# Asset Pricing

**Topics:**Rational pricing, Put option, Risk aversion

**Pages:**83 (11489 words)

**Published:**October 2, 2014

Chapt~

1 ExJ>ected Utilicy and Risk Aversion ..............................................................................• !

Chapt€11" 2 Mean-Varian.ce Analysis ................................................................................................ 6

Chapter 3 CAPM, Atbitmge, and Linear Factor Models .............................................................. 12 Chapter 4 Consumption-Savings Decisions and State Pricing...................................................... 17 Chapter 5 A Multi period Discrete-Time Model of Consumption and Portfolio Choice............... 24 Chapt~ 6Multi~riod

Market .EQ.t.JilibriliDl .................................................................................. 33

Chapta-- ?Basics of Derivative Pricing ......................................................................................... 37 Chapter 8 Essentials of Diffusion Processes and ItO's Lemma..................................................... 41 Chaptf!Jf' 9Dynamic Hedging and PDE Valuation ......................................................................... 45 Chapf(3{" 10 Arbitmge, Martingales, 31ld Pric.ing Ke111els .............................................................. 50

Chapter 11 Mixing Diffusion and Jump Processes •...................................................................... 59 Chapter 12 Continuous-Time Consumption and Portfolio Choice ............................................... 62 Chapf(31" 13 Equilibrium. Asset Ret:l..ln'ls........................................................................•...•...•...•...•. 74 Chapt~ 1~ ~i~-~e~l>le 1LJtili~ ............................................................................................. ~5»

Chaptf!!" 15 Behavioral Fina.Ilce and Asset Pric.ing ........................................................................ 85 Chapter 16 Asset Pricing with Differential Information ............................................................... 91 Chapter 17Models of the Term Structure of Interest Rates .......................................................... 97 Chapter 18 Models of Defat.JJt Risk............................................................................................. l 04

Answers to Chapter 1 Exerci:xs

n

1.

Suppose there are two lotteries P = {11, . .. , Pn} and P • = { p;', . . . , p~ }. Let V (p,, .. . , pJ = L: PP 1 i=J

be an individual's expected utility function defined over these lotteries. Let w (p,, ... , pJ = n

L: p Q

i=l

1

1

V (p;, . . . , p~ )

where Q i = a + bU i and a and b are constants. If p • f P, so that

>

V(!1, . .. , Pn), must it be the cae that W(p;, . . . , p~ ) > W(Pt, .. . , p,.)? In other words, is W also a valid expected utility function for the individual? Are there any restrictions needed on a and b for this to be the cae?

n

n

Answer : If V(I1', . .. , p;.) >V(Pt, . .. , p,.) then this implies L: p:u 1 > L; pp bill

....

1

•

If b is a positive

constant, then we can multiply both sides of the inequality without changing the sign: n

n

n

U. l

.V.I

n

L: p:bU > L: PtbU,. Since L: p: = L: p = ~ we can then add the constant a to each .U: I

1

n

.U. I

1

n

side of the inequality to obtain L:;p: (a + bU) > L:;p1 (a + bU ). But this is simply

~·

tv (-p;', . .. , p~) > W( 11, . .. , Pn) . Hence for W to~· a valid expected utility function for the be

individual, a can be a constant of any sign but b must be positive. 2.

(Allais paradox) Asset A pays $1,500 with certainty, while asset B pays $2,000 with probability 0.8 or $100 with probability 0.2. If offered the choice between aset A orB, a particular individual would choose aset A. Suppose, instead, that the individual is offered the choice between aset C and asset D. Asset C pays $1,500 wifh probability 0.25 or$100 with probability 0.75, while aset D pays $2,000 with probability 0.2 or $100 with probability 0.8. If...

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