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January 27.docx

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Actuarial Science
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Jack Pitt

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January 27, 2014 p.362 McD (50.071e 0.08– 5) * e+-0.03/√3 Arbitrage - Mismatch in pricing - Creating an opportunity for profit (free money) - Risk-free is not necessarily part of arbitrage - Arbitrageurs Risk-free vs. risk-neutral A: Au or Ad B: Bu guaranteed C: Cu or 0 B has certainty -> “risk-free” (minimal risk) FV(B) = Bu FV(A) = pAu + qAd The market should price A and B to be equivalent Risk-averse investor would prefer B Risk-neutral is indifferent between A and B Risk-free: q = 0 Risk-neutral: PV(A) = PV(B) Portfolios: aA = bB + cC a, b, c are weights (quantities) of A, B, C p, q, u, d – these are different for A, B, C A,B,C also have different applicable rates A: e , α = stock rate rh B: e , r = risk-free rate C: e , γ = call option rate (McD notation) Call option: C = e -γh[ Cu(e – d)/(u – d) + C (ud– e )/(u – d) ] γ = option discount (e – d)/(u – d) = prob that the stock goes to the up event (u –
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