COST SIMULATION OF AN INFLATION-LINKED AND A FLOATER BOND WITH BACKTESTING

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1 COST SIMULATION OF AN INFLATION-LINKED AND A FLOATER BOND WITH BACKTESTING Kaa Váradi, Ph.D. Ágnes Vidovics-Dancs Deparmen of Finance Corvinus Universiy of Budapes H-193, Fővám ér 8, Budapes, Hungary agnes.dancs@uni-corvinus.hu KEYWORDS Inflaion-linked bond, ineres rae models, financial simulaion ABSTRACT In his paper we focus on simulaing and backesing he coss of wo special governmen securiies, from he poin of view of he issuer. Our research has wo main goals. The firs one is o assess he cosliness of an inflaion-linked bond in comparison wih a floaer one. The second one is o backes he simulaion resuls on real marke daa. We carry ou he cos simulaions wih Mone Carlo simulaion. The basis of he calculaions is he Cox-Ingersoll-Ross ineres rae model for he floaer bond; and a firs order auoregressive model for he inflaion-linked bond. Our findings are: (i) he inflaion-linked bond appears o be more expensive han he floaer one and his relaionship holds rue for exane (simulaed) and ex-pos (acually realised) coss as well; and (ii) he simulaions predic he oal presen value of he coss adequaely for boh insrumens, bu he individual cash flows of he floaer bond are significanly under- or overesimaed in he differen years. This shorcoming is in line wih our expecaions, since he model is calibraed on a ranquil period bu applied on a very volaile one. INTRODUCTION A wide range of financial models, inending o describe he behaviour of differen marke processes and o predic he fuure movemens in he marke have a grea and general problem. Namely, he model parameers are esimaed from hisorical daabases, bu hen he models are applied o capure fuure marke movemens when he circumsances are no necessarily he same. The evens of he las decade or so provide grea examples of rapidly changing marke environmens. Buil upon his observaion, one of our moivaions in his paper is o examine wha happens when we calibrae a model on a ranquil period bu apply i o predic financial marke movemens in a more volaile environmen. This phenomenon will appear in his paper when we esimae he fuure cash flows of wo hypoheic bonds as if hey were issued in Hungary in 26. The model calibraions are carried ou on a daabase of a ranquil period ( ), while he backesing of he esimaions is based on a very volaile period (26-211). We expec ha discree esimaions migh have only modes predicing power bu since we simulae more (four or five) cash flows of he bonds chosen, we give a chance ha on he long run he models approximae he average cosliness of he insrumens accepably. The examined bonds are an inflaion-linked and a floaer bond. The core moivaion was o measure he cosliness of he indexed bond because he issuance of such a Hungarian governmen securiy was a relevan and curren opic in 26. As benchmark insrumen we chose a floaer bond since hese wo ypes of bonds have a very imporan common feaure: heir fuure nominal cash flows are no known in advance, i.e. have o be esimaed. Since we analyse bonds wih five years mauriy, we already know he ex-pos, realised values of he relevan risk facors (especially inerbank ineres rae and inflaion), hence we can perform a comprehensive backes as well. The res of he paper is organised as follows. Firs we inroduce he basic feaures of radiional (fixed or floaer) and inflaion-linked bonds. Aferwards, we shed some ligh on he evoluion of he indexed bonds marke, highlighing also he scarce experiences ha Hungary has wih his bond ype. Then, we presen he heoreical background and he oupus of he cos simulaions. Finally, we analyse and backes he resuls and conclude our findings. TRADITIONAL BONDS A radiional bond is a deb insrumen ha obligaes he issuer o make specified paymens on predeermined daes for he bondholder. The mos imporan feaures of a bond are is face value (i is also called principal or noional amoun) which is he deb ha has o be paid back; and is coupon rae which deermines he ineres paymen ha has o be paid afer he ousanding noional amoun (Bodie e al., 28). There are wo basic ypes of bonds, he fixed rae and he floaing rae (or floaer) bond. In case of he firs ype he coupon rae is a fixed percenage of he face value, while in case of a floaer i is varying according Proceedings 27h European Conference on Modelling and Simulaion ECMS Webjørn Rekdalsbakken, Robin T. Bye, Houxiang Zhang (Ediors) ISBN: / ISBN: (CD)

2 o a curren marke rae called fixing or benchmark rae. In pracice, he ineres paymen of a floaer is usually he chosen marke rae plus a spread. Since he marke rae is changing coninuously, he cash flow of a floaer bond will change from one paymen dae o he oher as well. I is imporan o menion ha he paymen is deermined always one period in advance, according o he curren value of he fixing rae. The benchmark is usually an inerbank rae, i.e. he ineres rae ha banks use for lending o each oher, like for example he London Inerbank Offered Rae (Libor). Besides hese wo ypes of bonds, here are numerous innovaions in he bond markes (e. g. he inverse floaer or he asse-backed bonds) ou of which we inroduce one special ype, he inflaion-linked bond in more deail, since his is in he focus of our research. INFLATION-LINKED BONDS Inflaion-linked bonds (IL-bonds) belong o he class of indexed bonds. The specialiy of hese insrumens is ha heir paymens are ied o a general price index (Bodie e al., 28). An IL-bond, conrary o a fixed rae bond where he coupon rae is expressed in nominal erms, has a real coupon which is a fix percenage of he real value of he principal. More precisely, when he consecuive cash flow of he IL-bond falls due, he face value is muliplied wih an index facor ha represens he inflaion of he ime period passed since he las paymen. The cash flow is deermined hen as he produc of he real coupon and his modified face value. Calculaing he fuure cash flows of an IL-bond is no as eviden as in case of a radiional fixed bond, hence he pricing of he bond poses some problems as well. The firs difficuly is ha in mos of he cases we do no know wha he exac rae of he inflaion in he las ime period was. These daa are available only wih a few monhs delay, which means ha we have o have a cerain delay in he indexaion as well. The second problem is he definiion of he inflaion. I is no clear which indicaor should be used. There are several possibiliies, like he GDP deflaor or he consumer price index. I is one of he mos imporan quesions a he issuance of an IL-bond, which indicaor o be used. An imporan characerisic of an IL-bond is he paymen mehod of he principal s inflaion incremens. These incremens could be redeemed a he ime of he corresponding coupon paymen, bu in pracice i is more widespread ha hey are paid in one sum a mauriy. A his poin i is worh o menion ha since economies migh face no only inflaion bu deflaion as well, being indexed o a price level does no necessary mean increasing paymens in nominal erms. From he poin of view of our analysis, i is imporan o emphasise ha fuure cash flows involve uncerainy eiher for floaer, or for IL-bonds. Wih oher words, boh insrumens have cash flow risk. An essenial difference is ha he following paymen of a floaer is always known in advance. In Table 1 we lised hose parameers ha define he cash flows of a fixed rae, an inflaion-linked and a floaer bond. Table 1: Facors defining he cash flows of bonds Fixed rae Inflaion- linked Floaing rae Face value Face value Face value Mauriy Mauriy Mauriy Frequency of coupon paymen Principal paymen mehod Frequency of coupon paymen Principal and inflaion incremen paymen mehod Frequency of coupon paymen Principal paymen mehod Coupon Real coupon Spread Price index Fixing curve Index Calculaion and Pricing The cenral quesion in deermining he cash flow and he price of an IL-bond is he calculaion of he index facor. For he purposes menioned i is indispensable o use a mehod ha enables us o deermine he price index a any ime. Given ha inflaion saisics are available only monhly, his migh be difficul, bu here are several ways o handle his problem. In pracice he prevailing mehod is he Canadian model, for his reason we inroduce i briefly. The Canadian model was elaboraed in The essence of his model is ha we do no need he nominal value of he nex coupon paymen for deermining he price; we only need he value of he price index. The price index a any day is calculaed as he linear inerpolaion of wo preceding index values. Since he inflaion daa are published a leas wih a wo monhs delay and usually only monhly, his means ha hese indices will be he wo and hree monh earlier price index values. Equaion (1) shows he price index calculaion on an arbirary day. PI 1 D ( PI PI ) = PI M 3 + (1) M 2 M 3 where PI is he price index, M sands for he monh of, and D is he number of days in monh M. The index facor of Equaion (2) which is used o modify he principal is he raio of he price index on he examined day (PI ) and on he basis day (PI B ). IF PI = (2) PI B For more informaion abou inflaion-linked securiies in general see Deacon e al. (24).

3 Inernaional Markes IL-bonds have been issued in a bigger amoun afer he Second World War in counries like Brazil, Argenina, or Finland. Tha ime he main reason for he issuance in hese counries was he wo-digi inflaion rae. Wih he issuance he governmen waned o show is commimen o decrease inflaion in he following years. (Pecchia and Piga, 1995). The global marke for ILbonds sared o grow noably in 1981, when he Briish governmen has sared o issue IL bonds, called IL- Gils. The reason for he issuance was ha he inflaion expecaion of he governmen was lower han ha of he marke. The governmen hoped ha i could save on ineres expenses in his way (Farkas e al., 25). The marke experienced anoher significan increase when several counries inroduced inflaion argeing moneary policy, like Canada, Sweden, Ausralia, ec. Nowadays, he oal ousanding amoun of he IL-bonds on he hree bigges markes are $5 billion TIPS (Treasury Inflaion-Proeced Securiies) in he USA, $3 billion IL-Gils in he UK, and $2 billion OATi/OAT i IL-bonds in France 1. Since he basic of our simulaions and backesing is a Hungarian IL-bond, we summarise he experiences of his counry wih indexed governmen bonds. Hungarian Marke The Hungarian Governmen Deb Managemen Agency (GDMA) sared he issuance of he firs (and only one so far) inflaion-linked governmen securiy in As a consequence of he lack of ineres from invesors, he IL-bond was aucioned only four imes, wih coninuously decreasing demand. Afer he mauriy of he IL-bond, Farkas e al. (25) analysed he cos efficiency of he insrumen from he viewpoin of he GDMA. The auhors used wo mehods, cos analysis wih fuure value calculaion, and break-even inflaion calculaion. Their main resul was ha he ex-pos cos efficiency of he IL-bond is raher quesionable. Afer he mauriy of he firs IL-bond, i has been suggesed ha GDMA migh have ried o issue a new one. I seemed o be possible ha he marke of Hungarian governmen bonds became more maure and ha he issuance of a new IL-bond could be successful. This was he main reason why Dancs (26) made an analysis and simulaed he fuure coss of a hypoheic five year mauriy IL-bond assuming an issuance in 26. In wha follows we reproduce hese simulaions wih sligh modificaions and exend he analysis wih backess 2. 1 Daa sources: US Deparmen of he Treasury, UK Deb Managemen Office, Agence France Tresor. 2 We have o complee he sory by adding ha in 26 GDMA decided on no issuing new IL-bond. I did no launch EX-ANTE COST-ESTIMATION In his par we are simulaing he expeced coss of wo hypoheic governmen bonds issued by he GDMA on he 1 s of March 26. The nex par will backes he resuls. The characerisics of he wo hypoheic bonds are summarised in Table 2. Table 2: Characerisics of he bonds Type Inflaionlinked Floaer Currency EUR EUR Face value 1, 1, Issue dae (d/m/y) 1/3/26 1/3/26 Mauriy (d/m/y) 1/3/211 1/3/211 Ineres paymen period Principal paymen mehod Real coupon / Spread Price index / Fixing curve annual a mauriy wih inflaion incremens annual a mauriy 1.9%.1% HICP 3 euro area (ex obacco) Libor 12M When deermining he characerisics of he bonds, our main goal was o ensure comparabiliy. No only he wo bonds have he same issue and paymen daes, boh are also denominaed in he same currency (euro), hence we do no have o esimae fuure FX raes. The mos decisive poin was choosing he real coupon of he ILbond and he spread of he floaer. We inended o examine bonds ha have he same issue price which for he sake of simpliciy equals he face value. In his way, he iniial revenue of he issuer is idenical for he wo bonds. Marke circumsances (i.e. comparable daa of relevan Hungarian and European sovereign bonds) and expers esimaions were considered o deermine he real coupon and he spread ha maches his crierion. However, we have o keep in mind ha possible underor overesimaion of hese parameers may influence which bond urns ou o be more expensive. For boh bonds, we give ex-ane esimaions on heir fuure cash flows. The mehodology used is Mone Carlo simulaion, so he firs sep is idenifying he sochasic processes ha deermine he cash flows. In case of he floaer bond we model fuure Libor pah wih he Cox-Ingersoll-Ross ineres rae model, while in case of he IL-bond we esimae he index-facor wih he help of an auoregressive model. Parameer calibraions are based on hisorical daa. such insrumen for insiuional invesors in he following years eiher. However, from 29 here exiss a similar reail securiy for small invesors. 3 Harmonised Index of Consumer Prices, a comparable indicaor of inflaion in he EU saes. HICP for he euro area is he weighed average of he price indices in he member counries.

4 Modelling he Libor The Cox-Ingersoll-Ross model (CIR-model) is a coninuous, one facor sochasic ineres rae model, firs proposed by Cox e al. (1985). In his model he insananeous ineres rae dynamics are given by he following sochasic differenial equaion: dr = α( β r )d + σ r dw (3) where α, β and σ are posiive consans, r is he ineres rae, is ime. W denoes he sandard Wiener process, a coninuous-ime sochasic process used very frequenly in quaniaive finance. The mos imporan characerisics of he Wiener process are as follows: (i) he rajecories are coninuous, (ii) he incremens on disjuncive ime inervals are independen, (iii) he incremens are saionary i.e. incremens on ime inervals wih he same lengh have he same probabiliy disribuion, and (iv) he incremen W -W s is disribued normally wih zero expeced value and (-s) variance. For furher informaion on Wiener process and generally on he mahemaical background of quaniaive finance see Medvegyev (27), while Cairns (24) gives a comprehensive discussion specifically abou ineres rae models. As one may observe, he ineres rae in he CIR-model follows a mean-revering process wih long-erm average β: when r <β, he drif erm in Equaion (3) becomes posiive so he ineres rae will increase and vice versa. The speed of adjusmen o he long run mean is measured by α. The volailiy erm is proporional o he square roo of he ineres rae level. Cox e al. (1985) also showed ha he fuure ineres rae in heir model (condiional on is curren value) has a non-cenral chi-squared disribuion. When using he CIR-model for simulaion purposes, we have o find he values of he model s hree parameers. Here we presen a possible mehod developed by Chan e al. (1992). This approach is based on he economeric esimaion procedure called Generalised Mehod of Momens (GMM). For more informaion abou GMM in general see Hansen (1982). Anoher applicaion of he mehod for ineres rae models can be found in Li (2). Chan e al. (1992) developed heir procedure o esimae he parameers of he following general ineres rae model: dr = α( β r )d + σr dw (4) I is easy o see, ha Equaion (4) gives he CIR-model if we subsiue γ=.5. γ In Equaion (5) we discreise (4) wih he Euler approximaion. r = αβδ + (1 αδ )r + σr δ e (5) 1 γ 1 where δ is he lengh of ime beween wo observaions of r, and e are independen, sandard normal random variables. Le us rewrie Equaion (5) in he following form: r r = αβδ αδ r + ε 1 1 (6) The firs wo momens (expeced value and variance) of he variable ε can be deermined quickly by comparing Equaion (5) and (6): E( ε ) = (7) 2 2 2γ E ( ε ) = σ δ r (8) 1 where E() denoes expeced value. The parameers are esimaed wih he null hypoheses of Equaions (6), (7) and (8). For esimaing he fuure cash flows of he floaer bond we model he fuure Libor raes wih he CIR-model defined in Equaion (3). Model calibraion is based on a hisorical daabase which conains daily Libor raes from 1 s December 2 o 1 s March 26, all in all a sample of 1,34 observaions. We use he above described GMM mehod and subsiue δ =1/25=.4 in Equaion (6). (We have observaions for rading days, hence one calendar year conains 25 Libor raes.) Table 3 shows he resuls of he parameer esimaions. Table 3: Calibraion of he CIR-model Parameer Esimaed value -saisic p-value α β σ Once he parameer values of he CIR-model are deermined, hen we can esimae he fuure cash flows of he floaer bond. As i has been poined ou, he nex cash flow and he principal paymen a mauriy of a floaer bond are always known. Therefore, from all cash flows of he bond here remain only four unknown ineres paymens o be esimaed. Table 4 illusraes in deails which cash flows are subjecs of our simulaions and which are fixed a issuance. Aferwards, Figure 1 shows relaive frequencies of he four esimaed paymens generaed from 1, simulaions.

5 Table 4: Cash flows of he floaer bond (ialic expressions are o be esimaed) Dae Cash flow Paymen ype 1/3/26 +1, Issue price 1/3/27-39 Ineres 1/3/28-1,*Libor 1/3/27 Ineres 1/3/29-1,*Libor 1/3/28 Ineres 1/3/21-1,*Libor 1/3/29 Ineres 1/3/211-1,*Libor 1/3/21 Ineres 1/3/211-1, Principal Relaive frequencies from 1, simulaions EUR Y2 Y3 Y4 Y5 Figure 1: Relaive frequencies of he floaer bond s esimaed cash flows We will analyse he resuls in comparison wih he cash flows of he IL-bond. Modelling he Index Facor For esimaing he fuure coss of he IL-bond we have o predic fuure index facors. Our goal is capuring he main characerisics of he price index chosen wihou building a complicaed model abou he whole economy and making assumpions on wide range of macroeconomic aggregaes. We will model he inflaion wih he following firs order auoregressive process: observaions. Table 5 shows he resuls of he parameer esimaions. Table 5: Esimaion of he auoregressive model Parameer Esimaed value -saisic p-value a b The adjused R-square of he auoregressive model is 72 percen. From he following simulaions poin of view, i is imporan o es he normaliy of he residuals. We performed Jarque-Bera es and received a p-value of 68 percen. I means ha rejecing he null hypohesis of normaliy would be a wrong decision wih probabiliy of 68 percen. In case of he IL-bond, we have o esimae five cash flows. The iniial revenue of he issuer is known (under our assumpion he real coupon is se so ha he issue price is he face value), bu all he oher paymens, including he principal redempion a mauriy, depend on fuure inflaion. Similarly o he floaer bond, we summarise in a able he cash flows indicaing he facors ha should be esimaed (Table 6). Relaive frequencies of he five esimaed ineres paymens generaed from 1, simulaions are depiced in Figure 2. Table 6: Cash flows of he IL bond (ialic expressions are o be esimaed) Dae Cash flow Paymen ype 1/3/26 +1, Issue price 1/3/27-1,*IF 1/3/27 *1.9% Ineres 1/3/28-1,*IF 1/3/28 *1.9% Ineres 1/3/29-1,*IF 1/3/29 *1.9% Ineres 1/3/21-1,*IF 1/3/21 *1.9% Ineres 1/3/211-1,*IF 1/3/211 *1.9% Ineres 1/3/211-1,*IF 1/3/211 Principal Δ M M 1 M HICP = aδhicp + blibor + η (9) where ΔHICP M is he monh-on-monh inflaion measured by he annual rae of change of he price index given in Table 2, Libor M is he average level of he Libor rae in monh M and η is normally disribued residual erm. The auoregressive feaure of he model defined in Equaion (9) is easily jusifiable: sequenial monh-on-monh saisics measure he inflaion of highly overlapping periods. We esimae regression of Equaion (9) wih Ordinary Leas Squares mehod. We use hisorical daa of HICP in he euro area from mid-1999 o mid-25. Since daa are available on a monhly basis, we have 74 Relaive frequencies from 1, simulaions EUR Y1 Y2 Y3 Y4 Y5 Figure 2: Relaive frequencies of he IL-bond s esimaed cash flows

6 Inerpreing he Resuls In Figure 1 and Figure 2 i is worh o observe ha he cash flows disribuion is flaer in each year for he floaer bond. This means higher variance which is in line wih he consrucion of he bonds. In case of he IL-bond he magniude of he coss is predeermined by he real coupon and only he modifying index facor is unknown, while in case of he floaer bond i is he coupon iself ha we esimae. The laer means higher uncerainy especially for iniial years where he index facor represens he inflaion of shorer periods. Anoher observaion is ha boh he mean and he variance (he flaness) of he IL-bond cash flows are increasing significanly in ime. This is due o fac ha laer cash flows have o compensae he invesor for he inflaion of a longer period. This feaure resuls in higher and more volaile nominal cash flows as ime passes. In he nex secion we will compare he esimaed cash flows of he wo bonds and will also backes he resuls. ANALYSIS AND BACKTEST OF THE RESULTS In Table 7 and Table 8 we summarise he resuls of our esimaions and also inform he reader abou wha cash flows would have acually realised ex-pos. From he esimaions we presen he mean and he 95 h percenile (pcl. in he Tables) of he 1, simulaions. Since we are alking abou he issuer, from our poin of view he main risk is having higher coss han expeced or esimaed. This is why we included in he Tables an upper percenile. Furhermore, we also calculaed he presen values of he annual cash flows (PV in he Tables), which is imporan because of comparabiliy. We would like o know which bond is cheaper on he whole, so we have o add all he fuure coss of he bonds, and since i is no fair o sum up cash flows due a differen imes, we discouned all he paymens o he dae of he issuance. For discouning we used a fla 3% yield curve. The choice of he fair discoun curve is of course influencing he resuls, bu from our poins of view (comparing he wo bonds and esing he simulaions) his impac is so small ha we decided on no going ino he very deph of his financial problem. Table 7: Acual and esimaed cash flows of he floaer bond Dae acual Cash flow esimaed (ex-ane) (ex pos) mean 95% pcl. 1/3/ /3/ /3/ /3/ /3/211 1, , , PV 1,31.6 9,89.1 1,82.7 Table 8: Acual and esimaed cash flows of he inflaion-linked bond Dae acual Cash flow esimaed (ex-ane) (ex pos) mean 95% pcl. 1/3/ /3/ /3/ /3/ /3/211 11, , ,267.8 PV 1, , ,465.6 The firs purpose of our calculaions was comparing he coss of he wo bonds. Our resuls show ha he ILbond urns ou o be more expensive, he presen value of all he fuure paymens is higher for his insrumen. This saemen holds rue for he ex-ane, esimaed coss and for he ex-pos, acually realised cash flows as well. A his poin we have o come back o he problem of seing he real coupon and he spread of he bonds. The calibraion of hese parameers is of course influencing he final conclusion. If he bonds wih hese parameers could no have been issued a face value, we should have included he issue price in he calculaions as well. Because of his uncerainy i is useful o menion ha if he real coupon is unchanged, he spread of he floaer bond should be increased o 8-9 basis poins so ha he acual presen values of he wo insrumens were approximaely equal. All in all, our opinion is ha he assumpions do no involve so much uncerainy ha he relaive cosliness of he bonds would change. Our second goal was backesing he simulaion resuls. As we expeced, Libor showed much higher volailiy beween 26 and 211 han i was esimaed according o he previous, much ranquil period. The acual cash flows are significanly underesimaed in he firs wo years and hen significanly overesimaed in he second wo years. However, for ha very reason he oal cash flow (in presen value) is esimaed quie well. For he IL-bond, he paymen esimaions are generally accepable separaely and in presen value as well he excepion is he second cash flow which is higher han he esimaed 95 h percenile. We have o remark ha he main uncerainies in our assumpions, namely he value of he real coupon and he spread of he floaer bond are no affecing he accuracy of he esimaions. If hese parameers were differen, ha would change he acual and he esimaed cash flows in he same way.

7 CONCLUSION In his paper we presened he main feaures of he inflaion-linked bonds. Since i was a case a issue for Hungary in 26, we examined a hypoheic IL-bond launched in ha year by GDMA. We analysed his bond from he poin of view of cosliness, he benchmark insrumen was a floaer bond. We made ex-ane (as we were in 26) cos-simulaions for boh bonds and also backesed he resuls. The base of he Mone Carlo simulaions was he CIR-model for he floaer and an auoregression for he IL-bond. Our simulaions sugges ha he IL-bond would have been more expensive and his resul is confirmed by he ex-pos daa as well. Backess also showed ha he CIR-model failed o capure he individual annual coss of he floaer bond. This was an anicipaed shorcoming since we calibraed he model according o a period prior o 26, i.e. no aking ino accoun he financial crises which brough high volailiy and unexpeced movemens in he financial markes. Neverheless, he simulaions prediced he oal presen values of he cash flows adequaely for boh bonds. REFERENCES Bodie, Z., Kane, A., and Marcus A. J. 28. Essenial of Invesmens. McGarw-Hill Irwin, New York. 7 h ediion. Cairns, A. 24. Ineres Rae Models: An Inroducion. Princeon Universiy Press. Princeon-Oxford. Chan, K., Karolyi, A., Longsaff, A., and Sanders, A An Empirical Comparison of Alernaive Models of he Shor-Term Ineres Rae. The Journal of Finance, No. 3, Cox, J., Ingersoll, E., and Ross, A A Theory of he Term-Srucure of Ineres Raes. Economerica, No. 53, Dancs, Á. 26. Tőkeindexál államkövények. Thesis work, Corvinus Universiy of Budapes, Budapes. Deacon, M., Derry, A. and Mirfendereski, D. 24. Inflaion- Indexed Securiies: Bonds, Swaps and Oher Derivaives. John Wiley & Sons, Chiceser. 2 nd ediion. Farkas, R., Mosolygó, Zs. and Páles, J. 25 A őkeindexál állmkövény jellemzői, nemzeközi helyzee és hazai apaszalaai. Hielinézei szemle, Vol. 4, No. 5-6, Hansen, L Large Sample Properies of Generalized Mehod of Momen Esimaors. Economerica, No. 4, Li, S. 2. An Empirical Sudy of Ausralian Shor-Term Ineres Rae: A Comparison of Single Facor Models. Working Paper Series, School of Finance and Business Economics, Augus. Medvegyev, P. 27. Sochasic Inegraion Theory. Oxford Universiy Press, Oxford-New York. Pecchi, L. and Piga, G Who s Afraid of Index-Linked Bonds?. In Managing Public Deb: Index-Linked Bonds in Theory and Pracice 1997, De Cecco, M., Pecchi, L. and Piga, G (Eds.). Edward Elgar Publishing, Chelenham- Brookfield, AUTHOR BIOGRAPHIES KATA VÁRADI is currenly a lecurer a he Corvinus Universiy of Budapes (CUB), a he Deparmen of Finance. She graduaed also a he CUB in 29, and afer i obained a PhD in 212. Her main research area is marke liquidiy he opic of her PhD disseraion was he liquidiy of he sock markes, bu she also does researches relaed o he bonds markes and capial srucure of companies. She also worked as a risk analys a a mulinaional bank in Her e- mail address is: kaa.varadi@uni-corvinus.hu ÁGNES VIDOVICS-DANCS is an assisan professor of he Deparmen of Finance a Corvinus Universiy of Budapes. Her main research areas are governmen deb managemen in general and especially sovereign crises and defauls. She worked as a junior risk manager in he Hungarian Governmen Deb Managemen Agency in Her address is: agnes.dancs@unicorvinus.hu