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6. Delta (3pts). BSM Formula for a call is C(0) = e-rT [FA(0,T)N(d) KN(D2)] = A(0)N(di) Ke-rT N(d2) One might be tempted to calculate N(d)
6. Delta (3pts). BSM Formula for a call is C(0) = e-rT [FA(0,T)N(d) KN(D2)] = A(0)N(di) Ke-rT N(d2) One might be tempted to calculate N(d) as the Delta, i.e., ac aA = N(di) = = = = However, this overlooks the fact that d1,2 are functions of FA(0,T) A(Q)eT. Calculate Delta using the Chain Rule as follows. Let F = FA(0,T) for notational convenience. Since C(0)e'T = FN(d) KN(d2) and F = " ) A(0)erT na a[FN(d) KN(d2)] ac aA ar adi ad2 N(d1) + FN'(d) af KN'(d2) OF = atical Trainique de colina y 1000 pyri 9 20 ", A QUAN S. (a) Compute the terms adi ad2 aF' aF (b) Complete the following steps and solve for Z 1 N'(d1,2) = 5d1,2 = V21 27 1 K vzd=127 V24 F (c) Using the above results, provide an expression for 8C/aA. 6. Delta (3pts). BSM Formula for a call is C(0) = e-rT [FA(0,T)N(d) KN(D2)] = A(0)N(di) Ke-rT N(d2) One might be tempted to calculate N(d) as the Delta, i.e., ac aA = N(di) = = = = However, this overlooks the fact that d1,2 are functions of FA(0,T) A(Q)eT. Calculate Delta using the Chain Rule as follows. Let F = FA(0,T) for notational convenience. Since C(0)e'T = FN(d) KN(d2) and F = " ) A(0)erT na a[FN(d) KN(d2)] ac aA ar adi ad2 N(d1) + FN'(d) af KN'(d2) OF = atical Trainique de colina y 1000 pyri 9 20 ", A QUAN S. (a) Compute the terms adi ad2 aF' aF (b) Complete the following steps and solve for Z 1 N'(d1,2) = 5d1,2 = V21 27 1 K vzd=127 V24 F (c) Using the above results, provide an expression for 8C/aA
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