lecture7 - • Solved as LP • Most lucrative arbitrage...

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e62: lecture 6 4/10/10 A Market for Contingent Claims Payoff matrix Price vector Portfolio Portfolio payoff Portfolio price 1 P ∈± M × N ρ ∈± N x ∈± N Px ∈± M ρ x ∈± e62: lecture 6 4/10/10 Replication Liabilities Replicating Portfolio Price of Replication Always possible when market is complete P has M linearly independent columns P has full row rank 2 b ∈± M Px = b ρ x e62: lecture 6 4/10/10 Super-Replication What if there is no replicating portfolio? Incomplete market Super-Replication Minimize price 3 Px b min ρ x s . t . Px b e62: lecture 6 4/10/10 Example 4 !
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e62: lecture 6 4/10/10 Redundancy Redundancy: existence of portfolio such that Price ! x ! 0 " arbitrage 5 x ± =0 Px =0 e62: lecture 6 4/10/10 Arbitrage Def. arbitrage opportunity
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Unformatted text preview: • Solved as LP • Most lucrative arbitrage opportunity • Arbitrage opportunity that makes $1 6 x ∈ ± N s . t . ρ x < 0 and Px ≥ min ρ x s . t . Px ≥ x →∞ min · · · s . t . ρ x =-1 Px ≥ e62: lecture 6 4/10/10 Minimizing Shares Traded 7 min ∑ N n =1 | x n | s . t . ρ x =-1 Px ≥ ! min ∑ N n =1 ( x + n + x-n ) s . t . ρ ( x +-x-) =-1 P ( x +-x-) ≥ x + ≥ x-≥ e62: lecture 6 4/10/10 Minimize Dollars Traded 8 min ∑ N n =1 | ρ n x n | s . t . ρ x =-1 Px ≥ ! min ρ ( x + + x-) s . t . ρ ( x +-x-) =-1 P ( x +-x-) ≥ x + ≥ x-≥...
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This note was uploaded on 07/29/2011 for the course MS&E 111 at Stanford.

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lecture7 - • Solved as LP • Most lucrative arbitrage...

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