ψ A = ψ B = 1 • swap’s market value � T � � � � P − p d �� V 0 = E Q exp − r t d t 0 • swap rate � T Cov Q � � � � exp − 0 r t d t , S T p d = E P [ S T ] + ≤ E P [ S T ] � T � � �� E Q exp − 0 r t d t Where is the flaw? • credit enhancement can make ψ A , ψ B close to 1 , but can’t be costless! • focus on costs accruing from MTM procedure (e.g., Johannes/Sundaresan, 2007) 15/28
Motivation Counterparty risk Bilateral default risk Collateralization Examples Conclusion Agenda 1 Motivation 2 Counterparty risk 3 Bilateral default risk 4 Collateralization 5 Examples 6 Conclusion 16/28
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