MODEL SETTINGS. September Part III: CVA Pricing Frameworks 1. Market im plied default probabilities. CDS spread. Ha n d e ls b a n ke n Nokia

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1 MODEL SETTINGS I C Ha n d e ls b a n ke n Nokia CDS spreads Market im plied default probabilities Ha n d e ls b a n ke n Nokia CDS spread Prob a b ility Time (years ) Time (years ) 6 Part III: CVA Pricing Frameworks 1

2 Yie ld cu rve Yie ld Tim e (ye a rs ) RECOVERY RATE R R C = R I = R = LIBOR MARKET MODEL CREDIT MODEL MODEL DEPENDENCY Part III: CVA Pricing Frameworks 2

3 ρ k, k (I, C) ρ I,C SAMPLE SIZE N s = 10 5 N s = 10 6 N s = Con ve rg e n ce of BCVA EFE De fa u lt Mod e l BCVA (EUR) Nu m b e r of s im u la tion s PRICING N s = Part III: CVA Pricing Frameworks 3

4 INTEREST RATE SWAP S = CLOSED FORM PRICING DISCOUNTED CASH FLOW APPROACH t T 1,..., T i,..., T n T 1,..., T i,..., T N T1,..., T i,..., TÑ T i L i K T i K T i S T i K T i L i(t i 1 ) T i K T j S T i = T j, K T k L k(t) T i = T k, K T j S K T k L k(t) T i = T j T i = T k. P Ñ = P (t, T N i )c i c i (1 {ci >0} P C (t, T i ) + 1 {ci <0} P I (t, T ) i ), Part III: CVA Pricing Frameworks 4

5 VARIABLE EXPOSURE APPROACH t T 1 T 1 T 2 T 1 T i 1 T i C i ( T i ) = n j=β( T i ) P ( T i, T j )K T j S N j=η( T i ) P ( T i, T j )K T jl j ( T i ), β( T i ) = k T k 1 < T i < T k η( T i ) = k T k 1 < T i < T k = = Ñ (C i ( T i )) Ñ T ( i C i (t) s C ( T i )Q( T i < τ C )1 {Ci (t)>0} + s I ( T i )Q( T ) i < τ I )1 {Ci (t)<0} + 1 Ñ 2 T ( i C i (t) s C ( T i )Q( T i 1 < τ C < T i )1 {Ci (t)>0} + s I ( T i )Q( T i 1 < τ I < T ) i )1 {Ci (t)<0}, s I (T ) s C (T ) T C i (t) T i t C i (t) = n j=β( T i ) P (t, T j )K T j S N j=η( T i ) P (t, T j)k T jl j ( T i ). Part III: CVA Pricing Frameworks 5

6 MONTE CARLO PRICING EXPECTED FUTURE EXPOSURE APPROACH N (1 R) ( t i ) (Q(τ t i ) Q(τ t i 1 )), (1 R C ) N ( t i )Q(τ I > t i ) (Q(τ C t i ) Q(τ C t i 1 )) (1 R I ) N ( t i )Q(τ C > t i ) (Q(τ I t i ) Q(τ I t i 1 )), t i = (t i 1 +t i )/2 (t i ) 1 N s (t i ) 1 N s V (0, T ) = v 0. N s j=1 N s j=1 D j (0, t i )(V j (t i, T )) +, D j (0, t i )( V j (t i, T )) +, DEFAULT MODEL APPROACH ( 1 N s N ) 1 N {ti 1 <τ j t i }(1 R)D j (0, t i )(V j ( t i, T )) +, s 1 N s j=1 N s j=1 1 N s ( N ) 1 {ti 1 <τ j C t i,τ j C <τ j I } (1 R C)D j (0, t i )(V j ( t i, T )) + N s ( N ) 1 {ti 1 <τ j I t i,τ j I <τ C} j (1 R I)D j (0, t i )( V j ( t i, T )) +, j=1 Part III: CVA Pricing Frameworks 6

7 t i = (t i 1 + t i )/2 RESULTS ρ I = ρ C = ρ I,C = 0 PROJECTED CASH FLOWS T 1 = 0.5 T 2 = 1 T 3 = 1.5 T 4 = 2 T 5 = T 6 = 3 T 7 = 3.5 T 8 = 4 T 9 = 4.5 T 10 = RECEIVER SWAP Part III: CVA Pricing Frameworks 7

8 Re ce ive r s wa p EPE ENE Expsoure (EUR) Tim e (ye a rs ) T 1 = 0.5 T 1 = Part III: CVA Pricing Frameworks 8

9 DEPENDENCIES IN THE DEFAULT MODEL APPROACH ρ C < 0 (ρ C > 0) ρ I > 0 (ρ I < 0) ρ I ρ C ρ I,C ρ I,C > 0.9 Part III: CVA Pricing Frameworks 9

10 SUMMARY Part III: CVA Pricing Frameworks 10

11 REFERENCES Part III: CVA Pricing Frameworks 11

12 CONTACT US FREDRIK DAVÉUS +46(0) DAG UTTERBORN +46(0) DISCLAIMER Part III: CVA Pricing Frameworks 12