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ACT370H1 (9)
Jack Pitt (9)
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February 3.docx

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Department
Actuarial Science
Course
ACT370H1
Professor
Jack Pitt
Semester
Winter

Description
February 3, 2014 Binomial -> normal The binomial distribution tends to a normal distribution as n->∞ The normal approximation of the binomial k n-k Because for large n, P(k|n) = (nCk) p q is hard to compute For binomial payoff = 1, 0 failure, 1 success n = number of trials p = prob of success q = prob of failure mean = np variance = npq Lognormal 2 Suppose r have some returns r ~ N(µ, σ ) Then e has a lognormal distribution - e > 0 - not symmetrical (even if r is) - r ~ N(µ, σ )2 r 2 2 2 - e ~ lognormal(exp[µ+σ /2], exp[(σ /2-1)exp(2µ+σ )]) - median for e is e µ Black-Scholes partial differential equation model for option pricing S 1 2 ln( )+(r–δ+ σ )T d = K 2 1 σ T √ d2=d −1 T √ S = current stock price K = strike price T = time unti
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