Applications of Arbitrage-free Models New Frontiers in Interest Rate, Credit and Energy Risks

7/25/2019 Applications of Arbitrage-free Models New Frontiers in Interest Rate, Credit and Energy Risks

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T H O M A S S . Y . H O P h D

P R E S I D E N T

T H C

O C T O B E R 2 6 , 2 0 0 9

T O M . H O @ T H O M A S H O . C O M

Applications of Arbitrage-free Models:New Frontiers in Interest Rate, Credit and

Energ Ris!sThird Annual Bl!"#r$ %#&'ur# in (inan


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"al#ation $odels Deri%ati%e pricing &relati%e %al#ation' #nder interest rate, credit and

other ris! dri%ers

Applications (rading

Portfolio $anage$ent Enterprise ris! $anage$ent

I$pacts on the $ar!ets Price disco%er process Reg#lator policies in the financial $ar!ets

)*+*+Introd#ction

)

Arbitrage-free (er$ .tr#ct#re Models


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/hat are the $odel0s econo$ic principles that $a!ethe $odel pop#lar and f#nda$ental1

/hat are the frontiers of applications of the $odel ingoing forward1

/hat are $ ca#tionar notes on the #se of the $odel1

Detail disc#ssions are a%ailable in the references

)*+*+Introd#ction

2

3#estions Addressed


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A$in, 4a#shi! I5, and Andrew 65 Morton, +77, 8 I$plied "olatilit F#nctions in Arbitrage-free (er$ .tr#ct#re Models, 8 6o#rnal of Financial Econo$ics, 29&)', ++-+;a#ger and


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.alient feat#res of the $odel A perspecti%e of arbitrage-free ter$ str#ct#re $odels A fra$ewor! to eplore new frontiers in applications

Appl the fra$ewor! to J Interest rate ris! Credit ris! Energ ris!

Going forward: Managing $odel ris!s Edwards De$ing approach to ris! $anage$ent

)*+*+Introd#ction

9

#tline


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"al#ation co$ponent

C& ., t' .pecif the contingent clai$d. K r&t' .dt L &t' .dB .pecif the #nderling ris! process

Application co$ponent

Delta: dna$ic replication

Calibration to deter$ine the i$plied %olatilit

)*+*+Arbitrage-free Models

(he


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C K C& r , p&t, (', t' Contingent clai$s on the disco#nt f#nction

dr K F& p&t, (', t'dt L &r, t' dw .hort rate $odel Forward rate $odel

Mar!et $odel

&n-+,i' K ;59 p&n,i'&


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Callable bond

Mat#rit ););-+;-+9

.A fied co#pon rate959O


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7

I$plied "olatilit F#nctionCalibration: Application Co$ponent of the Model


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(he ter$ str#ct#re $odel: (i$e di$ension, rate, a

8flow concept@ Fro$ the econo$ic $odeling perspecti%e, the


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8.toc!@ %ers#s 8Flow@

Arbitrage-free $odels ha%e two co$ponents"al#ation co$ponent &so$e ea$ples'

M#lti-factor $odels(i$e and state dependent i$plied %olatilit f#nction

Hnspanned stochastic %olatilit f#nctionApplication co$ponent

Effecti%eness of dna$ic hedging and i$plications of thei$plied %olatilities


++

Proposed Perspecti%e of (er$ .tr#ct#re Models


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"al#ation of fied-inco$e instr#$ents with credit ris!

Red#ced for$ and str#ct#ral $odels

Credit defa#lt swap &CD.'.#r%i%al f#nction %s disco#nt f#nction

.tate and ti$e dependent s#r%i%al rate s&n,i'

)*+*+Applications: Credit Ris! Modeling

+)

Credit (er$ .tr#ct#re

>o, (ho$as .5 5 and .ang


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Ma!e-whole ption

&n-+,i' K ;59 p&n' s&n,i' &


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)*+*+Applications: Credit Rs! Modeling

+

"al#ation of E$bedded Credit ptions


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Deter$ine the credit !e rate d#rations for credit

hedging .pecif the precise dollar credit epos#re in the ter$

str#ct#re

Identif the i$plied credit %olatilitiesHse of the str#ct#ral $odels

Interest rate and credit ris! relationshipApplications to a callable instr#$ents


+9

I$plications of the Credit (er$ .tr#ct#reApplication Co$ponent of the Model


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Dna$ic $o%e$ents of the ter$ str#ct#re of credit

.pecif the e$bedded $a!e whole option inco$$ercial $ortgages I$pact of the correlation to the interest rate le%el

Relating a red#ced for$ $odel to the str#ct#ral $odel M#lti-factor credit $odel


+

Applications of the (er$ .tr#ct#re Credit Model


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enr >#b data

/ell head cost, gathering and processing costs

.torage and cost to carr

De$and: /eather affects heatingQ power generation

In?ection season: April - ctober/ithdrawal season: No%e$ber March

>o, (ho$as .5 5 and .ang


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Dereg#lation of power ind#str

.#ppl: >oriBontal rigs

Power pricesDepending on the bid stac! and power de$and


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Abadic, =#is M and 6ose Cha$orra &);;' ) factor $odel with the stochastic f#el price $ean re%erting to a

stochastic long ter$ price (he stochastic long ter$ price $ean re%erting to a constant price

Edeland, Aleander and 4rBsBtof /olniec &);;2'

and


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F#t#res and spot dail prices fro$ +*2*);;

-+)*)*);;F#t#res deli%er dates: $onthl fro$ +*+*);; and

+*+*);+;

I$plied cost of carr c&t, (' K &+*&(-t''ln F&t,('*.&t'Hse the principal co$ponent approach to specif the

$o%e$entsData .o#rce: =ogical Infor$ation Machines &=IM'

)*+*+Applications: Energ Ris! Modeling

);

Data and Methodolog


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)+

>enr >#b MM


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)*+*+Applications: Energ Ris! Model

))

(er$ .tr#ct#re of >enr >#b F#t#res Prices+;*+*);;7

59

9

959

59

59

(u'ur#) Pri)


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)2

Nat#ral Gas F#t#res (er$ .tr#ct#reMo%e$ents

7

+;

++

+)

+2 +*2*);;

+**);;

+*9*);;

+**);;

+*7*);;

+*+;*);;

+*++*);;

+*+)*);;

+*+2*);;

+*+*);;

+*+*);;

+*+7*);;

+*);*);;

+*)2*);;

+*)*);;

+*)9*);;

+*)*);;

+*)*);;

+*2;*);;

+*2+*);;


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Contingent clai$s on the NG spot and f#t#res prices

I$plied cost to carr: (he ter$ str#ct#re F#t#res contracts deter$ining the i$plied cost of carr (he one period cost to carr is e#i%alent to the s#r%i%al rate

Dna$ics of the ter$ str#ct#re: (he ter$ str#ct#re ofcost to carr and the spot rates d. K c&t' . dt L &t' . dB dc&t' K F& c&t, (', t' dt L S dw


)

Arbitrage-free Nat#ral Gas Model"al#ation Co$ponent of the Model


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(he f#t#res ter$ str#ct#re $o%e$ents ha%e two

factors: 8Price@ &9O', 8Cost to Carr@ &+O', 2rd%ector&;52O'

(he cost of carr $o%e$ents has one factor: le%el$o%e$ent &7759O' and )ndfactor &;5O'

Correlation of the spot price and cost to carr: low

(he #se of !e rate d#rations on the cost to carr andthe spot price for hedging


)9

Preli$inar Res#lts on Dna$ic >edgingApplication Co$ponent of the Model


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)

+stPrincipal Mo%e$ent of the Cost to Carr

-;5+

-;5+-;5+

-;5+

-;5+

-;5+

-;5+

-;5+

-;5+

-;5+

Pri

Ma'uri'*

Ra'# Shi+'


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)

)ndPrincipal Mo%e$ent of the Cost to Carr

-;52

-;5)

-;5+

;

;5+

;5)

;52

Sl#

Ma'uri'*

Ra'# Shi+'


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)

Calibrate the Model to the I$plied "olatilitiesApplication co$ponent of the Model

+ ) 2 9 7 +; ++ +) +2 + +9 + + + +7 ); )+ )) )2 )

;

+;

);

2;

;

9;

;

);;-;+-;2);;-;+-;

);;-;+-;9

);;-;+-;

);;-;+-;7

);;-;+-+;

);;-;+-++

);;-;+-+)

);;-;+-+2

);;-;+-+);;-;+-+

);;-;+-+7

);;-;+-);

);;-;+-)2

);;-;+-)

);;-;+-)9


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3#antitati%e analsis of NG contracts and the changing

shape of the i$plied cost to carr c#r%eRelate the NG f#t#res option prices and to other

deri%ati%esApplications to the calendar basis trades Hse of the $#lti-factor $odel to deter$ine the correlations of the ccles

Correlation of interest rates with the cost to carr c#r%e

Power stac! f#nction: relation to coal and cr#de oil

)*+*+Applications: Nat#ral Gas Contracts

)7

I$plications to Energ (rading


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A lesson learnt fro$ the financial crisis

Mispricing and hence $isallocation of reso#rces

6#stification for the dna$ic replication and %olatilitcalibration

Re%isiting the application co$ponent of an arbitrage-free $odel Internal consistenc of the $odel

)*+*+Manage Model Ris!s

2;

Going Forward


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Ea$ple of $is-%al#ation: (he CD cop#la $odel (he #se of i$plied correlations

>ow to $anage $odel ris!1

)*+*+Managing Model Ris!s

2+

Managing Model Ris!


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De$ing: .tatistical approach to #alit control Defects are often traced directl to the ca#se5


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)*+*+Data so#rce:


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Eplanator power of the $odel1

Mean re%ersion beha%ior of the resid#als1

Effecti%eness of the dna$ic replication1

Detect 8defects@ in the ti$e series in relation to e%ents

)*+*+Manage Model Ris!s

2

Analsis of the Model Ris!


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.epte$ber and Dece$ber 9 ear f#t#res o%er the

$onth of .epte$berMar!et price K Mid #otes

+; $in#te inter%als fro$ :;;a$ till 9:2; p$


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)*+*+Data so#rce:


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)*+*+Data so#rce:


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)*+*+Data so#rce:


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)*+*+Data so#rce:


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)*+*+Data so#rce:


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(er$ str#ct#re $odels deal with 8rates@, flows & interest rate, defa#lt rate,

cost to carr, inflation rate 'Contrast to the


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(rading Ret#rn attrib#tions on perfor$ance $eas#re

Model ris! .tatistical Approach: eplanator, $ean re%ersion, replication

.ec#rities %al#ation

Interest rate, defa#lt rate, inflation rate, li#idit, cost to carr >brid $odels

Identifies the price for$ation process Fro$ the basic %al#ation b#ilding bloc!s to eotic str#ct#res Reg#lator polic on $ar!et transparenc and the role of echanges

)*+*+Concl#sions

)

Concl#sions and I$plications


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A$in, 4a#shi! I5, and Andrew 65 Morton, +77, 8 I$plied "olatilit F#nctions in Arbitrage-free (er$ .tr#ct#re Models, 8 6o#rnal of Financial Econo$ics, 29&)', ++-+;a#ger and

Applications of Arbitrage-free Models New Frontiers in Interest Rate, Credit and Energy Risks

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