lecture05

# lecture05 - Pricing in a binomial world Iniesta Lecture 5...

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Pricing in a binomial world Iniesta Lecture 5 - Risk-neutral probabilities BUSI 588, Fall 2011 Diego Garc´ ıa Kenan-Flagler Business School UNC at Chapel Hill September 12th, 2011 c ± Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 5 - Risk-neutral probabilities 1 / 21 Pricing in a binomial world Iniesta Outline and handouts 1 Pricing in a binomial world A no-arbitrage theory An example 2 Iniesta Binomial pricing Trinomial trees Handouts today: Class slides. Case 5 solutions (Iniesta). c ± Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 5 - Risk-neutral probabilities 2 / 21

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Pricing in a binomial world Iniesta Where are we? Static trades: Put-call parity C - P = S - K (1 + r f ) T Bull and butterﬂy spread relations C ( K 1 ) - C ( K 2 ) < ( K 2 - K 1 ) (1 + r f ) T C ( K 2 ) < 1 2 [ C ( K 1 ) + C ( K 3 )] . Non optimality of exercise of calls on non-divident paying stocks. Futures pricing F t = S t (1 + r f ) T - t Today we transition between static and dynamic arbitrage strategies. c ± Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 5 - Risk-neutral probabilities 3 / 21 Pricing in a binomial world Iniesta A binomial world Only two things can happen at one point in time: high returns ( u -state) or low returns ( d -state). ± ± ± ± ±* H H H H Hj uS dS S ± ± ± ± ± * H H H H H j Br Br B Note: u , d and r are “1 plus rate of return.” c ± Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 5 - Risk-neutral probabilities 4 / 21
Pricing in a binomial world Iniesta The basic idea In a binomial world we have made lots of assumptions already. We know the values of two diﬀerent assets. Only two diﬀerent things can happen. This is enough to price any security using a no-arbitrage argument. Look for “synthetic (or replicating) portfolio.” Do risk-neutral pricing. c ± Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 5 - Risk-neutral probabilities 5 / 21 Pricing in a binomial world Iniesta State prices Can we ﬁnd what is the value of a security that gives \$1 in the up state, nothing in the down state? Let synthetic portfolio have Δ units of stock and B in bonds. Δ uS + Br = 1 Δ dS + Br = 0 So Δ = 1 S ( u - d ) ; B = - d r ( u - d ) Cost of replicating portfolio Δ S + B = r - d r ( u - d ) c ± Diego Garc´ ıa, BUSI 588, Kenan-Flagler, Fall 2011 Lecture 5 - Risk-neutral probabilities 6 / 21

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Pricing in a binomial world Iniesta First punchline We can price via no arbitrage a security that gives \$1 in the up
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## This note was uploaded on 11/25/2011 for the course BUSI 588 taught by Professor Staff during the Fall '10 term at UNC.

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lecture05 - Pricing in a binomial world Iniesta Lecture 5...

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