Derivatives ppt @ mab finance

1. Derivatives

8. Risk Transfer and Reduction Accept Transfer Insure: indemnity, guarantee, options Hedge On Balance Sheet (Operational) Off Balance Sheet (Financial) Assess

75. The Formula for a Call C = U 0 N(d 1 ) – Ke -r(T-t) N(d 2 ) where σ √ (T – t) σ √ (T – t) ln + [r + ] (T – t) ln + [r – ] (T – t) d 1 = U 0 K d 2 = U 0 K σ 2 2 σ 2 2 Note that the only difference between the d 1 and d 2 formulae is in this sign. Therefore, d 2 = d 1 – σ 2 (T – t) σ √ (T – t) = d 1 – σ √ (T – t)

86. Sensitivity Summary Every option is a race between gamma and theta. Position Delta Gamma Theta Rho Vega Long call + + - + + Long put - + - - + Short call - - + - - Short put + - + + -

135. Calculating Duration, 2 (1 + r t ) n+1 – (1 + r t ) – (r t x n) 100 x n r t 2 (1 + r t ) n (1 + r t ) n Duration = PV ] + C [ coupons principal PV i = C [ ] + 100 (1 + r i ) n r i 1 - (1 + r i ) n 1

139. Modified Duration, 3 CF 1 n(100 - ) r i 2 (1 + r i ) n (1 + r i ) n+1 [ 1 - ] + CF r i m.d. = PV

142. Convexity, 2 2 x CF 1 2 x CF x n n(n + 1)(100 – [ ]) (r i ) 3 (1 + r i ) n r i 2 (1 + r i ) n+1 (1 + r i ) n+2 [ 1 - ] ­ + Convexity = CF r i 2 x PV This term = 0 when trading at par