Mah 77 op Faal Mah Pro Dr. Grall pr..5 Mgmg Ma Sud D: 76
h Co groll ad Ro Modl h CR modl a qulbrum a prg modl for h rm ruur of r ra. dfd udr h aumpo: dr r d r dz hr ar oa. rpr h ra of ma rvro rpr h log ru avrag. umg h h r ra urd o b pov < pobl for r o rah zro aaouly bu ll vr bom gav. Udr h quval r-ural maur b om dr r d r dz hr rpr h r adum h movg o h r-ural rbuo. h CR modl aff ad ha a o-ral h-quard rbuo h dgr of frdom v. y h Ra quao h omal r-fr bod pr P h paym of $ a m gv by P p r p[ ] Whr
*all h r ra ar pov. h ououly ompoudd yld dfd a: P Y l a b ho ha Y 3
Whh dpd of r. f r < h rm ruur upard lopg fgur ; f > r doard lopg fgur ; < r < ll b upard fr h doard lopg fgur 3. Fgur Fgur Fgur 3
MULFCOR CR MODL h CR modl frquly prd a a o-faor modl; Co groll ad Ro985 hy hod ho o d h mulpl faor. h mulfaor CR modl up udr h aumpo: d d dz K K ar dpd ad roa moo Z ar muually dpd. lo hr aum modl bom: o ur h povy. Smlarly udr h r-ural maur h d d dz for K Hr aumd h mar pr of r a a fd paramr. h aaou dfaul-fr hor r ra ad dfaul y ar aumd o b h pov lar ombao of faor udr gh ad r follo from horal daa Ch So 995: ma from Wly Daa 98-988 7 Faor.397.88. -.73 Faor.798.3.6885 -.73 5
h omal r-fr bod pr P h paym of $ a m gv by r P p p p ] p[ p p L L S h faor ar dpd by h aumpo ad ad hav h form gv by 6
ad h h dfaulabl bod pr udr rovry ra q ar gv by: ] p[ ] [p q q q q q q q r P L L h ouou ompoudd yld for h bod follo by: P Y l K K K ] l[ L L l W a obrv ha h rm ruur ur ou o b a lar fuo of h uobrvabl a varabl. Hr ho h urv of o-faor CR bod pr ad yl 7
Dfaul dgal payoff h pr for a dfaul dgal pu h maury proo lg of a dfaul dgal ap CR modl : d D r d M Whr ] p[ M Proof: Fr h quao h pao opraor a b mplfd: r p 8
p h for ah fd p p by h dpd of faor p M Whr M dfd a abov. h do h hag of maur o P ho rro o udr h aoad Rado-Nodym y.r. P ad h pro W a P -roa moo: dw dw d W h O h ohr had udr p M P [ ] P h CR r ra ha h dyam: d [ ] d dw d gv o-ral h-quar radom varabl rbud udr P h gh: Dgr of frdom: No-raly: η v 9
] [ / hrfor h pao of udr P : ] [ P v η P r M M ] [ P M M ] [ d fally ombg h h gral h quao for h pr for a dfaul dgal pu provd. Numral mao of Mulfaor CR Modl W ma h CR modl by h r mhod Ch So 995 h dvdual r ra ar prformd a r rprao by v for K N Y l K hr rpr h lgh of h m rval; rpr h rror rm ha a odoal pao zro ad odoal vara hh : v
. h pao for h formao ll - gv by ; ] [ Covrly h mao of uobrvabl varabl a b ompud by olar Kalma flr. Rfr: Ch R-Ra ad Lou So 995. Mulfaor Co-groll-Ro Modl of h rm Sruur: ma ad from a Kalma Flr Modl:-3 Grall Mahu5. Crd R ad r Ra Modllg:959 Shobuhr J.Phllp3. Crd Drvav Prg Modl: Modl Prg ad mplmao:7-76885-86 Hull Joh989. Opo Fuur ad ohr drvav ur: 7-76