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ACT370H1 (9)
Jack Pitt (9)
Lecture

February 5.docx

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Department
Actuarial Science
Course
ACT370H1
Professor
Jack Pitt
Semester
Winter

Description
February 5, 2014 r δ currency rd rf futures r r commodities r lease bonds r coupon rate (≠ bond yield) u = e (r-δ)h + σ√h We saw rh u = e (this form) |r – r|f 0.01 d2= d –1σ√T d2< d c1rrection -rT C = S N(d ) 1 Ke N(d 2 N(d 1 = Δ B = ΔS – C Δ = ∂Π/∂S delta hedging C = ΔS – B N(d 2 is probability that the option will expire in the money lognormal distribution and Brownian motion linear combination of normals If A ~ N(µ A σ A and B ~ N(µ , σ )B B2 C = aA + bB also has a normal distribution µ = aµ + bµ C A B If Y ~ lognormal and Z ~ lognormal W = YZ also has a lognormal distribution If X ~ N(µ, σ ), then Y = e is lognormal 2 µ Y exp(µ + X /2) X σ Y exp(σ – 1)X* exp(2µ + σ ) X X2 Var(X) = E(X ) – E(X) 2 2 2 2 σ Y exp(σ – 1X * µ Y σ Y exp(σ )µ X µ Y2 Y2 2 2 like E(Y ) – E(Y) d < R < u R = 1 + r R(t) = ln(S t S 0 Used to develop Black-Scholes solutions R(t) S(t) = S 0 ~ lognormal R ~ normal Ex 14 (McD) T = ¼ year (3 months) S = 41 K = 40 σ = 30% r = 0.08 δ = 0 (no dividends) d1= [ln(41/40) + (0.08 + 0.3 /2) ¼] / (0.3 √¼) = 0.37295 d2= d –10.3 √¼ = 0.22295 N(d 1 = 0.645407 N(d 2 = 0.588213 C = 41 N(d )1– 40e -0.08N(d 2 = 3.3991 Ex 15 (McD) – Related put -rT -δT P = Ke N(-d 2 – Se N(-d 1 N(-d 1 = 0.354593 N(-d 2 = 0.411787 P = 40e -0.08N(-d 2 – 41 N(-d )1= 1.6070 Check work using call-put parity: (could use this instead of B-S to find P) P = C + Kv
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