Pricing and Hedging in Stochastic Volatility Regime Switching Models

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1 Jornal of Mahemaical Finance hp://xoiorg/436/jmf336 Pblihe Online Febrary 3 (hp://wwwcirporg/jornal/jmf) Pricing an Heging in Sochaic Volailiy Regime Swiching Moel Séphane Goe Cenre Naional e la Recherche Scienifiqe (CNRS) Unieri Pari 7 Diero Laboraoire e Probabilié e Moèle Aléaoire (LPMA) Pari France goe@mahni-pari-ierofr Receie Ocober ; reie December 4 ; accepe December 8 ABSRAC We conier general regime wiching ochaic olailiy moel where boh he ae an he olailiy ynamic epen on he ale of a Marko jmp proce De o he ochaic olailiy an he Marko regime wiching hi financial marke i h incomplee an perfec pricing an heging of opion are no poible h we are ineree in fining formlae o ole he problem of pricing an heging opion in hi framework For hi we e he local rik minimizaion approach o obain pricing an heging formlae bae on oling a yem of parial ifferenial eqaion hen we ge alo formlae o price olailiy an ariance wap opion on hee general regime wiching ochaic olailiy moel Keywor: Sochaic Volailiy; Marko Swiching; Local Rik Minimizaion; Heging; Volailiy Deriaie Inrocion In hi paper we conier general regime wiching ochaic olailiy moel where boh he ae an he olailiy ynamic epen on he ale of a Marko jmp proce We are ineree in fining formlae o ole he problem of pricing an heging coningen claim in hi framework Howeer e o he ochaic olailiy an he Marko regime wiching he marke i incomplee an h perfec pricing an heging are no poible Hence o hege eriaie we aop firly he local-rik minimizaion approach ie by Föllmer an Schweizer in [] hi approach coni of con- rolling he heging error a each inan by minimizing he coniional ariance of he inananeo co incremen Healh e al in [] proie comparaie heoreical an nmerical rel on rik ale an heging raegie for hi approach er he meanariance (ee [3] or [4] for more eail on hi approach) in he pecific cae of ochaic olailiy moel We propoe in hi paper o apply he local rik minimizaion approach o a more global cla of ochaic olailiy moel ince we will ame in he eqel ha all parameer of he moel epen on he ale of a Marko jmp proce Hence we will work on a global cla of regime wiching ochaic olailiy moel We will obain formlae o gie he price of coningen claim by oling a yem of parial ifferenial eqaion We will alo obain he opimal raegy which ole he local rik minimizaion heging problem here ha been conierable inere in applicaion of regime wiching moel rien by a Marko proce o ario financial problem Ellio e al in [5] proie an oeriew of hien Marko chain moel Inee he e of Marko wiching in iffion allow o hae ifferen leel of rif or olailiy ring ime Moreoer hee regime wiching aciiie are a beer fi for economic ime erie aa han non regime wiching moel an alo allow o beer capre ome marke feare or economic behaior ch a receion an financial crii perio (ee for example Goe an Zo in [6]) h Di Mai e al in [7] coniere he problem of heging an Eropean call opion for a (nonochaic olailiy) iffion moel where he rif an olailiy are fncion of a Marko jmp proce Frhermore we are alo ineree in pricing olailiy eriaie ch a ariance an olailiy wap Broaie e al in [8] ie he pricing an heging of ariance wap an oher olailiy eriaie in he claical Heon ochaic olailiy moel inroce by Heon in [9] Ellio e al in [] hen eelope a moel for pricing he ame cla of eriaie b ner a Marko-molae erion of hi ochaic olailiy moel In heir paper hey only coniere he cae where no all he parameer of he moel epen on he ae of he Marko proce Moreoer hey ie only he Heon ochaic olailiy moel Hence bae on hee wo preceing work we will exen hi mehoology o or global cla of regime wiching ochaic Copyrigh 3 SciRe

2 S GOUE 7 olailiy moel h we will obain formlae o price opion on he ochaic olailiy proce ch a ariance an olailiy wap hi paper i arrange a follow: Secion gie he noion of he regime wiching framework an preen or regime wiching ochaic olailiy moel Secion ole he problem of pricing an heging ing he local rik minimizaion approach Secion 3 hen gie he formla o price opion on he olailiy proce he Sochaic Regime Swiching Volailiy Moel Le P be a filere probabiliy pace wih fiaion aifying he al coniion for ome fixe b arbirary ime horizon We conier a general ochaic olailiy moel efine by he ochaic ifferenial eqaion: S SS W a b W () W W wih where W an W are wo correlae Brownian moion In fac he proce S repreen he icone price proce of a raable ae price proce S iie by a Bon price proce B he proce B repreen he aing accon in a rikle ae i a real ochaic proce which i - aape an i a Marko jmp proce on finie ae pace : N I can be iewe a an oberable exogeno qaniy We ame ha he ime inarian marix Q enoe he infinieimal generaor q of where i an infinieimal ij i j m ineniy of hi generaor i efine a qij for all i j an qii q for all i ji; js ij hen he emi-maringale ecompoiion for i gien by q ij Q M where M i an N -ale maringale wih repec o : which i he naral fiaion generae by he Marko proce ner P Hence in or moel here are hree orce of ran- omne: W W an We will enoe by : W W he fiaion ge- Copyrigh 3 SciRe nerae by he wo Brownian moion Finally we will enoe by he global fiaion : Le n be he eqenial jmp ime of (ie n ) an a jmp meare of ie he in eger-ale ranom meare gien by () n n hen he -compenaor of i gien by j qij (3) j i j Ampion ) We ame all he hypo hei o enre he exi- an he reglariie of he olion of or moel ence () (ee for example [] for more eail) Hence he yem of ochaic ifferenial Eqaion () ami a niqe rong conino olion for he ecor proce S wih a ricly poiie price proce S an a olailiy proce ) We ame moreoer ha he Marko proce i inepenen o boh procee S an Remark hi inepenence implie ha he Marko proce i an exogeno facor of he marke informaion h i can be iewe a an exogeno facor ch a an economic impac facor An economic inerpreaion of hi i ha hi Marko proce can repreen a crei raing of a firm A Inee ame ha or ochaic olailiy moel ecribe he price of a commoiy proce by he firm A hen he Marko proce can repreen he crei raing of hi firm gien by an exogeno raing company a Sanar an Poor h i i naral o hink ha he ynamic of he commoiy price proce by he firm A epen on he ale of hi noaion o excle arbirage opporniie we ame ha he proce S ami an eqialen local maringale meare (ELMM) Q In he ene ha i i a probabiliy meare wih he a me nll e a P an ch ha he proce S i a local maringale ner Q We will enoe in he eqel by he e of all ELMM Q Remark ) We can rewrie he Brownian m oion W a 3 3 W W W where he proce W i anoher Brownian moion ch ha procee W an 3 W are now inepenen ) he coniion ha S hol be a Q -local mar- ingale fixe he effec of he Girano ranformaion of W b allow for ifferen ranformaion on he inepenen Brownian moion W 3 efine in poin Coneqenly if he correlaion facor aifie hen he e conain more han one elemen an o he financial marke i hen incomplee Moreoer here i an oher orce of incompleene of he marke which i he epenence of procee S an wih n

3 7 S GOUE repec o he Marko proce We gie now ome examp le of claical ochaic olailiy moel which are conaine in or moel () Example Hll-Whie: a an b S S S W W Sein-Sein: an b a S S S W Heon: W 4 8 a an b S S S W W 3 Pricing an Heging ia Local Rik Minimizaion Approach We are ineree in hi ecion in he heging of an Eropean coningen claim wih an -mearable qare inegrable ranom ariable H bae on he ynamic gien by () A an example of hi payoff we can ake an Eropean call opion: H hs S K wih mariy an rike K > We conier here he local rik-minimizaion approach o hege in hi incomplee marke We recall ome efiniion of hi approach Definiion An heging raegy i a pair ch ha i a preicable pro ce which aifie S (4) an i an aape proce ch ha (5) We will enoe by aify (4) an (5) he e of raegie which he heging raegy efine a porfolio where enoe he nmber of hare of he riky ae S hel by he ineor a ime an enoe he amon inee a ime in he bon Definiion Gien a heging raegy we call he Vale proce V of hi correponing porfolio he righ conino proce gien by V S (6) Definiion 3 Gien a heging raegy we call he Co proce C of hi correponing porfolio he proce gien by C V S (7) We can ee ha he qaniy S repreen he heging gain or loe p o ime following he heging raegy A heging raegy i calle elf-financing if i co p roce i P -a conan oer he ime an mean elf-financing if C i a P -maringale If C i qare inegrable hen he rik proce of i efine by R : C C (8) Remark 3 Since he coningen claim H i - mearable an i aape here alway exi a heging raegy ch ha V H Inee we can ake an H for all 3 Local Rik Minimizaion Approach We only conier heging raegie which replicae coningen claim H a ime hi mean ha we only allow heging raegie ch ha V H P a (9) h he heging problem i o o fin he raegy which minimize a ime he qaraic rik: min : min R H C () he iea i o o conrol he heging error a each inan by minimizing he coniional ariance of he inananeo co incremen eqenially oer ime Remark 4 An alernaie approach o hege in incomplee marke i he mean-ariance approach (ee [3]) In fac in hi approach he aim i o minimize he global rik oer he enire ime Hence i i a ifferen approach han he local rik minimizaion which foce on he minimizaion of he econ momen of he infinieimal co incremen (8) Copyrigh 3 SciRe

4 S GOUE 73 herefore he y of hi minimizaion problem in a general emimaringale cae i e o Schweizer [3] an i reqire more ampion on he ae ynamic S We ame firly ha S can be ecompoe a S S M A where M i a real ale locally qare inegrable local P -maringale nll a zero an A i a real ale aape conino proce of finie ariaion alo nll a zero We recall now he Definiion of he Srcre Coniion (SC) We ay ha he proce S aifie he (SC) if here exi a preicable proce ch ha he proce A i abolely conino wih repec o M (i e he obliqe bracke) In he ene ha A M an ch ha he o calle mean ariance raeoff proce (MV) K aifie K : M Pa Lemma Since we hae ha if he proce S i conino hen (SC) i aifie Proof See heorem of Schweizer [4] Propoiion 4 of Föllmer an Schweizer in [] how ha fining a locally rik minimizing raegy for a gien coningen claim H L P i eqialen o fining a ecompoiion of H of he form: H H S L () where H i a conan i a preicable proce aifying Coniion (4) an L i a qare inegrable P -maringale nll a an rongly orhogonal o M (ie LM i a P-maringale) he repreenaion ( ) i ally referre o a he Föllmer-Schweizer (FS) ecompoiion of he ranom ariable H Once we hae () hen he eire heging raegy which i locally rik minimizing i hen gien for all by an where wih () V S (3) V C S (4) C H L (5) In iew of hee rel fining he Föllmer-Schweizer ecompoiion () of a gien coningen claim H i imporan becae i allow o obain he locally rik minimizing raegy Mona an Sicker in [] an Pham e al in [3] gie fficien coniion o proe he exience of hi ecompoiion We herefore explain how one can ofen obain hi ecompoiion by wiching o a iably choen maringale meare for S Inee a i i hown in [] an [4] here exi a meare P which i he o calle minimal eqialen local maringale meare (minimal ELMM) ch ha V H F (6) where enoe he coniional expecaion ner P Rem ark 5 If here exi a locally rik minimizing raegy hen we can e he expreion of V appearing in (6) a a price of he coningen claim H a ime In he cae where he proce S i conino (wh ich i or cae) heorem of [] allow o conrc niqely P Inee we hae he following rel: Propoiion P exi if an only if for all Z expm S (7) i a qare inegrable maringale ner P P Moreoer : Z L P efine a probabiliy P meare P eqialen o P which i in ince one eaily erifie ha ẐS i a local P -maringale 3 Markoian Regime Swiching Cae Le S an g ien by he m oel () hen he local rik minimizing heging raegy can be obaine in wo ep: ) Deermine P an ece he ynamic of S ner P ) Fin he Galchok-Knia-Waanabe ecompoiion of H wih repec o S ner P hen he opi mal local rik minimizing heging raegy i gien by () an (3) 3 Fining P Accoring o he preio becion he eniy proce of he minimal ELMM P wih repec o P i gien by he Eqaion (7) We can firly remark ha Since S : exp Z M S exp M K i conino we hae fir of all o eer- Copyrigh 3 SciRe

5 74 S GOUE mine he canonical ecompoiion S S M M of he ae proce S ner P Propoiion Ame ha he regime ochaic olailiy moel follow () hen we hae for all ha M S W A S M S herefore we obain Z A M S an K W exp Proof I come immeiaely from he efiniion of he ynamic of or moel () We are now able o eermine he ynamic of or moel ner P Propoiion 3 Ame ha Ẑ i a re P -maringale hen he ynamic of he m oel () n er P i gi by en for all wih S W S (8) a 3 b W W a a b (9) Proof Since Ẑ i a P -maringale Girano he- orem implie ha W : W an 3 3 W := W are inepenen P -Brow nian moion Hence S SS W SS W S W an a b W 3 a b W W a b W 3 W a b 3 b W W 3 Decompoiion of he Coningen Claim H wih Repec o S ner P Le H be a coningen claim of he form H hs hen fining he Galchok-Knia- Waanabe ecompoiion of H ner P rece o ole a yem of parial ifferenial eqaion if one exploi he Markoian rcre Inee ing he Marko propery we can rewrie (6): V hs S for ome fncion efine on Propoiion 4 For all if i hen i he olion o h e yem of parial ifferenial eqaion gien by S i a i S i y q S j S i ij ji js S S i b i S i yy Sb i y S i () wih erminal coniion for all i gien by S i hs i : H an where : y : : : yy an : y S S Proof Since Copyrigh 3 SciRe

6 S GOUE 75 S S S S S S S S S S S S S S S S () an noice ha for any fncion g on which i righ conino an wih lef limi in we hae g S g S g S j g S q j j g S j g S j g S jg S j = g S j g S j Qg S Hence replacing he la eqaliy in () gie S S S S S W S S S S S 3 a b W W S S S b Sb S js j Q S he fncion i a P -maringale o all bonary erm are nll Hence we obain ha nee o aify S S S S S S a b S Sb S Q S wih erminal coniion S h S Moreoer Q S q S j S i ij ji j where mean ha a ime S i he Mark o proce i in ae i (ie i ) Hence wih i N we obain he expece rel Exam ple (Pricing E ropean call opion on he nerlying proce S) he ale of an Eropean call opion on he ock price S wih mariy an rike K i gien by hs K S Hence we can apply Propoiion 4 wih C h S S K S where he erminal coniion for all i are gien by C i y is i K Accoring o () an (5) we are now able o fin he ecompoiion of H wih repec o S ner P an o he locally rik minimizing H -amiible raegy heorem For all we hae ha he locally rik-minimizing heging raegy of H : i gien by where an S y S b S S () V (3) V V S L L S b W 3 y S j S S j Remark 6 Moreoer aking he problem a ime we ge Copyrigh 3 SciRe

7 76 S GOUE hs H : V V S L which i he o-calle Föllmer-Schweizer ecompoiion of he ranom ariable H Proof Le apply Io formla o S hs : H hen by () we obain: h S y x S S S S â S y 3 b W W S b yy y S S b S S j S j Q S We apply now he rel of Propoiion 4 o obain R 3 y b W y x S S S 3 b S b W W y S js j y x S S S S y S S b W 3 y S js j Combining hi rel wih V V S L gie he expece rel We can alo obain a formlaion of he coniional expece qare co on he ime ineral for he locally rik-minimizing raegy Propoiion 5 We hae for all ha he coniional expece qare co on he ineral for he locally rik-minimizing raegy i gien by Q Q 3 b W j j Proof Applying he rel of heorem in (8) we obain y R C C E L L 3 y b W j j 3 y b W j j bw 3 y j j We can alo implify he econ expecaion j j j j q j j Q Q Copyrigh 3 SciRe

8 S GOUE 77 o apply all he rel abo local rik minimizing heging raegy i remain o proe ha Ẑ i a re P-maringale an qare inegrable ner P A wellknown fficien coniion for boh i he bonene of he mean ariance raeoff proce K ae in Propoiion niformly in an ( ee [-4]) Propoiion 6 If he mean ariance raeoff proce K efine in Propoiion i niformly bone in an hen we hae ha: ) Ẑ i a re P -maringale an qare inegrable ner P ) H ami a Föllmer-Schweizer ecompoiion gien by () 3) : efine in () an (3) i he local rik minimizing heging raegy Example 3 (Heon moel) We can ake for he moel () a Heon moel cae Hence by Example we ake N wih a N 4 8 N N wih an b N an he conan i i an i are all nonnegaie for all i An we ame for he exience an poiiiy of he olion ha for all i i i i he moel i hen gien by S S S W W an he correponing mean ariance raeoff proce i hen gien by K Hence he MV proce K i eerminiic o bone niformly in an hi implie ha Z i a P-maringale an o ha we can apply all he rel menione before 4 Pricing Opion on he Volailiy: We are now ineree in eablihing ome formlae o price opion bae on he ochaic olaili y proce 4 Variance Swap A ariance wap i a forwar conrac on he annalize ariance which i he qare of he realize annal olailiy h le R enoe he realize annal ock ariance oer he life of he conrac hen i i gien by: R (34) Le K an M enoe he eliery price for ariance an he no ional amon of he wap in ollar per annalize olailiy poin qare hen he payoff H of he ariance wap a he mariy ime i gien by H M R K Iniiely he byer will receie M ollar for each poin by which he realize annal ariance R ha exceee he ariance eliery price K he rel proie in he eqel are an exenion of he rel obaine in [] Inee firly we y more general cla of ochaic olailiy moel an econly we apply or rel in he pariclar cae of Heon moel b where no only he long-erm olailiy leel epen on he regime b alo he pee of mean reerion on he olailiy of he olailiy Hence we ar by coniering he ealaion of he coniional price of a eriaie H gien he informaion abo he ample pah of he Marko proce from ime o ime (ie ) hi mean ha we ame o know all he hioric al pah of he Marko proce Ame alo ha we are ner he minimal ELMM P h we recall ha in hi cae or regime wiching moel i gien by: S S W a 3 b W W wih a a b In pariclar gien he coniional price of he ariance wap P i gien by P H F M R K F (35) M R F MK Hence if we enoe a preio Copyrigh 3 SciRe

9 78 S GOUE 3 W W W we obain by Iô formla ha for all a b b W h gien we ge F : a b So (36) (37) a b (38) Ampion 3 Ame ha we know he olion of Eqaion (38) which we will enoe by y for all Propoiion 37 Uner Ampion 3 we hae for all ha he coniional ariance wap price P() i gien by P M y K (39) Example 34 (Heon Moel) Ame ha we are in he Heon moel cae Hence a menione in Example we ake an a 4 8 b hen he ynamic of i gien by W Moreoer (38) become re Le y : hen we hae o ole he iffey y he olion nial eqaion of hi ifferenial eqaion i gien for all y y exp h we ge exp exp exp exp exp by (33) We can now obain he coniional ariance wap price by applying Propoiion 37: exp P M exp K exp We can alo obain he ale of he coniional ariance gien he fll hi ory of Lemma 3 For all he coniional ariance of i gien by Var 4a 6 b a b a b Proof By Io lemma we ge 4 4 a 6 b 4 b W Hence gien we fin ha 4 4 (33) 4 a 6 b Uing (37) an he efiniion of he ariance gie he rel Example 35 (Heon Moel) We conine he y of he Heon moel cae (ee Example 34) h Eqaion (33) gie 4 E 4 3 E Copyrigh 3 SciRe

10 S GOUE 79 Gien (33) we know ha exp exp exp hich i a fncion of w ime an he Marko proce Le : 4 z hen we hae o ole he ifferenial eqaion gien by z y 3 z he olion of hi ifferenial eqaion i gien for by z q z all where exp q y exp y exp exp We finally obain in he Heon moel cae ha 4 e e y 4 e an ha he coniional ariance i eqal o Var e e y exp exp exp exp exp 4 Pricing Volailiy Swap In hi ecion we follow he ame mehoology ie by Broaie an Jain in [8] where here i no regime wiching componen We recall ha he realize annal ock ariance oer he life of he conrac i gien by (34) an epen on he ale of he Marko proce Denoe by I he accmlae ariance beween ime o We recall ha he proce i he olion of he ochaic ifferenial eqaion gien by W a b b Hence I i he olion of he ochaic ifferenial eqaion gien by I Le efine by E he expecaion a ime wih repec o E (33) Hence E epen on he ariance proce of he nerlying ae an on he Marko proce We call by fair coniional ariance rike price he qaniy K which i efine ch ha Eqaion 35 anihe: P H F M R K F M R K hen we hae ha K R F an for ime we obain ha E K We efine now he forwar price proce Z a Z F (333) Propoiion 38 he forwar price proce Z can be expree a a fncion F I an i i he olion of he yem of ochaic ifferenial eqaion gien by F F F a b I F 4 b QF I (334) wih bonary coniion gien by I F I Proof Rewrie Z a Copyrigh 3 SciRe

11 8 S GOUE Z I : F I Applying Iô Lemma o F ing (36) an he fac ha he forwar price meare F i a maringale gie he expece rel 5 Conclion Marke MAHEMAICAL Finance Vol No 4 pp oi:/ [3] M Schweizer Opion Heging for Semimaringale Sochaic Procee an heir Applicaion Vol 37 No 99 pp oi:6/34-449(9)953-f [4] M Schweizer On he Minimal Maringale Meare an he Föllmer-Schweizer Decompoiion Sochaic Analyi an Applicaion Vol 3 No pp oi:8/ [5] R J Ellio L Aggon an J B Moore Hien Marko Moel: Eimaion an Conrol Springer-Verlag New ork [6] S Goe an B Zo Conino ime Regime Swiching Moel Applie o Foreign Exchange Rae CREA In hi paper we ie he problem of pricin g an heging opion bae on an ae which i moele by a regime wiching ochaic olailiy moel We preene firly hi cla of regime wiching ochaic olailiy moel We hown ha hi cla of regime wiching moel encompae a large panel of claical Dicion Paper Serie -6 Cener for Reearch in financial moel We alo explaine he inere in appli- Economic Analyi Unieriy of Lxemborg Lxemborg Ciy caion of hi kin of moel Seconly we e he local rik minimizaion approach o ole he problem of [7] G B Di Mai M Kabano an W J Rnggalier pricing an heging coningen claim in hi incomplee Mean Variance Heging of Opion on Sock wih Marko Volailiie heory of Probabiliy an I Ap- marke h we obaine pricing an heging formlae plicaion Vol 39 No 994 pp 7-8 an alo he formla of he opimal heging raegy oi:37/398 Finally we fn formlae o price olailiy an ariance [8] M Broaie an A Jain Pricing an Heging Volailiy wap opion by oling a yem of ochaic iffe- Deriaie Jornal of Deriaie Vol 5 No 3 8 renial eqaion pp 7-4 oi:395/jo8753 Some poible fre irecion in hi fiel of re- [9] S L Heon A Cloe-Form Solion for Opion wih earch are he following: Sochaic wih Applicaion o Bon an Crrency Opion - Deelop a meho o eimae all he parameer of Reiew of Financial Sie Vol 6 No 993 hi cla of regime wiching moel incling he pp oi:93/rf/637 hien Marko chain (i raniion marix); [] R J Ellio K Si L Chan an J W La Pricing - Apply hee pricing an heging formlae o eco- Volailiy Swap Uner Heon Sochaic Volailiy nomic an financial aa Inee regaring he exi- Moel wih Regime Swiching Applie Mahemaical Finance Vol 4 No 6 pp 4-6 ing lierare a goo caniae col be he elecrioi:8/ ciy po price; [] M Romano an N ozi Coningen Claim an Marke Compleene in a Sochaic Volailiy Moel Mahe- - Conrc a meho o ealae qickly he olion of he yem of ochaic ifferenial Eqaion maical Finance Vol 7 No pp () an (334) A yem of paial an ime icreizaion gri col be coniere an inei- [] P Mona an C Sricker Föllmer Schweizer Decompo- oi:/ gae iion an Mean-Variance Heging of General Claim Annal of Probabiliy Vol 3 No 995 pp oi:4/aop/ REFERENCES [3] H Pham Rheinläner an M Schweizer Mean-Va- [] H Föllmer an M Schweizer Heging Coningen riance Heging for Conino Procee: New Rel Claim ner Incomplee Informaion In: M H A an Example Finance an Sochaic Vol No Dai an R J Ellio E Applie Sochaic Analyi 998 pp oi:7/78537 Sochaic Monographe Goron an Breach 99 [4] D Lepingle an J Mémin Sr l Inégrabilié Uniforme e Maringale Exponenielle Zeichrif für Wahrcheinlichkeiheorie [] D Healh E Plaen an M Schweizer A Comparion n erwane Gebiee Vol 4 of wo Qaraic Approache o Heging in Incomplee 978 pp 75-3 Copyrigh 3 SciRe