Question 1. Understanding market completeness/incompleteness. There are four assets and four states: where k is a real number. a₁ = [10-k 40-4k 0 0]' 81₂ = 0 2+2K 2+ +24]' [10 40-4k 0 0]' nj 0 1 + k 11+2k]' aj 1 (a) Write the payoff matrix A(), for general k. (b) For what values of k is the market complete? (c) Consider the payoff b) = [11+k4 1+k 11+2k]'. For what values of k can this payoff be hedged perfectly (i.e., with no hedging error)?

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
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Question 1. Understanding market completeness/incompleteness.
There are four assets and four states:
a, = [10 - k 40- 4k 0 0)'
%3D
n2 = [0 0 2+ 2k: 2 + 2k]
[10 40 – 4k 0 0'
n, = [0 0 1+ k 11 + 2k]'
where k is a rcal number.
(n) Write the payoff matrix A4), for general k.
(b) For what values of k is the market complete?
(c) Consider the payoff
b4) = [11+k 4 1+k 11+ 2k]'.
%3D
For what values of k can this payoff be hedged perfectly (i.e., with no hedging
error)?
Transcribed Image Text:Question 1. Understanding market completeness/incompleteness. There are four assets and four states: a, = [10 - k 40- 4k 0 0)' %3D n2 = [0 0 2+ 2k: 2 + 2k] [10 40 – 4k 0 0' n, = [0 0 1+ k 11 + 2k]' where k is a rcal number. (n) Write the payoff matrix A4), for general k. (b) For what values of k is the market complete? (c) Consider the payoff b4) = [11+k 4 1+k 11+ 2k]'. %3D For what values of k can this payoff be hedged perfectly (i.e., with no hedging error)?
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