# L4v(1)-1 - ECON 3107 Lecture 4 Valuation Completing the...

This preview shows pages 1–6. Sign up to view the full content.

ECON 3107 Lecture 4: Valuation Completing the Markets Multiple Times Valentyn Panchenko

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Completing the Market Consider an example. Markets are incomplete: Q ( 3 × 2 ) = 20 43 20 28 20 28 Bond Stock Good Weather Fair Weather Bad Weather p S ( 1 × 2 ) = ( 19 35 ) Bond Stock Suppose that an investor asks an investment ﬁrm to create a product with the following payment: c ( 3 × 1 ) = 40 30 20 Good Weather Fair Weather Bad Weather The Questions: How to do it? What should the ﬁrm charge?
Completing the Markets I The Problem: No matter how many bond and stock are chosen, the payments in the ”Fair Weather” state and the ”Bad Weather” state will be the same! I Suppose the ﬁrm will select 40 in ’GW’ and 30 in ’FW’ or ’BW’ to cover all outﬂows. Markets are suﬃciently complete to do it: Q ( 2 × 2 ) = ± 20 43 20 28 ² Bond Stock Good W. Fair or Bad W. c ( 2 × 1 ) = ± 40 30 ² Good W. Fair or Bad W. n = Q - 1 · c = ± 20 43 20 28 ² - 1 ± 40 30 ² = ± 0.566 67 0.666 67 ² Bond Stock p = p S · n = ( 19 35 ) ± 0.566 67 0.666 67 ² = 34. 10

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Completing the Markets I It costs 34.10 PA to purchase a portfolio, n , that would cover all future outﬂows: I The ﬁrm will receive 10 in ’BW’ state; I Investor will be assured to receive all the promised payments. I Since 10 BA equals to 3.9 PA, the ﬁrm will be happy to sell the product for 34.10PA. What if it oﬀers the product for 32PA? Q ( 3 × 3 ) = 20 43 40 20 28 30 20 28 20 Bond Stock Product Good W. Fair W. Bad W. p S ( 1 × 3 ) = ( 19 35 32 ) Bond Stock Product p atom = p S · Q - 1 = ( 19 35 32 ) 20 43 40 20 28 30 20 28 20 - 1 = ( 0.56 0.18 0.21 ) Good W. Fair W . Bad W.
Hedging at Minimum Cost Recall our original example. Market are incomplete: c ( 3 × 1 ) = 40 30 20 Good Weather Fair Weather

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 07/13/2011 for the course ECON 3107 at University of New South Wales.

### Page1 / 19

L4v(1)-1 - ECON 3107 Lecture 4 Valuation Completing the...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online