Pricing Model for Owner s Payment Bond in China

Transcription

1 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 Pricing Moel for Owner s Payent Bon in China Hi Wang, Xiaoei Deng, an Weiha Yang Abstract o reveal the pricing echanis of an owner s payent bon an iprove warrantor risk anageent, a pricing oel of an owner s payent bon was evelope in a risk netral valation fraework he pricing oel cobines the niqe characteristics of an owner s payent bon sing a binoial tree etho A nerical silation sing a real estate project as an exaple was create by copiling a progra in the C# langage base on the oel he finings of the silation not only verifie the reliability of the oel bt also escribe explicitly the relationship between bon prices an the ain inflencing factors Inex ers Beran pt option, binoial tree etho, owner s payent bon, pricing oel I IRODUCIO HE Chinese constrction arket is a byer s arket If owners efalt on an fail to ake on-tie payents regaring the contractors engineering costs accoring to the constrction contract, the contractors interests will be seriosly violate, an the son evelopent of the constrction instry will also be hapere [], [] o avoi owners payent efalts, the Chinese governent has focse on the ipleentation of an owner s payent bon syste since 3 In the agreeent of the owner s payent bon, the warrantor provies the contractor with a written bon that the project owner will pay on tie as agree in the constrction contracts an will pay the contractor if the owner efalts his creation in the history of constrction contract bons focses on solving constrction payent arrears [], [3] However, the prei of an owner s payent bon contines to ecline after ecaes of evelopent, which leas to a sitation in which the incoe an risk of warrantors are neqal, an any warrantors refse to nerwrite owner s payent bons hese phenoena restrict the evelopent of the srety instry an pose an ipeient to the establishent of a constrction arket s creit syste o stanarize the bon prei in the srety instry, soe provincial an nicipal athorities Manscript receive Mar 3, 5; revise Jn, 5 his work is spporte by the ational atral Science Fonation of China (SFC) (74734) Hi Wang is with the Departent of Constrction Manageent, singha University, Beijing, an with the Departent of Military Finance, Military Econoics Acaey, Whan, China (e-ail: hi-wang@ailstsinghaecn) Xiaoei Deng is with Departent of Constrction Manageent, singha University, Beijing, China (Corresponing Athor, phone: (86) ; e-ail: engx@tsinghaecn) Weiha Yang is with the Departent of Military Finance, Military Econoics Acaey, Whan, China (e-ail: lalabirch@hotailco) have isse specific reglations For exaple, the city of Xiaen reqires that the prei be eterine accoring to the length of the bon valiity perio [4] Henan Province refers to the eterination etho of the loan interest rate an charges the bon prei base on ifferent vales of collaterals that warrantees provie to warrantors [5] he vast ifferences in bon prei reglation in ifferent regions have shown that the pricing ethos of owner s payent bons have not yet reache consenss; oreover, ifferent reglations have le to confsion in bon pricing herefore, the perforance of prei reglations is not satisfactory o create a fair traing environent an se the owner s payent bon to reasonably share the constrction risks, it is highly necessary to sty the pricing echanis of the owner s payent bon his sty aie to evelop a pricing oel for an owner s payent bon base on the binoial tree etho to reveal the bon pricing echanis in a risk netral valation fraework he evelope oel can help the ifferent parties involve in the bon transactions to achieve a consenss regaring the owner s payent bon pricing etho After nerical silations sing an exaple an copiling a progra in the C# langage base on the oel, this sty se ipact analysis to escribe explicitly the relationship between the bon price an the ain inflencing factors he paper is organize as follows After a brief introction of the Chinese constrction contract bon syste in Section, the anscript presents relate sties in Section 3 Section 4 introces the research etho, an Section 5 evelops a pricing oel for the owner s payent bon base on the binoial tree etho Section 6 focses on a nerical silation with an application create by copiling a progra in the C# langage base on the oel Section 7 iscsses the practical an theoretical iplications of the finings he final section sarizes the paper an offers sggestions for frther research II BACKGROUD IFORMAIO It has been hypothesize that the Chinese constrction contract bon syste is the echanis throgh which the ean of the constrction arket creit can be et Owners an contractors are the two basic sbjects in the constrction arket herefore, the constrction contract bon syste shol avoi efalt risks of owners an contractors an exten their creit On the one han, to avoi efalt risks of contractors, (Avance online pblication: 4 oveber 5)

2 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 they (contractors) can be reqire to provie bi bons, perforance bons, payent bons, avance payent bons, aintenance bons, etc Uner these contracts, contractors will perfor as agree in the plans, specifications, an constrction contracts he bi bons, perforance bons, an payent bons are anatory bon procts in real estate evelopent projects beyon a certain scale in China Of corse, they can also be se in other constrction projects On the other han, owners payent efalts becae the priary origin of chaos in the Chinese constrction arket at the beginning of the st centry Accoring to the inforation of the ational Brea of Statistics of the People s Repblic of China, the clative total of constrction payent arrears in the whole constrction instry was 36 billion yan in 996 an increase to billion yan in 999 At the en of, the total exceee 78 billion yan Frtherore, it shol be note that part of the arrears were e to by nscrplos owners who elaye payent intentionally herefore, the Chinese governent place ephasis on the ipleentation of owners payent bons to avoi the proble arising fro owners payent efalts he following escribes the basic coponents of the owner s payent bon in China Accoring to the reglations of the MOHURD (Ministry of Hosing an Urban-Rral Developent of the People s Repblic of China, forerly known as the China Ministry of Constrction), if the contract vale of a real estate project excees illion yan (approxiately $63 illion), real estate evelopers st sbit an owner s payent bon to the contractor Soe regions have ae other reglations base on this, eg, the city of Xiaen reqires an owner s payent bon for all constrction projects with a constrction area over sqare eters or total project costs above illion yan (approxiately $6 illion) An owner s payent bon, which is an accessory contract base on a constrction contract, can be written by a srety copany or bank he owners first sbit an application to the warrantor, an then, by exaining the creit stats an paying a certain aont of prei, the warrantor provies a bon he bone aont shall not be lower than a certain proportion of the contract price, sch as at least % in any cities of China, an no less than the axi aont of the progress payents agree pon in the contract When a schele payent is coplete, the bon will be atoatically converte to the next stage, an this process contines ntil the owner akes all of the payents ner the secre constrction contract he warrantor will ipleent payent obligation to ensre the payent on behalf of the principal (owner) if he/she efalts If a warrantor pai, he/she has the right of recorse against the owner If the entire bone aont has been se p becase of the owner s efalt, he/she shall resbit another owner s payent bon with the sae aont as the previos one within an allotte tie Otherwise, the contractor shall exercise the right to sspen work an clai aages If the garantors pai, they ay recover fro the owner In essence, contractors are epowere with rights (not obligations) regaring the agreeent of an owner s payent bon If the contractor oes not receive the constrction payent on tie, he/she can choose to exercise the owner s payent bon to protect the contractor s own rights an interests III RELAED SUDIES he pricing of bons is ifferent fro the pricing of orinary cooities he pricing of orinary cooities has been a research focs in the fiel of icro-econoics he ain theories incle the labor theory of vale, the tility theory of vale an the general eqilibri theory in neoclassical econoics, etc Althogh eriving fro ifferent aspects, these theories iply one coon intrinsic character: they are base on historical costs he concept of ftre can harly be fon in the pricing of orinary cooities, which therefore avois the ipact of ncertainty regaring the ftre vales of assets However, bon pricing st face the ftre he theory of bon pricing i not ake ch breakthrogh ntil the creation of the creit rationing theory, the averse selection of loan interest rates an the incentive effect theory, which provies a theoretical basis for bon pricing Merton (973) [6] first illstrate that the theory of warrant pricing is analogos to that of a pt option Hence, the theory of options has been wiely se in the pricing of creit loan garantees Jones an Mason (98) [7] se the etho of Markov chains to evelop nerical soltions of loan garantees base on the option etho Lai (99) [8] constrcte a iscrete-tie oel to vale private loan garantees accoring to the option-pricing theory Dietsch an Petey () [9] estiate the creit risk vale of sall coercial loans sing a VaR (Vale at Risk) oel L an Ko (5) [] gage the creit risk of garantee isses sing a arket-base risk netral approach Chang et al (6) [] constrcte oels to analyze the vales an efalt probability of joint loan garantees sing an option approach In contrast to creit loan garantee pricing, harly any sties have investigate the isse of constrction contract bon pricing Becase this conventional bon is regare as a syste to avoi contract efalt throgh the screening of constrction risks [], the ost iportant link is the nerwriting process herefore, any scholars have focse on nerwriting technologies an ethos to help nerwriters assess the efalt risks of contractors [3], [4], [5], [6] In reality, any warrantors wol have to pay copensation for the efalts of contractors an even go bankrpt Sch phenoena are ore coon when econoies go ownwars [7] hs, the efalt risk vale shol be taken into accont when calclating the bon prei In spite of this proble, the literatre on estiating the efalt risk vale of constrction contract bons is sparse Hang (8) [8] referre to the creit efalt swap (CDS) oel to eterine the price of contractor perforance bons, an Ci (8) [9] se the real option theory to evalate the warranty ters of the o 44 highway in ew Mexico Base on the characteristics of the ters of exercise in the agreeent of bons, creit loan garantees can be exercise only pon the atrity ate of the garantee loan, siilarly to the Eropean pt option Contractors garantee by perforance bons or warranty bons ay (Avance online pblication: 4 oveber 5)

3 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 efalt at any tie ring the entire garantee perio Fro the view of warrantors, the perforance or warranty bon can be exercise at any tie, siilarly to the Aerican pt option However, the owner s payent bon can only be exercise at finite tie points preeterine in the constrction contract, which is siilar to the Beran pt option Althogh siilar to the Beran pt option, an owner s payent bon has three istinct featres First, a constrction payent seqence exists in the owner s payent bon agreeent, which inicates the existence of a strike price seqence For the financial option contract, there is sally only one strike price, naely the preeterine ftre price of the nerlying asset [], [] However, for the constrction project pai accoring to the constrction schele, the whole constrction project is ivie into finite intereiate constrction procts that contractors finish ring each payent perio In aition, the vales of each intereiate constrction proct, ie, the constrction payent reqire in each perio, for the strike price seqence agree to in the owner s payent bon Each eleent of the strike price seqence is an aitional factor that eterines whether the owner s payent bon will be exercise Secon, the risk vale of the owner s payent bon originates ainly fro the ncertainty of the vale of the owner s assets, an whether the bon is exercise ainly epens on the coparison between the vale of the owner s assets an the payent seqence In a financial option contract, the option vale (ie, the fair price of an option) ainly erives fro the ncertainty of the nerlying asset s ftre vale he coparison between the asset s ftre price an the strike price eterines whether the option will be exercise he ftre price an strike price are base on the sae nerlying asset, sch as stocks or foreign crrencies However, owner s payent bons are ifferent he payent seqence (ie, strike price seqence) is base on the vale of the constrction project propose However, the vale of the owner s assets epens on all of the assets of the owner, incling the constrction project hs, an owner s payent bon involves two sbject atters: one is the constrction project, an the other is the owner s assets Althogh the vale of the constrction project ay change ring the constrction process e to changes in prices, policy, engineering change, etc, this will also change the vale of the owner s assets For exaple, if the vale of the constrction project rises, so will the vale of the owner s assets, an the owner can refinance base on the project s increental vale to ake p the aitional aont of the crrent payent herefore, to siplify the research qestion, the vale of the constrction project propose can be viewe as constant, an the risk vale of the owner s payent bon ainly erives fro the ncertainty of the vale of the owner s assets hir, the change in the vale of the owner s assets is a specific jp-own process e to payent in aition to the iffsion process In aition to general flctations (often referre to as the iffsion process), the ftre vale change of the nerlying asset will also constitte a jp process e to policy an arket changes Frtherore, this jp-iffsion process is rano However, the changes in owner asset vale incle a specific jp-own process e to payent for the crrent projects, in aition to the general rano iffsion process he tie an size of the vale jps can be preeterine accoring to the propose constrction organization esign, constrction contract, an other ocents, an provies convenient pricing o sarize, base on the characteristics of the ters of exercise in the bon agreeent, the pricing etho for existing creit loan garantees an contractor s perforance bons cannot be applie irectly to the pricing of owner s payent bons Moreover, the owner s payent bon has its own featres that istingish it fro the Beran pt option; ths, the pricing etho of the Beran pt option also cannot be applie irectly to the pricing of owner s payent bons herefore, this sty constrcts a pricing oel for owner s payent bons sing a binoial tree etho with reference to the pricing theory of the Beran pt option, verifies the reliability of the oel, an escribes explicitly the relationship between the bon price an the ain inflencing factors throgh a nerical silation application IV RESEARCH MEHOD he Beran option is a type of exotic option [] Lattice an finite ifference ethos, sch as the binoial tree etho [3], a lattice etho base on an approxiation to the transition ensity fnction of the Lévy process [4], an low-iscrepancy esh ethos [5], are sally se to price Beran options [6] he binoial tree etho can clearly ece the possible ftre vales of nerlying assets [7] It is a siple an irect etho to escribe the iffsion an jp-own processes of the ftre vale of owner s assets, an it is easy for all parties of the bon transaction to accept herefore, this paper ses the binoial tree etho to price the owner s payent bon he binoial tree etho is a coon approach for pricing varios coplicate options an other financial erivatives It is asse that the vale changes of an nerlying asset can be escribe by any one-perio an two-state oels ring the entire contract perio Backwar ection can then be applie to calclate the vale of the financial erivative at the initial oent [8] his constittes the basic iea of the binoial tree etho he one-perio an two-state oels asse that the arket is copletely non-arbitrage Unerlying assets are trae at the initial tie t= an at the terinal tie t= only ring the vali perio [, ] of the option contract In aition, the asset has two possible states at the terinal tie t=: S S, S S, where, S an S represent the p-ove an own-ove of the asset s vale, respectively, is the p factor, an is the own factor he p an own factors can be calclate sing the nerlying asset s historical volatility an the tie length t : exp( t), exp( t) he -Heging techniqe is then applie to efine the risk-netral probability easre Q, ie, in the ftre at tie (Avance online pblication: 4 oveber 5)

4 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 he increasing probability of S is shown in Eq (): q Pr ob { Q S S} he ecreasing probability of S is shown in Eq (): q Pr ob { Q S S} () where the interest rate factor is exp( r t), an r is the risk free interest rate, which is sally eterine by referring to the crrent reasry rate he asset s vales S an S are copare with the striking price to assess the bon vales V an V at the terinal tie, an the backwar ection an isconte ethos are then se to achieve the bon fair price V at the initial oent, as shown in Eq (3): Q V E ( V) [ qv ( q) V ] (3) If the lifetie of the bon contract is ivie into finite continos sbintervals, all of the possible evelopent paths of the owner s asset vale can be silate by assing that the vales of the owner s assets are in line with the one-perio an two-state oels in each sbinterval an consiering the jp-own process at every constrction payent tie point he possible bon vales at the terinal oent (ie, possible copensation) can then be calclate Base on these possible bon vales, we can obtain the initial vale of the payent bon (ie, the fair price of the bon) sing backwar ection an the isconte etho For an owner s payent bon, we shol copare the warrantor s possible copensations with the expecte vales calclate throgh the isconte etho at each constrction payent point he bon vale shol be the greater vale at this tie point V PRICIG MODEL FOR OWER S PAYME BOD A Basic Assptions Assption I: he capital arket is a coplete, frictionless, an arbitrage-free arket, which eans when the owner is sing the crrent assets to finance, the transaction costs o not nee to be taken into consieration, an the owner can reaily obtain the eqivalent aont of capital with the assets Assption II: Once the owner s payent bon has been execte, the agreeent between the warrantor an warrantee is terinate, even if the aont pai is lower than the aont of the bon Assption III: Vale changes in the owner s assets are sbject to the binoial process he rising or falling process of its vale can be escribe throgh a large nber of one-perio an two-state oels In an agreeent of an owner s payent bon, the vali ate is enote as [, ] Accoring to the constrction contract, the payent is to be coplete by tie he tie seqence is recore as M ={,,, i,, }, where < < < i < < = he corresponing payent seqence is enote as C={C, C,, C i,,c }, where the () axi vale in the seqence is recore as C M At the tie point, the vale of the owner s assets is recore as S he contract aont of the garantee project is P, an the reqire ini secrity percentage is l herefore, the bone aont of the owner payent bon can be escribe as G ax( C, lp) B Binoial Evoltion of Vale of Owner s Assets he vali ate [, ] of the owner s payent bon is first ivie into sbintervals: = t <t <t < <t n = =, where he nber of segents t in each sbinterval is enote as M = {,,, i,, } he initial vale of the owner s assets is S In the first payent perio [, ], the vale of the assets wol evolve into a binoial oel, as shown in Figre Fig M Binoial tree oel for vale of owner s assets in the first payent perio At tie, these possible vales of the owner s assets will jp own ieiately after the owner pays an aont of C, as shown in Eq (4): ( ) S S C (4),, the vale of the owner s If S C assets is greater than the crrent project payent he owners will choose to pay, an the assets vale will contine to evolve to the next stage If S C, the vale of the owner s assets is not able to cover the crrent project payent, an the owner will fail to pay If the contractor chooses to exercise the bon, the evolving process of the vale of the owner s assets ceases o calclate the vale of the bon easily sing backwar inction, we can asse that the evoltion of the vale of the owner s assets contines, bt the vale is negative In the secon payent perio (, ], the possible ( ) vales S at tie becoe the initial vale he vales of the owner s assets evolve into a grop of new binoial branches At tie, the possible vales of the owner s assets are escribe as in Eq (5) after the payent of C where S S C (5) (, ) ( ), Siilar evoltions contine to the last payent perio ( -, ] At tie, the possible vales of the owner s assets are escribe in Eq (6) after the payent of C (,,, ) (,,, ) (6) S S C (Avance online pblication: 4 oveber 5)

5 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 where,,, V (,,,, ) t, C Backwar Inction of he Owner s Payent Bon Accoring to the whole binoial tree oel for the vale of the owner s assets, the fair price of the owner s payent bon can be calclate sing backwar inction he vale of the owner s payent bon at the final tie At tie, the contractor has the right to exercise the owner s bon payent option Whether the right is ipleente epens on the coparison between the assets vale an the crrent payent (,,, ) If S C, inicating that the vale of the owner s assets is greater than the crrent project payent, the owner will choose to pay; otherwise, the contractor col exercise the owner s payent bon, an the warrantor wol pay on behalf of the principal he warrantor is entitle to recorse fro the owner In the en, the owner wol not only nee to recover the losses of the warrantor bt also lose the owner s own creit At this tie, the vale of the owner s payent bon (,,,, ) V is (,,, ) If S C, inicating that the owner is not able to pay the crrent project costs, the contractor chooses to exercise the bon becase of the owner s payent efalt he vale of the bon is the aont actally pai at that oent If (,,, ), the pai aont is C S G (,,, ) C S ; otherwise, the pai aont is G hs, at the final payent tie, the vale of the owner s payent bon is escribe in Eq (7): (,,,, ) V C S in(, ), where (,,, ), (,,, ) C S G C (,,, ) S,,,, he vale of the owner s payent bon at the penltiate tie - Base on the bon vale at, we can obtain the bon s possible vales at tie t t, ie, closely preceing t, as shown in Eq (8): (7) [ (,,,, ) ( ) (,,,, ) qv q V ] (8) (,,,, ) Base on the bon vale of at tie V t t, the bon vale at tie can be obtaine throgh backwar inction However, at tie, the bon vale shol be copare with the corresponing (,,, ) vale of the owner s assets If S S (,,, ), inicating that the crrent vale of the owner s assets is insfficient to pay C, the owner s payent bon will be exercise, an the bon vale wol (,,, ) be S at this oent; otherwise, the bon vale is the aont calclate by backwar inction, as shown in Eq (9): (,,,, ) V l l (,,,, l) ( ) ( ), q q V S l l ( ) (,,, ), S S (9)! where represents the nber of l l! l! cobinations;,,,, V (,,, ) he bon vales of V (,,, i ) i (, ),, V, V ( ),, can be obtaine throgh siilar backwar inction Finally, we can calclate the initial vale of the owner s payent bon (ie, the fair ( ) price) on the basis of V, as shown in Eq (): l l ( ) V q ( q) V l l () VI SIMULAIO APPLICAIO OF HE PRICIG MODEL A Project Profile A is a real estate evelopent copany that is planning to bil a resiential biling hrogh pblic biing, constrction copany Z is selecte as the sccessfl tener to sign the contract he contract aont P is illion yan he tie liit of the project is year, an a progress payent will be ae each qarter Copany Z has calclate the payent seqence accoring to the propose constrction organization esign: C= {C, C, C 3, C 4 } = {3 illion yan, 3 illion yan, 3 illion yan, 3 illion yan} Before signing the constrction contract, copany Z provies a contractor s perforance bon to copany A, an copany A is reqire to offer an owner s payent (Avance online pblication: 4 oveber 5)

6 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 bon in retrn Accoring to the reqireents of local constrction athorities, the owner s payent bon shall not be less than % of the contract aont, an shall not be less than the axi aont of the progress payents Hence, the bon aont of this owner s payent bon can be escribe as Gax( C,% P) ax(3,) 3 (illion yan) M We asse that copany A file an application to the srety copany HM to isse the owner s payent bon an that, throgh an nerwriting investigation, HM then eterines that copany A s crrent asset vale is illion yan he onthly stanar eviation of changes in assets (ie, volatility of owner s assets) is 5, an the crrent one-year treasry rate r is 4% If copany HM agree to nerwrite an owner s payent bon with a -year perio of valiity for copany A, we then ai to eterine the fair price of the owner s payent bon hrogh nerical silation by copiling a progra in the C# langage base on the previos pricing oel, the fair price of the owner s payent bon is eterine to be 54, yan an the prei rate is 8%, which is in line with the experience of previos charges B Ipact Analysis of Major Paraeter Changes Accoring to the pricing oel for the owner s payent bon, the fair price of the owner s payent bon is eterine by the initial vale of the owner s assets S, the owner s asset volatility σ, the risk-free interest rate r, the bone aont G, an the perio of valiity An ipact analysis was concte to evalate the effects of these paraeter changes on the fair price of the bon base on the previos exaple Ipact of Change in he Initial Vale of he Owner s Assets on Pricing he relation crve of the initial vale of the owner s assets S an the fair price of the owner s payent bon is shown in Figre When S is illion yan, the price of the payent bon is 759 thosan yan an the prei rate is 353%, inicating that the owner s efalt risks increase sharply with the ecline of S when the initial vale of the owner s assets is lower than the contract price, an the price of the bon increases rapily in parallel In contrast, when S is 3 illion yan, the price of the bon is 67 yan, an the prei rate is %, inicating that the owner s efalt risks are rece rapily with the increase in S when the initial vale of the owner s assets is higher than the contract price an the price eclines ring this perio hs, the initial vale of the owner s assets has a significant inflence on the pricing of the owner s payent bon When S oves towar the irection that is lower than the contract price, the owner s efalt risks increase rapily, in parallel to the price of the bon When S oves towar the irection that is higher than the contract price, the owner s efalt risks ecline rapily, an the price of the bon will go own ( ) he Fair Price of he Bon ten thosan yan he Initial Vale of he Owner s Assets S (ten thosan yan) Fig Ipact of the initial vale of the owner s assets S on the pricing of the owner s payent bon Ipact of change in the owner s asset volatility on pricing he relation crve between the owner s asset volatility σ an the pricing of the payent bon is shown in Figre 3 When σ is, the price is 3 thosan yan; when σ is, the price increases to 4955 thosan yan his fining inicates that when the owner s ftre asset volatility σ eclines, the price of the bon will ecrease as well, whereas when the owner s ftre asset volatility σ increases, the probability of efalt increases, an the bon price will increase he Fair Price of he Bon (ten thosan yan) he Owner s Asset Volatility σ Fig 3 Ipact of the owner s asset volatility σ on the pricing of the owner s payent bon Ipact of change in risk-free interest rate on pricing he relation crve between the risk-free rate r an the pricing of bons is shown in Figre 4 When r is 5%, the price is yan, an when r is %, the price is 98 thosan yan, inicating that the price of the owner s payent bon eclines as the risk-free interest rate rises (Avance online pblication: 4 oveber 5)

7 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 he Fair Price of he Bon (ten thosan yan) Risk-free Interest Rate r Fig 4 Ipact of risk-free interest rate r on the pricing of the owner s payent bon Ipact of change in bone aont on pricing he relation crve between the bone aont G an the pricing of bons is shown in Figre 5 When G is thosan yan, the price is 36 thosan yan, an as the bone aont increases, the bon price goes p, whereas when G increases to approxiately illion yan, the bon price stabilizes at 54 thosan yan espite any frther increase in G By exaining the evoltion of the vale of the owner s assets, it can be eterine that even if the vale of the owner s assets contine to ecrease, the axi aont of copensation wol be 7 illion yan after the final payent herefore, the expecte loss of the bon oes not change even if the bone aont excees 7 illion yan, which eans that the bon price will increase as the bone aont increases; however, the price will reain nchange when the bone aont reaches a certain level he FairPrice of he Bon (ten thosan yan) Bone Aont G (ten thosan yan) Fig 5 Ipact of bone aont G on the pricing of the owner s payent bon Ipact of change in the bon vali perio on pricing o copare the effects of the vali perio on the owner s payent bon as the other oel variables reain nchange, the bon prices were calclate when the vali perios were 4, 8,, 6,, 4, 8, 3, 36, 4, 44, an 48 onths he corresponing bon prices are shown in Figre 6 he lowest price, approxiately 534 thosan yan, is obtaine when is 4 onths, whereas highest price, ie, reaching 546 thosan yan, is fon when is 48 onths he bon price increases with an increase in the perio of valiity, bt the range of this change is sall he Fair Price of he Bon (ten thosan yan) Vali Perio (onth) Fig 6 Ipact of the bon vali perio on the pricing of the owner s payent bon VII DISCUSSIO Base on the reslts of the silation, the relationship between bon price an the variables in the pricing oel, sch as the initial vale of the owner s assets, the volatility of the owner s assets, the bone aont, an the vali perio, are in line with people s coon nerstaning his fining illstrates that the pricing oel for owner s payent bons agrees with reality In China s constrction contract bon practice, it is generally believe that high-risk-free rates coe along with high opportnity costs, which shol bring ore profit to the warrantor However, the relationship between risk-free rates an bon price escribe by the oel appears ifferent fro the sal nerstaning of this relationship In fact, it shol be note that the constrction contract bon is ifferent fro coon investents When risk-free rates increase, on the one han, the owner s ROE (retrn on asset) increases an ths reces the risk of payent efalt; on the other han, the present vale of ftre engineering payent eclines, an the corresponing present vale of the bone aont also ecreases hs, the price of the owner s payent bon ecreases he inflence of ifferent variables reveale fro the pricing oel for owner s payent bons can offer reference for the risk anageent of warrantors Meanwhile, there are ltiple factors that affect the pricing of owner s payent bons If the bon price is reglate only by a certain factor, sch as the length of the constrction perio or the aont of conter garantee, it is nreasonable an wol even lea to spervisory isarray hs, it is recoene to start with the prootion of the owner s payent bon pricing etho to achieve a consenss aong the ifferent parties involve he fair price of the owner s payent bon, as eterine by the pricing echanis, col provie a theoretical basis for fair trae an a easreent of the fair vale of warrantor incoes (Avance online pblication: 4 oveber 5)

8 IAEG International Jornal of Applie Matheatics, 45:4, IJAM_45_4_9 In aition, when the bone aont excees the largest possible copensation of the owner, the risk vale of the owner s payent bon oes not increase Accoring to the reglations on owner s payent bons, ie, the bone aont shall not be lower than a certain proportion of the contract price an no less than the axi aont of installents agree pon in the constrction contract, it appears that the reglations lea to a garantee srpls for an honest owner However, there are any ishonest (or bone rationality) owners, as entione in Section his srpls can contribte to the prevention of alicios arrears VIII COCLUSIOS AD FURHER RESEARCH his sty reveale the pricing echanis of owner s payent bons throgh a risk-netral pricing oel base on the binoial tree etho he silation of an application case not only verifie the reliability of the oel bt also escribe explicitly the relationship between the bon price an the ain inflencing factors hese finings not only establish a theoretical basis for the fair trae an reglation of owner s payent bons bt also offer reference for the risk anageent of warrantors o siplify the oel, a series of assptions were ae: the arket is arbitrage-free, the volatility of the owner s assets is known, an there are no transaction costs, etc In reality, the actal transaction price of an owner s payent bon wol be affecte by any other factors, sch as spply-ean relationships, transaction costs, an risk preferences In particlar, the preiction of the volatility of an owner s ftre assets is a coplicate process becase asset volatility is associate with the characteristics of the instry in which an owner operates, the historical inforation of the owner s assets, an the historical prices of the transaction of the bon herefore, frther research will focs on relaxing the assptions in the owner s payent bon pricing oel an incling ore reality factors base on ata acclation to graally iprove the pricing theory syste of owner s payent bons REFERECES [] X Meng, Garantees for Contractor s Perforance an Owner s Payent in China Jornal of Constrction Engineering an Manageent, vol 8, no 3, pp 3-37, [] H Abl-Rahan, M Kho, an C Wang, Late Payent an onpayent Encontere by Contracting Firs in a Fast-Developing Econoy Jornal of Professional Isses in Engineering Ecation an Practice, vol 4, no, pp 433, 4 [3] X Deng Sty on the Constrction Boning Syste in China (n e) Beijing: China Architectre an Biling Press, (Chinese) [4] XCAB (Xiaoen Constrction & Ainistration Brea) he otice on he Prei of Srety Bons Sho Be Incle in Constrction Cost (o5, 8), 8 Available: , (Chinese) [5] HACPB (Henan Association for Constrction Project Biing) he Giance on he Prei Stanar of Srety Bons (o, 9), 9 Available: 工 程 担 保 &sallclassnae= 相 关 文 件, (Chinese) [6] R C Merton, heory of rational option pricing Bell Jornal of Econoics an Manageent Science, vol 4, no, pp 4-83, 973 [7] E P Jones, an S P Mason, he valation of loan garantee Jornal of Banking an Finance, vol 4, no, pp 89-7, 98 [8] V S Lai, An analysis of private loan garantees Jornal of Financial Services Research, vol 6, pp 3-48, 99 [9] M Dietsch, an J Petey, he creit risk in SME loans portfolios: Moeling isses, pricing, an capital reqireents Jornal of Banking an Finance, vol 6, pp 33-3, [] S-L L, an C J Ko, How to gage the creit risk of garantee isses in aiwanese bill finance copany: An epirical investigation sing a arket-base approach Applie Financial Econoics, vol 5, no 6, pp 53 64, 5 [] C-C Chang, S-L Chng, an M- Y, Loan garantee portfolios an joint loan garantees with stochastic interest rates he Qarterly Review of Econoics an Finance, vol 46, pp 6-35, 6 [] A Wabach, an A R Engel, Srety Bons with Fair an Unfair Pricing he Geneva Risk an Insrance Review, vol 36, pp 36 5, [3] J S Rssell Unerwriting Process for Constrction Contract Bons Jornal of Manageent in Engineering, vol 8, no, pp 63-8, 99 [4] G D Severson, J S Rssell, an E J Jaselskis, Preicting contract srety bon clais sing contractor financial ata Jornal of Constrction Engineering an Manageent, vol, no, pp 45-4, 994 [5] K Marsh, an A R Fayek, SretyAssist: Fzzy Expert Syste to Assist Srety Unerwriters in Evalating Constrction Contractors for Boning he Jornal of Constrction Engineering an Manageent, vol 36, no, pp 9-6, [6] M E Bayraktar, an M Hastak Scoring Approach to Constrction Bon Unerwriting Jornal of Constrction Engineering an Manageent, vol 36, no 9, pp , [7] M E Bayraktar, Q Ci, M Hastak, an I Minkarah, Warranty Bons fro the Perspective of Srety Copanies Jornal of Constrction Engineering an Manageent, vol 3, no 4, PP , 6 [8] Y-L Hang he pricing of conitional perforance garantees with risky collateral Constrction Manageent an Econoics, vol 6, no 9, pp , 8 [9] Q Ci, P Johnson, A Qick, an M Hastak, Valing the Warranty Ceiling Clase on ew Mexico Highway 44 Using a Binoial Lattice Moel Jornal of Constrction Engineering an Manageent, vol 34, no, pp 7, 8 [] G Li, Q Zhao, an G G, A Siple Control Variate Metho for Options Pricing with Stochastic Volatility Moels IAEG International Jornal of Applie Matheatics, vol 45, no, pp 64-7, 5 [] K D, G Li, an G G, A Class of Control Variates for Pricing Asian Options ner Stochastic Volatility Moels IAEG International Jornal of Applie Matheatics, vol 43, no, pp 45-53, 3 [] R opkins Options Explaine (n e) Hapshire: Palgrave Macillan, 994 [3] J Lin, an J Liang, Pricing of perpetal Aerican an Beran options by binoial tree etho Frontiers of Matheatics in China, vol, no, pp 43-56, 7 [4] E Këllezi, an Webber, Valing Beran options when asset retrns are Lévy processes Qantitative Finance, vol 4, no, pp 87, 4 [5] P P Boyle, A W Kolkiewicz, an K S an, Pricing Beran options sing low-iscrepancy esh ethos Qantitative Finance, vol 3, no 6, pp 84 86, 3 [6] M Broaie, an J B Deteple, Option pricing: valation oels an applications Manageent Science, vol 5, no 9, pp 45 77, 4 [7] C R wozo, an S E Fagba, On the Accracy of Binoial Moel for the Valation of Stanar Options with Divien Yiel in the Context of Black-Scholes Moel IAEG International Jornal of Applie Matheatics, vol 44, no, pp 33-44, 4 [8] J C Cox, S A Ross, an M Rbinstein, Option pricing: A siplifie approach Jornal of Financial Econoics, vol 7, no 3, pp 9-63, 979 (Avance online pblication: 4 oveber 5)