L2v-3 - Valuation Denition: Valuation is the process of...

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ECON 3107/ECON5106 Lecture 2: Valuation Valentyn Panchenko Valuation Defnition: Valuation is the process of determining the present value of a security or productive investment. Example 2.1: How much is a tree worth today ( at time 0)? !"#$ ' ())* +$,-.$/ 0,* +$,-.$/ 12 ,334$5 67 ,334$5 3 ( 8 &9:7; 3 0 8 &911; Present Value of a tree: PV = 0.285 · 63 + 0.665 · 48 = 49. 875 In matrix notation Example: Valuation of a tree (cont’d) The vector of atomic prices: ( 1 × states ) p = ° 0.285 0.665 ± Good Weather Bad Weather The vector of quantities: ( states × 1 ) q = ² 63 48 ³ Good Weather Bad Weather The Present Value: PV = p · q = ° 0.285 0.665 ± ² 63 48 ³ = 49. 875 Check the dimensions: ( 1 × states ) ´ µ¶ · p · ( states × 1 ) ´ µ¶ · q = ( 1 × 1 ) ´ µ¶ · PV MATLAB as a matrix calculator Example: Valuation of a tree (cont’d) The following MATLAB commands (entered in the command prompt) will do the job: >> p = [0.285 0.665] p= 0.2850 0.6650 >> q = [63 48]’ q= 63 48 >> PV = p*q PV = 49.8750
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Riskless Securities Defnition: A riskless security pays the same amount at a given time, no matter what state of the world occurs. ° A riskless security is equivalent to a bundle of equal amounts of atomic claims for a time period. ° In our example, a riskless security pays a Fxed amount (say X apples) at time period 1, whether the weather has been good or bad. ° Equivalently, it is a bundle of X good weather apples (GA) and X bad weather apples (BA). Riskless Securities Example: Valuation of a tree (cont’d) Question: What is the present value of a riskless security that pays 20 apples in time 1?
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L2v-3 - Valuation Denition: Valuation is the process of...

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