Class Notes (808,649)
ACT370H1 (9)
Jack Pitt (9)
Lecture

January 15.docx

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School
University of Toronto St. George
Department
Actuarial Science
Course
ACT370H1
Professor
Jack Pitt
Semester
Winter

Description
January 15, 2014 Binomial pricing C Und C D P Und P D Two contribute! Portfolio A = Portfolio B assets U+V+W+X+Y = G+H+I+J ΔS – C = B “bond” Δ shares and 1 call option C = ΔS – B Ex 6 Hull At time T, Portfolio A: [Δ22-(22-21)]/U or [Δ18-0]/D Portfolio B: B*R where R = 1+r 12% continuous compounding for 3 months We want: Δ22-1 = Δ18 Δ = 1/4 Therefore, at expiration, Δ18 = 18/4 = 22/4 – 1 = 4.5 = B*R - 0.12*(3/12) B = 4.5e = 4.367005 ΔS – C = B => C = ΔS – B C = (1/4)(20) – 4.367005 = 0.632995 Ex 7 Hull (risk-neutral) We want weights P(U) = p P(D) = q so that we would be indifferent towards portfolio A or B 22p + 18q = 20e 0.12*(3/12) q = 1 – p Weighted sum E(S(T)) 4p + 18 = 20e 0.12*(3/12) p = 0.6522727 = P(U) q = 1 – p = 0.3477273 = P(D) -0.03 C(0) = [(0.6522727) max(S – U, 0) + 0.3477273 max(S – K, D)]*e = 0.6329951 Δ = ∂C/∂S or C UT) – C (D) / S UT) – S DT)
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