Advanced Treasury Management

8/13/2019 Advanced Treasury Management

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National University of Ireland, Dublin

Master of Science (Finance)

Intake 15

Module:Advanced Treasury Management Financial Engineering

ssay !itle:PCA

Sub"itted by:NGUYEN PHUONG ANH

Student Nu"ber: 1!""#

#ecturer:Mr$ %ames &'an

Sub"ission Date:( May 1"

$ord %ount: 1!)*


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Discuss &o' an increase in t&e value of eac& of t&e deter"inants of t&e otion rice in t&e lack*

Sc&oles otion ricin+ "odel for uroean otions is likely to c&an+e t&e rice of a call otion

1 Introduction

T+e ,lac-./c+0les m0del is used t0 measure t+e value 0 call 02ti0ns$ 3+en it 'as irst intr0duced 4y

Myr0n /c+0les and Fisc+er ,lac- in 1)5"6 t+e a22licati0n 'as limited t0 c0mm0n st0c- call 02ti0ns and

st0c- 'arrants$ 7ater6 40t+ in 2a2ers and in t+e real '0rld6 t+e m0del 4ecame a 202ular t00l t0 value all

call 02ti0n.li-e ty2es 0 inancial assets6 suc+ as em2l0yee st0c- 02ti0ns6 irm e8uity 0r c0r20rate real

02ti0ns$

- Deter"inants of t&e lack Sc&oles "odel

T+e ,lac-./c+0les e8uati0n is determined 4y ive 2arameters6 '+ic+ are t+e current 2rice 0 t+e

underlying asset6 e9ercise 2rice6 time until e92irati0n6 t+e v0latility 0 t+e asset and t+e ris- ree rate$ T+e

im2erecti0n 0 t+e m0del c0mes r0m its assum2ti0ns and inaccurate estimates 0 t+e varia4les$ Usually

it ta-es +ard '0r- t0 estimate t+e varia4les and in act6 in m0re 0 t+e cases s0me varia4les are 0ver 0r

under estimated$ Any miscalculated varia4le 'ill aect t+e 0verall result 0 t+e m0del6 '+ic+ in turn

mig+t interere 'it+ t+e decisi0n ma-ing 2r0cess$

As evidenced 4y a sim2le c0mm0n st0c- 02ti0n 4el0'6 e9ce2t 0r e9ercise 2rice6 t+e 0t+er 0ur varia4les

+ave 20sitive relati0ns+i2s 'it+ t+e value 0 t+e call 02ti0n$ :t means t+at any increase in t+e value 0 t+e

e9ercise 2rice 'ill cause a dr02 in t+e call 2rice$ T+e reverse +0lds true 0r /20t 2rice6 Time t0 e92irati0n6

;is- ree rate and c0nducts ris- measures 0 delta6 gamma6 t+eta6r+0 and vega 0r t+e 02ti0n 0 a c0mmercial 2r0?ect$ Deltaanalysis indicates t+at call value 4ec0mes

"ore and "oresensitive t0 varia4le Psas t+is varia4le 4ec0mes +ig+er and +ig+er$ :t means t+at 0r


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s0me reas0ns suc+ as underestimate in NP< t+e 2r0?ect e92ands in value6 t+e 02ti0n 'ill als0 increase

in value 4ut at a +ig+er rate$

-- .ercise rice

F0r c0mm0n st0c- 02ti0ns6 t+e e9ercise 2rice is usually i9ed since t+e lie 0 t+e 02ti0n is 0nly 'it+in

m0nt+s$ An +ig+er agreed 2rice and 0t+er varia4les +eld c0nstant means t+at invest0rs can 4uy t+e samest0c- 2rice 'it+ a +ig+er 2rice and t+us6 t+e 02ti0n 4ec0mes less attractive$ :n t+e case 0 'arrants '+ic+

+ave t+eir lie s2read 0ver years6 +0'ever6 e9ercise 2rice can c+ange several times 0n s2eciied dates

=,lac- and /c+0les6 1)5"> 0r t+e same reas0n t+ey e9tend Time t0 e92iry as e92lained 4el0'$

-/ !i"e to e.iration

T+e l0nger t+e time t0 e92irati0n6 t+e +ig+er t+e time value 0 t+e call 02ti0n6 +ence a m0re attractive call

02ti0n$ N0te t+at 0r a call 02ti0n6 t+e 4uyer can ma-e unlimited 2r0its i t+e s+are 2rice -ee2sincreasing6 '+ile in t+e '0rst case 0nly l0sing t+e 2remium$ T+is idea ma-es invest0rs suddenly crave 0r

uncertainty$ T+ere0re6 4et'een t'0 02ti0ns t+at +ave t+e same s20t 2rices6 e9ercise 2rices and return

variance and traded 0n t+e same mar-ets6 '+ic+ever 02ti0n 'it+ l0nger lie '+ic+ means +ig+er

v0latility 'ill '0rt+ m0re$ :t means t+at an increase in varia4le T 'ill als0 increase t+e 2rice 0 t+e call

02ti0n$

/ince 'arrantsare traded 2rivately 4et'een t+e irm and its invest0rs6 t+e irm can mani2ulate t+e terms

0 t+e call 02ti0ns s0 t+at it c0uld 4e e9ercised$ N0te t+at i t+e 02ti0n is n0t e9ercised6 t+e 2remium

2r0ceeds 'ill 4ec0me ta9a4le inc0me 0r t+e issuance irm6 and 0r t+is reas0n irms tend t0 e9tend t+e

maturity date i an 0ut.0.t+e.m0ney e92irati0n is 0reseea4le$ T+is means t+at at t+e 4eginning 0 t+e

02ti0n6 varia4le T 'as 2ut l0'er t+an it s+0uld 4e and t+e 2rice 0 t+e 02ti0n 'as als0 c+ea2er t+an its

real value$ /0metimes irms d0 t+at 'it+ 2ur20ses$ 3arrants tend t0 4e issued 4y smaller irms 'it+0ut

2u4lic traded calls =&remer and ;0eneldt6 1))#> 0r irms t+at +ave ?ust emerged r0m 4an-ru2tcy$ T+ese

c0m2anies need cas+ and mig+t intenti0nally s+0rten t+e lie 0 t+e 'arrant t0 ma-e t+e 2remium c+ea2er

t+an 2u4lic call 02ti0ns and t+us6 m0re attractive t0 4uyers$ : T +ad a +ig+er value6 t+e 2rice 0 t+e

'arrant '0uld als0 4ec0me m0re e92ensive and mig+t l0se its 2rice advantage against 2u4lic traded

02ti0ns$

A dierent 2r04lem arises in c0r20rate real 02ti0ns$ :n s0me cases6 estimates 0 t+e lie 0 t+e 02ti0ns can

4e 4iased$ :n an e9am2le 0 deerral 02ti0n 2r0vided 4y 6 t+e value 0 t+e American 02ti0n

at t+e end 0 year " is signiicantly +ig+er t+an t+e 02ti0n value at t+e ma9imum deerral 2eri0d =* years>$

:t means t+at at T @ "6 i t+e 2r0?ect is deerred 0r an0t+er year6 t+e 02ti0n 'ill l0se its value 4y m0re

t+an +al$ :t mig+t 4e e92lained t+at in t+ese 02ti0ns6 spotpriceis t+e 2resent value 0 uture cas+ l0's

generated during t+e lie 0 t+e 2r0?ect$ T+e urt+er t+e 2r0?ect is deerred6 t+e greater t+e im2act 0n t+e

disc0unted cas+ l0's$ T+e decrease in s20t 2rice 'ill m0re t+an 0set t+e decrease in t+e 2resent value


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0 e9ercise 2rice '+ic+ is t+e c0st 0 t+e 2r0?ect and t+us6 t+e 02ti0n value als0 decreases$ :n t+is case6

i varia4le T increases6 t+e value 0 t+e call 02ti0n decreases$

-0 isk free rate

:t is understanda4le t+at i t+e ris- ree rate increases6 t+e value 0 t+e call 02ti0n 'ill als0 increase6 since

is t+e 2r0ceed gained r0m t+e e9ercise 0 t+e 02ti0n ='+ic+ e8uals underlying st0c- 2rice minus e9ercise2rice> is reinvested at t+e ris-.ree interest6 +ig+er rate results in m0re cas+$ T+is ma-es t+e call 02ti0n

m0re attractive t0 invest0rs$

c0nducted sensitivity analysis 0n t+is varia4le6 in '+ic+ rta-es u2 values ranging r0m 5

t0 1$ :t is 0und t+at as ris- ree rate increases gradually 4y !6 t+e 02ti0n value 0nly increase 4y $

T+e aut+0r c0ncludes t+at t+e 02ti0n is insensitive t0 disc0unt rate6 4ut t+e analysis can 4e useul 0r

really ris-.averse invest0rs$

:n t+e ,lac- and /c+0les rame'0r-6 t+e ris-.ree interest rate is assumed constant$ F0r s+0rt.term

c0ntracts6 a c0nstant term structure 0 interest rates can 4e c0nsidered reas0na4leB yet6 0r medium 0r

l0ng.term c0ntracts t+is assum2ti0n d0es n0 l0nger +0ld true$ T+e reas0n is t+at in a num4er 0 cases6 ris-

ree rate is reerred r0m Treasury securities t+at +ave t+e same maturities as t+e 02ti0n$ F0r e9am2le6 i

t+e 02ti0n is e92ected t0 4e e9ercised in ! years6 t+en t+e a22r02riate ris-.ree rate s+0uld 4e t+e interest

rate 0n !.year Treasury n0tes$ F0r 02ti0ns t+at are measured 4y years 0r decades6 s0metimes t+e cl0sest

matc+ed T.n0tes are several years a2art r0m t+e lie 0 t+e 02ti0n6 causing numer0us l0ng dated 02ti0ns

t0 4e mis2riced$ F0r e9am2le6 a /inga20re.4ased c0m2any is devel02ing a 2r0duct t+at is e92ected t0 4e

launc+ed in yearsD time$ H0'ever6 since t+ere is n0 .year Treasury n0te availa4le (The Monetary

Authority of Singapore)6 t+e rate used t0 value t+e 02ti0n must 4e ta-en r0m t+e 1#.year n0te6 '+ic+ is

+ig+er$ T+e inlated ris-.ree rate causes t+e 02ti0n t0 4e 0ver2riced$

N0te t+at an increase in ris- ree rate can drive t+e call value u2 4y a su4stantial am0unt$ :n t+e case

c0nducted 4y Part+asarat+y and Mad+umat+i6 '+en rhoincreases 4y 1 r0m *$!! t0 !$!!6 t+e value

0 t+e 02ti0n m0re t+an d0u4les$

-5 2olatility

An increase in t+e ris- 'ill increase t+e value 0 t+e call 02ti0n 4ecause i t+e st0c- is m0re v0latile6

variance 'ill s2read 'ider and t+e c+ance 0r t+e st0c- 2rice t0 land inside t+e tails 0 t+e distri4uti0n is

+ig+er$ ;0t-0's-i =#11> 2l0ts t+e c+ange in t+e value 0 a +y20t+etical st0c- 02ti0n in c0rres20ndence

'it+ dierent standard deviati0ns$ :t is n0ticea4le t+at '+en standard deviati0n increases 4y !# =r0m

# t0 "#>6 call value increase 4y !# r0m #$ t0 #$!! d0llars$ :n t+e e9am2le 2r0vided 4y &+an6

Gu2ta and /ira?6 a !# increase in rho'ill result in a m0dest " increase in call 02ti0n value$

T+ere0re6 in s0me cases6 a miscalculati0n 0 standard deviati0n d0es n0t su4stantially alter t+e value 0


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t+e 02ti0n '+ile in 0t+er cases6 an 0ver estimate 0 t+is varia4le may c+ange t+e 02ti0n value t0 a large

e9tent$


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I#I34678

,lac-6 F6 /c+0les6 M 1)5"6 T+e Pricing 0 O2ti0ns and C0r20rate 7ia4ilities6 %0urnal O P0litical

Ec0n0my6 16 "6 2$ ("5

&+an6 M6 Gu2ta6 A6 /ira?6 / #1"6 Em2irical Testing 0 M0diied ,lac-./c+0les O2ti0n Pricing M0del

F0rmula 0n N/E erivative Mar-et in :ndia6 :nternati0nal %0urnal O Ec0n0mics Financial :ssues

=:%EF:>6 "6 16 22$ 5.)

&remer6 %6 ;0eneldt6 ; 1))"6 3arrant Pricing %um2.iusi0n vs$ ,lac-./c+0les6 %0urnal O

Financial Iuantitative Analysis6 6 6 22$ !!.5

7auter4ac+6 ,6 /c+ultJ6 P 1))#6 Pricing 3arrants An Em2irical /tudy 0 t+e ,lac-./c+0les M0del

and :ts Alternatives6 %0urnal O Finance6 *!6 *6 22$ 111.1#)

;0t-0's-i6 AM #116 Estimating /t0c- Price

Advanced Treasury Management

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