17-05-07 - UF-ESI-6321 17-05-07.xmcd page 1 of 2 17.5.7...

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Unformatted text preview: UF-ESI-6321 17-05-07.xmcd page 1 of 2 17.5.7 Consider two stocks. Stock 1 always sells for $10 or $20. S1 := ( 10 20 ) If stock 1 is selling for $10 today, there is a .80 chance that it will sell for $10 tomorrow. If stock 1 is selling for $20 today, there is a .90 chance that it will sell for $20 tomorrow. Let matrix rows represent selling prices today and columns represent selling prices tomorrow with corresponding elements representing probabilities of price transitions from today to tomorrow: p1 := .80 .20 .10 .90 0.8 1 + 0.1 2 T ( 1 2 ) p 1 0.2 1 + 0.9 2 2 = 1 - 1 0.7 1 + 0.1 T ( 1 1 - 1 ) p 1 -0.7 1 + 0.9 Using a Mathcad solve block requires making an initial guess value: 1 := 0.5 Given 1 T ( 1 1 - 1 ) p 1 = 1 - 1 1 := Find( 1) 2 := 1 - 1 1 1 3 = 2 2 3 Expected price of Stock 1 in dollars: P1 := S1 1 = 16.67 2 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 UF-ESI-6321 17-05-07.xmcd page 2 of 2 Stock 2 always sells for $10 or $25. S2 := ( 10 25 ) If stock 2 is selling for $10 today, there is a .90 chance that it will sell for $10 tomorrow. If stock 2 is selling for $25 today, there is a .85 chance that it will sell for $25 tomorrow. p2 := .90 .10 .15 .85 Given 1 T ( 1 1 - 1 ) p 2 = 1 - 1 1 := Find( 1) 2 := 1 - 1 3 5 = 2 2 5 1 Expected price of Stock 2 in dollars: P2 := S2 1 = 16.00 2 true P1 > P2 = 1 On the average, which stock will sell for a higher price? On the average, Stock 1 will sell for a higher price. Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 ...
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This note was uploaded on 05/12/2010 for the course ESI 6321 taught by Professor Josephgeunes during the Spring '07 term at University of Florida.

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17-05-07 - UF-ESI-6321 17-05-07.xmcd page 1 of 2 17.5.7...

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