FinEconNov8

FinEconNov8 - LUCAS MODEL BACKGROUND THE PROJECTION METHOD...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION S OLVING THE L UCAS A SSET P RICING M ODEL U SING A P ROJECTION M ETHOD A PPROACH Andrew Culham aculham@math.fsu.edu Department of Mathematics Florida State University November 8, 2005 SOLVING THE LUCAS ASSET PRICING MODEL USING A PROJECTION METHOD APPROACH ANDREW CULHAM LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION O UTLINE 1 THE LUCAS ASSET PRICING MODEL 2 LEGENDRE POLYNOMIALS AND QUADRATURE RULES 3 THE PROJECTION METHOD 4 RESULTS 5 CONCLUSION SOLVING THE LUCAS ASSET PRICING MODEL USING A PROJECTION METHOD APPROACH ANDREW CULHAM LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION T HE B ASIC S ETUP Assume: A large number of investors. One stock paying stochastic dividends. One risk-free bond. All agents are identical with utility function u ( c ) = c 1- - 1 1- , where > 0 is the level of risk aversion. SOLVING THE LUCAS ASSET PRICING MODEL USING A PROJECTION METHOD APPROACH ANDREW CULHAM LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION N OTATION Define the following notation: c t- the agents consumption in time t s t , b t- the agents holdings of the stock and bond, respectively S t , B t- the market holdings of the stock and bond, respectively ( S t = 1 and B t = 0 at equilibrium) p t , q t- the market price of the stock and bond, respectively d t- the per capita dividend paid by the stock For each t , the agent chooses { c t , s t + 1 , b t + 1 } . The individual states are z t = { s t , b t } and the aggregate states are Z t = { S t , B t , d t } . SOLVING THE LUCAS ASSET PRICING MODEL USING A PROJECTION METHOD APPROACH ANDREW CULHAM LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION T HE A GENT S P ROBLEM ( CONT ) The agent solves v ( z t , Z t ) = max { ct , s t + 1 , b t + 1 } E X t = t u ( c t ) , subject to c t + p t s t + 1 + q t b t + 1 s t ( p t + d t ) + b t t , where s and b are known. In addition, c t , t . SOLVING THE LUCAS ASSET PRICING MODEL USING A PROJECTION METHOD APPROACH ANDREW CULHAM LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION T HE E ULER E QUATIONS Stock: p t c- t = E t [ c- t + 1 ( p t + 1 + d t + 1 )] Bond: q t c- t = E t [ c- t + 1 ] or Stock: pc- = E [( c )- ( p + d )] Bond: qc- = E [( c )- ] SOLVING THE LUCAS ASSET PRICING MODEL USING A PROJECTION METHOD APPROACH ANDREW CULHAM LUCAS MODEL BACKGROUND THE PROJECTION METHOD RESULTS CONCLUSION A T RANSFORMATION Suppose dividends grow according to d t = e xt d t- 1 , where x t = ( 1- ) + x t- 1 + t with t being i.i.d. N ( , 2 ) and | | < 1. Let v t = p t d t and = 1- ....
View Full Document

This note was uploaded on 12/14/2011 for the course FIN 5515 taught by Professor Staff during the Spring '10 term at FSU.

Page1 / 27

FinEconNov8 - LUCAS MODEL BACKGROUND THE PROJECTION METHOD...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online