[PDF] - Lecture 1 Finance Pro ject Somesh Jha 1 Goals of the PDF Document

SLIDE 1 Lecture 1 Finance Pro ject Somesh Jha 1

SLIDE 2 Goals

f

the course

T

eac h the studen ts to systematic al ly design algorithms and systems for problems in the nance domain.

T

aking nance ideas from the ac ademic domain and making them real.

Maxim:

Learn b y doing. 2

SLIDE 3 Nature

f

the course

Largely

indep enden t in nature.

Je

and I are here to guide y

u,

but y

u

will w

rk

as indep enden t teams.

Think
f

the course as a structur e d indep endent study c

urse.

3

SLIDE 4 What w e will do in class

Je

and I will go through a systematic design

f

a system for pricing mortgage b acke d se curities

r

MBSs.

Use

the lectures as a guide for y

ur

pro ject.

There

will b e ve phases to the pro ject. These phases will b e dened later. 4

SLIDE 5 Logistics

Studen

ts will form a team

f

3-4.

Eac

h team will select a pap er from a set pro vided in class.

Eac

h team will design a system based

n

the pap er they select.

Eac

h team will go through the v e phases (to b e describ ed later). 5

SLIDE 6 Some useful tips

Pic

k a b alanc e d te am.

Stic

k to the sc hedule for eac h phase. 6

SLIDE 7 Grading

Grading

will b e done dep ending

n

the

utcome
f

eac h phase.

No

tests and homew

rks.

7

SLIDE 8 Fiv e phases Description

f

these phases will b e pro vided later, but here they are.

Requiremen

ts phase (Phase 1).

High-lev

el design phase (Phase 2).

Lo

w-lev el design phase (Phase 3). 8

SLIDE 9 Phases (Con td)

In

class presen tation (Phase 4).

Protot

yp e (Phase 5) 9

SLIDE 10 Protot yp e

This

will b e a sc ale d b ack v ersion

f

the design.

Mak

e as man y limiting assumptions as p

ssible,

but state them carefully .

Y
u

can use C,C++,JAVA to implemen t the protot yp e. Mak e sure y

u

tell Je the en vironmen t y

u

are using. 10

SLIDE 11 Presen tation

There

will b e

ne

presen tation p er team.

The

presen tation will b e a synopsis

f

phase 1,2, and 3.

Eac

h presen tation will b e 20 min utes long.

Last

three lectures will b e all presen tations. 11

SLIDE 12 P ap er 1

J.

Hull and A. White, Ecien t Pro cedures for V aluing Europ ean and American P ath-Dep enden t Options, Journal

f

Derivative, No 1, Pages 21-31, 1993. 12

SLIDE 13 P ap er 2

J.

Hull and A. White, V aluing Deriv ativ e Securities Using the Explicit Finite Dierence Metho d, Journal

f

Financial and Quantitative A nalysis, V

l

25. No 1, Pages 87-99, 1990. 13

SLIDE 14 P ap er 3

J.

Hull and A. White, Pricing In terest-Rate-Deriv ativ e Securities, The R eview

f

Financial Studies, V

l

3, No 4, Pages 573-592, 1990. 14

SLIDE 15 P ap er 4

A.

Li, P . Ritc hk en, and L. Sank arasubramanian, Lattice Mo dels for Pricing American In terest Rate Claims, Journal

f

Financ e, V

l

L, No 2, Pages 719-736, 1995. 15

SLIDE 16 P ap er 5

P

. Ritc hk en and L. Sank arasubramanian, V

latilit

y Structures

f

F

rw

ard Rates and the Dynamics

f

the T erm Structure,Ma th ematic al Financ e, V

l

5, No 1, Pages 55-72, 1995. 16

SLIDE 17 P ap er 6

P

. Ritc hk en and L. Sank arasubramanian, Pricing the Qualit y Option in T reasury Bond F utures, ,Mathematic al Financ e, V

l

2, No 3, Pages 197-214, 1995. 17

SLIDE 18 P ap er selection

Don't

c ho

se

pap ers 5

r

6 unless y

u

are comfortable with sto c hastic calculus.

F
cus
n

the tec hniques and algorithms in the pap er. It is OK if y

u

don't understand all the mathematical deriv ations. 18

SLIDE 19 Goals

f

reading the pap er

Decide

what nancial instruments y

u

w an t to price after reading the pap er. Pic k 2-3 instrumen ts. Y

u

will b e required to understand these instrumen ts completely .

Y
u

should ha v e a clear idea ab

ut

the algorithm prop

sed

in the pap er.

Mak

e a note

f

adv an tages/disadv an tages

f

this tec hnique/algorithm. 19

SLIDE 20 Requiremen ts do cumen t

Describ

e the nancial instrumen t in great detail.

Describ

e the assets the instrumen ts dep end up

n.

State the assumptions

n

the prices

f

these assets. Describ e the cash-o w c haracteristics.

Describ

e the nancial instrumen ts and there cash-o w c haracteristics. 20

SLIDE 21 Requiremen ts do cumen t

In

an abstract sense w e are describing what is the seman tics

f

eac h

p

eration that the user can do.

In

this very sp e cic example this amoun ts to dening the precise seman tics

f

mortgage b acke d se curities (MBSs). 21

SLIDE 22 Describing Mortgages

Fixe

d R ate: The ann ual in terest rate

f

the mortgage sta ys xed through

ut

the life

f

the mortgage.

A

djustable R ate Mortgages (ARMs): The ann ual in terest rate can b e adjusted b y the loaning agency . 22

SLIDE 23 Fixed Rate Mortgages

Let

M B b e the

riginal

mortgage balance.

Let

c b e the simple mon thly in terest rate.

Let

M P b e the mon thly mortgage pa ymen t.

Let

n b e the n um b er

f

mon ths. 23

SLIDE 24 Relationship b et w een M P and M B

The

follo wing equation should hold b et w een M P and M B : M B = M P n X i=1 (1 + c) i = M P 1

(1

+ c) n c

Hence

the mon thly mortgage pa ymen t M P is giv en in terms

f

the mortgage amoun t M B using the follo wi ng form ula: M P = M B c(1+c) n (1+c) n 1 24

SLIDE 25 Principal at time t

Let

M B t the remaining mortgage balance at time t.

W

e ha v e the follo wi ng relationship b et w een M B t and M P . M B t = M P 1

(1

+ c) (nt) c

So

w e ha v e the follo wi ng equation b et w een M B and M B t : M B t = M B (1 + c) n

(1

+ c) t (1 + c) n

1

25

SLIDE 26 Breaking the mortgage pa ymen ts

A

t time t the mortgage balance is M B t1 (t

1).
The

in terest I t

n

this is mortgage balance is: cM B t1

The

mortgage pa ymen t M P at time t is brok en in to t w

parts:

inter est p ayment I t and p ayment applie d towar ds princip al P t . W e ha v e the follo wi ng equation: M P = I t + P t 26

SLIDE 27 Scenarios

A

requiremen ts do cumen t for a large soft w are system has a h uge n um b er

f

scenarios.

Basically

, sc enarios describ e what should happ en in sp ecic cases.

F
r

example, in the requiremen ts do cumen t for an

nline

brok erage system a scenario migh t describ e what should happ en when a user logs

n

and buys a sto c k. 27

SLIDE 28 Examples

In

this case, scenarios are simply examples

f

cash

ws.
Consider

a mortgage

f

100; 000, ann ual mortgage rate (12c)

f

9:5% and time p erio d

f

30 y ears (360 mon ths).

Chec

k that the mon thly mortgage rate M P is 840:85. 28

SLIDE 29 Example con tin ued

Chec

k that I = 791:67 and P = 49:19.

Chec

k that I 215 = 574:95 and P 215 = 265:90.

I

t is a decreasing function

f

t and P t is an increasing function

f

t. (Why?). 29

SLIDE 30 ARMs

ARMs

start

ut

with an initial in terest rate.

ARMs

in terest rate can b e adjusted b y a margin m at a frequency sp ecied in the con tract.

Lifetime

c ap c L : This is an upp er b

und

that the in terest rate cannot exceed.

Lifetime
r

c F : This is a lo w er b

und
n

the in terest rate. 30

SLIDE 31 ARMs

Let

us the in terest rate is c(t

1)

at time t

1

and w e are adjusting at time t,

The

new in terest rate c ( t) is giv en b y the follo wi ng cases: { if x(t) + m > c(t

1)

min [x(t) + m; c L ; c(t

1)

+ c P ] { if x(t) + m

c(t
1)

min [x(t) + m; c F ; c(t

1)
c

P ] 31

SLIDE 32 Explanation

f

terms

x(t)

: Underlying index sp ecied in the con tract. Tw

widely

used indices are cost

f

funds index (COFI) and a constan t maturit y (one y ear

r

v e y ear) T reasury index.

c

L and c F are the lifetime cap and

r

resp ectiv ely .

c

P denotes the ARMs p erio dic cap, i.e., cannot adjust b y more than this amoun t. 32

SLIDE 33 New Mortgage P a ymen t

Assume

that curren t time is t, the in terest rate, mortgage balance at time t

1

are c(t

1)

and M B t1 .

The

new adjuste d in terest rate is c(t).

The

new mortgage pa ymen t M P (t) is giv en b y the follo wing expression: M B t1 1

(1

+ c(t)) (nt) c(t)

Ev

erything else sta ys the same. 33

SLIDE 34 Action Items

Pic

k y

ur

teams (3-4 studen ts) and send e-mail to Je

r

me.

Pic

k a pap er (Norene Mears has a cop y

f

eac h pap er) and cop y it. R eturn the master c

py.
P

ap ers should b e in London and New Y

rk

in 2-3 da ys.

Read

the pap er and decide

n

the nancial 34

SLIDE 35 instrumen ts y

u

are going to price.

Start

reading ab

ut

the nancial instrumen ts y

u

are going to price. 35