1. Vizsg´altam a piaci hozamok k¨oz¨otti korrel´aci´ok dinamik´aj´at ´es id˝osk´ala- f¨ugg´es´et.
• Megmutattam, hogy a hozamok k¨oz¨otti keresztkorrel´aci´ok nagy- m´ert´ekben megv´altoztak a vizsg´alt id˝oszakban: a korrel´aci´ok er˝o- sebb´e v´altak ´es maximumhely¨uk a nulla fel´e tol´odott. Ezen ered- m´enyek azt jelzik, hogy a piacok egy n¨ovekv˝o hat´ekonys´ag´u f´azis- ban vannak, melynek oka els˝osorban a piaci informatika elter- jed´ese ´es az inform´aci´ofeldolgoz´as gyorsul´asa. Ez a piaci szerep- l˝ok egy¨uttes viselked´es´enek megv´altoz´as´at jelzi, mely m¨og¨ott a piaci mechanizmusok ´es nem emberi saj´atoss´agok ´allnak [TK06].
• Vizsg´altam az egyidej˝u piaci korrel´aci´ok f¨ugg´es´et a∆tmintav´ete- lez´esi id˝osk´al´at´ol: a korrel´aci´ok kis ∆t eset´en j´oval alacsonyab- bak a csak n´eh´any ´or´as mintav´etelez´esi id˝osk´al´akon el´ert aszimp- totikus ´ert´ek¨ukn´el (Epps-effektus).
Megmutattam az Epps-effektusra adott kor´abbi, az aszinkronit´a- son alapul´o magyar´azat hi´anyoss´agait. Bel´attam, hogy a k¨ul¨on- b¨oz˝o id˝oszakokra m´ert Epps g¨orb´ek az aszimptotikus ´ert´ek¨ukkel sk´al´azhat´ok, m´ıg a piaci aktivit´assal t¨ort´en˝o sk´al´az´as nem m˝uk¨odik [TK07b].
Osszef¨ugg´est adtam a k¨¨ ul¨onb¨oz˝o id˝osk´al´akon m´ert korrel´aci´ok
´ert´ekei k¨oz¨ott. Az ´altalam kidolgozott m´odszerrel megadhat´o a teljes Epps g¨orbe csup´an a legr¨ovidebb ´ertelmes id˝osk´al´an v´egzett m´er´esek alapj´an. Megmutattam, hogy az Epps-effektus karak- terisztikus ideje az emberi reakci´oid˝ovel van kapcsolatban, mely megmagyar´azza, hogy mi´ert nem v´altozik a karakterisztikus id˝o a piaci aktivit´assal [TK07a].
2. M´odszert dolgoztam ki a fizika sz´amos ter¨ulet´en fell´ep˝o probl´ema keze- l´es´ere, aszinkron jelek k¨oz¨otti korrel´aci´ok pontos becsl´es´ere. A m´od- szerrel becs¨ulhet˝ok az aszimptotikus korrel´aci´ok hossz´u id˝oablakok al- kalmaz´asa, ´es ´ıgy a statisztika roml´asa n´elk¨ul. Az elv az Epps-effektus le´ır´asa sor´an kidolgozott dekompoz´ıci´os technika ´altal´anos´ıt´as´an ala- pul, melyben a nagyfrekvenci´as adatokon m´ert id˝of¨ugg˝o korrel´aci´okat haszn´alom fel. Ezzel k¨ozel egy nagys´agrenddel megn¨ovelhet˝o a korrel´a- ci´ok m´er´es´enek pontoss´aga illetve lecs¨okkenthet˝o a sz¨uks´eges m´er´esi kapacit´as mind val´odi, mind numerikus k´ıs´erletek eset´eben [TK08].
3. A londoni t˝ozsde (London Stock Exchange) aj´anlati k¨onyveinek adatait vizsg´altam nagy napk¨ozbeni ´arv´altoz´asok k¨ornyzet´eben.
• Vizsg´altam a volatilit´ast, a legjobb aj´anlatok ´ark¨ul¨onbs´eg´et (bid- ask spread), a kereslet-k´ın´alat ar´any´at, a k¨onyvben “v´arakoz´o”
aj´anlatok sz´am´at, a keresked˝ok aktivit´as´at, a k¨ul¨onb¨oz˝o t´ıpus´u aj´anlatok relat´ıv sz´am´at. Azt tapasztaltam, hogy a m´ert meny- nyis´egek megv´altoznak, az ´arugr´as pillanat´aban extr´emumot mu- tatva. A megv´altoz´as ut´an az ¨osszes mennyis´eg relax´aci´oja lass´u, hatv´anyf¨uggv´ennyel illesztve a legt¨obb esetben ≈0.4 exponens- sel jellemezhet˝o. A volatilit´as ´es a legjobb aj´anlatok ´ark¨ul¨onb- s´ege (bid-ask spread) megn˝o ´es hatv´anyf¨uggv´enyszer˝u lecseng´est mutat; a kereslet-k´ın´alat ar´anya eltol´odik, lassan relax´alva; a k¨onyvben v´arakoz´o aj´anlatok sz´ama megv´altozik, mely csak las- san cseng le, a lecseng´es a k¨onyv k´et oldal´an nagyon k¨ul¨onb¨oz˝o; a keresked˝ok aktivit´asa megn˝o, ez l´athat´o mind az ´uj aj´anlatok megjelen´es´enek, mind az aj´anlatok t¨orl´es´enek sz´am´aban; ezen v´altoz´ok ugyancsak hatv´anyf¨uggv´enyszer˝u relax´aci´ot mutatnak,
≈0.4 exponenssel. A k¨ul¨onb¨oz˝o t´ıpus´u aj´anlatok relat´ıv sz´am´at vizsg´alva (mely a keresked´esi strat´egi´ak stabilit´as´anak m´ert´ekek´ent is ´ertelmezhet˝o) nem tal´altam er˝os megv´altoz´ast a dinamik´aban, azt jelezve, hogy ´altal´anosan a piaci tev´ekenys´egek aktivit´asa n¨ovekszik, nem a piaci szerepl˝ok strat´egikus viselked´ese v´altozik meg. Vizsg´altam a legjobb aj´anlatokhoz k¨ozeli bet¨oltetlen ´arszin- tek sz´am´anak (gap) eloszl´as´at. Az eredm´enyek al´at´amasztj´ak azt az elm´eletet, miszerint a nagy ´arv´altoz´asokat els˝osorban alacsony likvidit´as, azaz nagysz´am´u egym´as melletti bet¨oltetlen ´arszint okozza: azt tal´altam, hogy a legjobb ´es az azut´an k¨ovetkez˝o aj´an- latok k¨oz¨otti ´ark¨ul¨onbs´eg eloszl´asa k¨ul¨onb¨ozik nagy ´arv´altoz´asok el˝otti peri´odusokban a norm´al peri´odusbeli eloszl´ast´ol [TKF08].
• Egy, a strat´egikus viselked´est figyelmen k´ıv¨ul hagy´o (´ugynevezett zero intelligence), ¨uleped´esi modellekhez hasonl´o modellt k´esz´ıtet- tem az aj´anlatok dinamik´aj´anak reproduk´al´as´ara. Vizsg´altam a modell stabil dinamik´aj´at, valamint a nagy ´arv´altoz´asok hat´as´at.
Azt tapasztaltam, hogy a modell kvalitat´ıve reproduk´alja az em- pirikusan tal´alt lass´u, hatv´anyf¨uggv´enyszer˝u lecseng´eseket a vola- tilit´as ´es legjobb aj´anlatok ´ark¨ul¨onbs´ege eset´eben. A szimul´aci´ok- ban tapasztalt lass´u lecseng´esek exponense valamivel magasabb az empirikus ´ert´ekekn´el. Ez azt jelezheti, hogy b´ar a val´odi le- cseng´esek kicsivel lass´ubbak a modellbeliekn´el, a relax´aci´ok jel- lege m´egis reproduk´alhat´o a keresked˝ok strat´egikus viselked´es´er˝ol tett feltev´esek n´elk¨ul. A modellt analitikusan vizsg´altam. Egy hat´aresetben, valamint ´altal´anos esetben r¨ovid id˝okre analitikus le´ır´ast adtam a bid-ask spread modellbeli lecseng´es´ere [TKF08].
4. Piaci megfigyel´esek ´es k´ıs´erleti eredm´enyek magyar´azata c´elj´ab´ol ¨ugy- n¨okalap´u modellt k´esz´ıtettem egy folytonos kett˝os aukci´on alapul´o t˝ozsd´et szimul´alva. A modellben az inform´aci´onak a keresked´esre
´es a piac hat´ekonys´ag´ara val´o hat´as´at vizsg´altam. Az inform´aci´ot a
j¨ov˝obeli ´arv´altoz´asok (az osztal´ek-id˝osor alapj´an t¨ort´en˝o) el˝orejelz´esi k´epess´egek´ent defini´altam. A szimul´aci´ok azt mutatt´ak, hogy a t¨obb- let inform´aci´o nem mindig hat pozit´ıvan a piaci teljes´ıtm´enyre: m´ıg a teljesen inform´alatlanok teljes´ıtm´enye a piaci ´atlagot ´eri el, addig a k¨ozepesen inform´altak az ´atlag alatt teljes´ıtenek ´es csak a legjob- ban inform´altak (“bennfentesek”) nyernek. A szimul´alt piac repro- duk´alja a val´odi piacokr´ol ismert f˝obb empirikus t´enyeket ´es inform´a- ci´os hat´ekonys´agot mutat. Megengedtem az ¨ugyn¨ok¨oknek a keresked´esi strat´egi´ak k¨oz¨otti v´alt´ast, amennyiben huzamosabb ideig a piaci ´at- lag alatt teljes´ıtettek. A lehets´eges k´et strat´egia: (1) haszn´alni az el˝orejelz´esi k´epess´eg¨uket (fundamentalista strat´egia), vagy (2) tren- deket k¨ovetni (“chartist” strat´egia). Az eredm´enyek azt mutatt´ak, hogy m´ıg a legjobban inform´altak fundamentalista strat´egi´at k¨ovetnek, haszn´alva az inform´aci´ojukat, addig a kev´esb´e inform´altak a k´et lehet- s´eges strat´egi´at v´altogatj´ak ´alland´oan [TSHK06, TSHK07b, TSHK07a, TS08]. Ez al´at´amasztja az eredm´enyt, miszerint a r´eszleges inform´aci´o nem mindig ´es felt´etlen¨ul hasznos.
Codes of strategy-states
We list the numerical codes of the strategy states mentioned in Chapter 6.
F = Fundamentalist; C = Chartist
A.1 3 traders
Table A.1
strategy code I1’s strategy I2’s strategy I3’s strategy
1 F F F
2 C F F
3 F C F
4 C C F
5 F F C
6 C F C
7 F C C
8 C C C
A.2 5 traders
97
Table A.2
strategy code I1’s strategy I2’s strategy I3’s strategy I4’s strategy I5’s strategy
1 F F F F F
2 C F F F F
3 F C F F F
4 C C F F F
5 F F C F F
6 C F C F F
7 F C C F F
8 C C C F F
9 F F F C F
10 C F F C F
11 F C F C F
12 C C F C F
13 F F C C F
14 C F C C F
15 F C C C F
16 C C C C F
17 F F F F C
18 C F F F C
19 F C F F C
20 C C F F C
21 F F C F C
22 C F C F C
23 F C C F C
24 C C C F C
25 F F F C C
26 C F F C C
27 F C F C C
28 C C F C C
29 F F C C C
30 C F C C C
31 F C C C C
32 C C C C C
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