Foreign Exchange Quanto Options

Transkript

1 Cenre for Pracical Quaniaive Finance No. 10 Foreign Exchange Quano Opions Uwe Wysup June 2008 Auhor: Prof. Dr. Uwe Wysup Frankfur School of Finance & Managemen Frankfur/Main Publisher: Frankfur School of Finance & Managemen Phone: +49 (0) Fax: +49 (0) Sonnemannsr D Frankfur/M. Germany

2 2 Wysup Absrac A quano opion can be any cash-seled opion, whose payoff is convered ino a hird currency a mauriy a a pre-specified rae, called he quano facor. There can be quano plain vanilla, quano barriers, quano forward sars, quano corridors, ec. The valuaion heory is covered for example in [3] and [1]. Conens 1 FX Quano Drif Adjusmen 2 2 Quano Plain Vanilla 5 3 Quano Forward 5 4 Quano Digial 6 5 Hedging of Quano Opions Vega Posiions of Quano Plain Vanilla Opions Vega Hedging Quano Plain Vanilla Opions Example Applicaion: Performance Linked Deposis Produc Descripion Example Composiion Variaions FX Quano Drif Adjusmen We ake he example of a Gold conrac wih underlying XAU/USD in XAU-USD quoaion ha is quanoed ino EUR. Since he payoff is in EUR, we le EUR be he numeraire or domesic or base currency and consider a Black-Scholes model XAU-EUR: ds (3) = (r EUR r XAU )S (3) d + σ 3 S (3) dw (3), (1) USD-EUR: d = (r EUR r USD ) d + σ 2 dw (2), (2) dw (3) dw (2) = ρ 23 d, (3) where we use a minus sign in fron of he correlaion, because boh S (3) and have he same base currency (DOM), which is EUR in his case. The scenario is displayed in

3 Foreign Exchange Quano Opions 3 XAU σ σ 3 1 ϕ 23 EUR π ϕ 23 σ 2 ϕ π ϕ12 12 USD Figure 1: XAU-USD-EUR FX Quano Triangle. The arrows poin in he direcion of he respecive base currencies. The lengh of he edges represens he volailiy. The cosine of he angles cos φ ij = ρ ij represens he correlaion of he currency pairs S (i) and S (j), if he base currency (DOM) of S (i) is he underlying currency (FOR) of S (j). If boh S (i) and S (j) have he same base currency (DOM), hen he correlaion is denoed by ρ ij = cos(π φ ij ). Figure 1. The acual underlying is hen XAU-USD: S (1) = S(3). (4) Using Iô s formula, we firs obain

4 4 Wysup and hence d 1 = 1 ( ds (1) = 1 ds (3) + S (3) d 1 = S(3) + S(3) ) 2 ds(2) ( = (r USD r EUR + σ 2 2) 1 (r EUR r XAU ) d + S(3) + ds (3) d 1 σ 3 dw (3) (r USD r EUR + σ2) 2 d S(3) ) 3 (ds(2) ) 2 1 d σ 2 dw (2), (5) σ 2 dw (2) + S(3) ρ 23 σ 2 σ 3 d = (r USD r XAU + σ ρ 23 σ 2 σ 3 )S (1) d + S (1) (σ 3 dw (3) σ 2 dw (2) ). Since S (1) is a geomeric Brownian moion wih volailiy σ 1, we inroduce a new Brownian moion W (1) and find ds (1) = (r USD r XAU + σ ρ 23 σ 2 σ 3 )S (1) d + σ 1 S (1) dw (1). (6) Now Figure 1 and he law of cosine imply which yields σ 2 3 = σ σ 2 2 2ρ 12 σ 1 σ 2, (7) σ 2 1 = σ σ ρ 23 σ 2 σ 3, (8) σ ρ 23 σ 2 σ 3 = ρ 12 σ 1 σ 2. (9) As explained in he currency riangle in Figure 1, ρ 12 is he correlaion beween XAU-USD and USD-EUR, whence ρ = ρ 12 is he correlaion beween XAU-USD and EUR-USD. Insering his ino Equaion (6), we obain he usual formula for he drif adjusmen ds (1) = (r USD r XAU ρσ 1 σ 2 )S (1) d + σ 1 S (1) dw (1). (10) This is he risk-neural process ha can be used for he valuaion of any derivaive depending on S (1) which is quanoed ino EUR.

5 Foreign Exchange Quano Opions 5 2 Quano Plain Vanilla Wih hese preparaions we can easily deermine he value of a quano plain vanilla paying Q[φ(S T K)] +, (11) where K denoes he srike, T he expiraion ime, φ he usual pu-call indicaor aking he value +1 for a call and 1 for a pu, S he underlying in FOR-DOM quoaion and Q he quano facor from he domesic currency ino he quano currency. We le µ = r d r f ρσ σ, (12) be he adjused drif, where r d and r f denoe he risk free raes of he domesic and foreign underlying currency pair respecively, σ = σ 1 he volailiy of his currency pair, σ = σ 2 he volailiy of he currency pair DOM-QUANTO and ρ = σ2 3 σ 2 σ 2 (13) 2σ σ he correlaion beween he currency pairs FOR-DOM and DOM-QUANTO in his quoaion. Furhermore we le r Q be he risk free rae of he quano currency. Then he formula for he value can be wrien as v = Qe rqt φ[s e µt 0 N (φd + ) KN (φd )], (14) d ± = ln S 0 + ( µ ± 1σ2) T K 2 σ, (15) T where N denoes he cumulaive sandard normal disribuion funcion and n is densiy. 3 Quano Forward Similarly, we can easily deermine he value of a quano forward paying Q[φ(S T K)], (16) where K denoes he srike, T he expiraion ime, φ he usual long-shor indicaor, S he underlying in FOR-DOM quoaion and Q he quano facor from he domesic currency ino he quano currency. Then he formula for he value can be wrien as v = Qe r QT φ[s 0 e µt K]. (17) This follows from he vanilla quano value formula by aking boh he normal probabiliies o be one. These normal probabiliies are exercise probabiliies under some measure. Since a forward conrac is always exercised, boh hese probabiliies mus be equal o one.

6 6 Wysup 4 Quano Digial The valuaion of European syle quano digials follows he same principle as in he quano plain vanilla opion case. The value is v = Qe r QT N (φd ). (18) We provide an example of European syle digial pu in USD/JPY quano ino EUR in Table 1. Noional Mauriy European syle Barrier Theoreical value Fixing source 100,000 EUR 3 monhs (92days) USD-JPY 71,555 EUR ECB Table 1: Example of a quano digial pu. The buyer receives 100,000 EUR if a mauriy, he ECB fixing for USD-JPY (compued via EUR-JPY and EUR-USD) is below Terms were creaed on Jan wih he following marke daa: USD-JPY spo ref , USD-JPY ATM vol 8.55%, EUR-JPY ATM vol 6.69%, EUR-USD ATM vol 10.99% (corresponding o a correlaion of % for USD-JPY agains JPY-EUR), USD rae 2.5%, JPY rae 0.1%, EUR rae 4%. 5 Hedging of Quano Opions Hedging of quano opions can be done by running a muli-currency opions book. All he usual Greeks can be hedged. An excepion is he correlaion risk, which can only be hedged wih oher derivaives depending on he same correlaion. This is normally no possible. In FX he correlaion risk can be ranslaed ino a vega posiion as shown in [4] or in [2]. We illusrae his approach for quano plain vanilla opions now. 5.1 Vega Posiions of Quano Plain Vanilla Opions Saring from Equaion (14), we obain he sensiiviies

7 Foreign Exchange Quano Opions 7 v [ σ = QS 0e ( µ r Q)T n(d + ) ] T φn (φd + )ρ σt, v σ = QS 0e ( µ r Q)T φn (φd + )ρσt, v ρ = QS 0e ( µ r Q)T φn (φd + )σ σt, v = v ρ σ 3 ρ σ 3 = v σ 3 ρ σ σ = QS 0 e ( µ r Q)T φn (φd + )σ σt σ 3 σ σ = QS 0 e ( µ r Q)T φn (φd + )σ 3 T = QS 0 e ( µ r Q)T φn (φd + ) σ 2 + σ 2 + 2ρσ σt. Noe ha he compuaion is sandard calculus and repeaedly using he ideniy S 0 e µt n(φd + ) = Kn(φd ). (19) 5.2 Vega Hedging Quano Plain Vanilla Opions This shows exacly how he hree vega posiions can be hedged wih plain vanilla opions in all hree legs, provided here is a liquid vanilla opions marke in all hree legs. In he example wih XAU-USD-EUR he currency pairs XAU-USD and EUR-USD are raded, however, here is no liquid vanilla marke in XAU-EUR. Therefore, he correlaion risk remains unhedgeable. Similar saemens would apply for quanoed socks or sock indices. However, in FX, here are siuaions wih all legs being hedgeable, for insance EUR-USD-JPY. The signs of he vega posiions are no uniquely deermined in all legs. The FOR-DOM vega is smaller han he corresponding vanilla vega in case of a call and posiive correlaion or pu and negaive correlaion, larger in case of a pu and posiive correlaion or call and negaive correlaion. The DOM-Q vega akes he sign of he correlaion in case of a call and is opposie sign in case of a pu. The FOR-Q vega akes he opposie sign of he pu-call indicaor φ. 5.3 Example We provide an example of pricing and vega hedging scenario in Table 2, where we noice, ha dominaing vega risk comes from he FOR-DOM pair, whence mos of he risk can be hedged.

8 8 Wysup daa se 1 daa se 2 daa se 3 FX pair FOR-DOM XAU-USD XAU-USD XAU-USD spo FOR-DOM srike FOR-DOM quano DOM-Q volailiy FOR-DOM 10.00% 10.00% 10.00% quano volailiy DOM-Q 12.00% 12.00% 12.00% correlaion FOR-DOM DOM-Q 25.00% 25.00% % domesic ineres rae DOM % % % foreign ineres rae FOR % % % quano currency rae Q % % % ime in years T =call -1=pu FOR quano vanilla opion value quano vanilla opion vega FOR-DOM quano vanilla opion vega DOM-Q quano vanilla opion vega FOR-Q quano vanilla opion correlaion risk quano vanilla opion vol FOR-Q % % % vanilla opion value vanilla opion vega Table 2: Example of a quano plain vanilla. 6 Applicaion: Performance Linked Deposis The sandard applicaion are performance linked deposi or performance noes as in [5]. Any ime he performance of an underlying asse needs o be convered ino he noional currency invesed, and he exchange rae risk is wih he seller, we need a quano produc.

9 Foreign Exchange Quano Opions 9 Naurally, an underlying like gold, which is quoed in USD, would be a defaul candidae for a quano produc, when he invesmen is in a currency oher han USD. 6.1 Produc Descripion A performance linked deposi is a deposi wih a paricipaion in an underlying marke. The sandard is ha a GBP invesor waives her coupon ha he money marke would pay and insead buys a EUR-GBP call wih he same mauriy dae as he coupon, srike K and noional N in EUR. These parameers have o be chosen in such a way ha he offer price of he EUR call equals he money marke ineres rae plus he sales margin. The srike is ofen chosen o be he curren spo. The noional is ofen a percenage p of he deposi amoun A, such as 50% or 25%. The annual coupon paid o he invesor is hen a pre-defined minimum coupon plus he paricipaion p max[s T S 0, 0] S 0, (20) which is he reurn of he exchange rae viewed as an asse, where he invesor is proeced agains negaive reurns. So, obviously, he invesor buys a EUR call GBP pu wih srike K = S 0 and noional N = pa GBP or N = pa/s 0 EUR. Thus, if he EUR goes up by 10% agains he GBP, he invesor ges a coupon of p 10% p.a. in addiion o he minimum coupon. 6.2 Example We consider he example shown in Table 3. In his case, if he EUR-GBP spo fixing is , he addiional coupon would be % p.a. The break-even poin is a , so his produc is advisable for a very srong EUR bullish view. For a weakly bullish view an alernaive would be o buy an up-and-ou call wih barrier a and 75% paricipaion, where we would find he bes case o be wih an addiional coupon of 4.275% p.a., which would lead o a oal coupon of 6.275% p.a. 6.3 Composiion ˆ From he money marke we ge 49, GBP a he mauriy dae. ˆ The invesor buys a EUR call GBP pu wih srike and wih noional 1.5 Million GBP. ˆ The offer price of he call is 26, GBP, assuming a volailiy of 8.0% and a EUR rae of 2.50%. ˆ The deferred premium is 24, GBP.

10 10 Wysup Noional 5,000,000 GBP Sar dae 3 June 2005 Mauriy Number of days 91 Money marke reference rae EUR-GBP spo reference Minimum rae Addiional coupon S T Fixing source 2 Sepember 2005 (91 days) 4.00% ac/ % ac/365 30% 100 max[s T ,0] ac/365 EUR-GBP fixing on 31 Augus 2005 (88 days) ECB Table 3: Example of a performance linked deposi, where he invesor is paid 30% of he EUR-GBP reurn. Noe ha in GBP he daycoun convenion in he money marke is ac/365 raher han ac/360. ˆ The invesor receives a minimum paymen of 24, GBP. ˆ Subracing he deferred premium and he minimum paymen from he money marke leaves a sales margin of GBP (awfully poor I admi). ˆ Noe ha he opion he invesor is buying mus be cash-seled. 6.4 Variaions There are many variaions of he performance linked noes. Of course, one can hink of European syle knock-ou calls or window-barrier calls. For a paricipaion in a downward rend, he invesor can buy pus. One of he frequen issues in Foreign Exchange, however, is he deposi currency being differen from he domesic currency of he exchange rae, which is quoed in FOR-DOM (foreign-domesic), meaning how many unis of domesic currency are required o buy one uni of foreign currency. So if we have a EUR invesor who wishes o paricipae in a EUR-USD movemen, we have a problem, he usual quano confusion ha can drive anybody up he wall in FX a various occasions. Wha is he problem? The payoff of he EUR call USD pu [S T K] + (21) is in domesic currency (USD). Of course, his payoff can be convered ino he foreign currency (EUR) a mauriy, bu a wha rae? If we conver a rae S T, which is wha

11 Foreign Exchange Quano Opions 11 we could do in he spo marke a no cos, hen he invesor buys a vanilla EUR call. Bu here, he invesor receives a coupon given by p max[s T S 0, 0] S T. (22) If he invesor wishes o have performance of Equaion (20) raher han Equaion (22), hen he payoff a mauriy is convered a a rae of ino EUR, and his rae is se a he beginning of he rade. This is he quano facor, and he vanilla is acually a self-quano vanilla, i.e., a EUR call USD pu, cash-seled in EUR, where he payoff in USD is convered ino EUR a a rae of This self quano plain vanilla can be valued by invering he exchange rae, i.e., looking a USD-EUR. This way he valuaion can incorporae he smile of EUR-USD. Similar consideraions need o be aken ino accoun if he currency pair o paricipae in does no conain he deposi currency a all. A ypical siuaion is a EUR invesor, who wishes o paricipae in he gold price, which is measured in USD, so he invesor needs o buy a XAU call USD pu quanoed ino EUR. So he invesor is promised a coupon as in Equaion (20) for a XAU-USD underlying, where he coupon is paid in EUR, his implicily means ha we mus use a quano plain vanilla wih a quano facor of References [1] Hakala, J. and Wysup, U. (2002). Foreign Exchange Risk. Risk Publicaions, London. [2] Hakala, J. and Wysup, U. (2002). Making he mos ou of Muliple Currency Exposure: Proecion wih Baske Opions. The Euromoney Foreign Exchange and Treasury Managemen Handbook Adrian Hornbrook. [3] Shreve, S.E. (2004). Sochasic Calculus for Finance I+II. Springer. [4] Wysup, U. (2001). How he Greeks would have hedged Correlaion Risk of Foreign Exchange Opions, Wilmo Research Repor, Augus Also in Foreign Exchange Risk, Risk Publicaions, London [5] Wysup, U. (2006). FX Opions and Srucured Producs. Wiley Finance Series.

12 Index correlaion, FX, 5 currency riangle, 4 law of cosine, 4 performance linked deposi, 8 quano digial, 6 quano drif adjusmen, 2 quano facor, 2 quano forward, 5 quano opions, 2 quano plain vanilla, 5, 8 self-quano, 11 vega, quano plain vanilla, 6 12

13 FRANKFURT SCHOOL / HFB WORKING PAPER SERIES No. Auhor/Tile Year 97. Heidorn, Thomas / Hölscher, Luise / Werner, Mahias Ralf Access o Finance and Venure Capial for Indusrial SMEs Böger, Marc / Guhoff, Anja / Heidorn, Thomas Loss Given Defaul Modelle zur Schäzung von Recovery Raes Almer, Thomas / Heidorn, Thomas / Schmalz, Chrisian The Dynamics of Shor- and Long-Term CDS-spreads of Banks Barhel, Erich / Wollersheim, Jua Kulurunerschiede bei Mergers & Acquisiions: Enwicklung eines Konzepes zur Durchführung einer Culural Due Diligence 93. Heidorn, Thomas / Kunze, Wolfgang / Schmalz, Chrisian Liquidiäsmodellierung von Kredizusagen (Term Faciliies and Revolver) Burger,Andreas Produkiviä und Effizienz in Banken Terminologie, Mehoden und Saus quo Löchel, Hors / Pecher, Florian The Sraegic Value of Invesmens in Chinese Banks by Foreign Financial Insiuions Schalas, Chrisoph / Morgenschweis, Bernd / Sprengeer, Hans Oo / Ockens, Klaas / Sachulez, Rainer / Safran, Rober Der deusche NPL Mark 2007: Akuelle Enwicklungen, Verkauf und Bewerung Beriche und Referae des NPL Forums Schalas, Chrisoph / Sralkowski, Ingo 10 Jahre deusche Buyous Bannier, Chrisina / Hirsch, Chrisian The Economics of Raing Wachliss: Evidence from Raing Changes Demidova-Menzel, Nadeshda / Heidorn, Thomas Gold in he Invesmen Porfolio Hölscher, Luise / Rosenhal, Johannes Leisungsmessung der Inernen Revision Bannier, Chrisina / Hänsel, Dennis Deerminans of banks' engagemen in loan securiizaion Bannier, Chrisina Smoohing versus Timeliness - Wann sind sabile Raings opimal und welche Anforderungen sind an opimale Berichsregeln zu sellen? 83. Bannier, Chrisina Heerogeneous Muliple Bank Financing: Does i Reduce Ine±cien Credi-Renegoiaion Incidences? Cremers, Heinz / Löhr, Andreas Deskripion und Bewerung srukurierer Produke uner besonderer Berücksichigung verschiedener Markszenarien Demidova-Menzel, Nadeshda / Heidorn, Thomas Commodiies in Asse Managemen Cremers, Heinz / Walzner, Jens Risikoseuerung mi Krediderivaen uner besonderer Berücksichigung von Credi Defaul Swaps Cremers, Heinz / Traughber, Parick Handlungsalernaiven einer Genossenschafsbank im Invesmenprozess uner Berücksichigung der Risikoragfähigkei Gerdesmeier, Dieer / Roffia, Barbara Moneary Analysis: A VAR Perspecive Heidorn, Thomas / Kaiser, Dieer G. / Muschiol, Andrea Porfolioopimierung mi Hedgefonds uner Berücksichigung höherer Momene der Vereilung Jobe, Clemens J. / Ockens, Klaas / Safran, Rober / Schalas, Chrisoph Work-Ou und Servicing von noleidenden Kredien Beriche und Referae des HfB-NPL Servicing Forums Abrar, Kamyar Fusionskonrolle in dynamischen Nezsekoren am Beispiel des Breibandkabelsekors Schalas, Chrisoph / Schanz, Kai-Michael Werpapierprospeke: Markeinführungspubliziä nach EU-Prospekverordnung und Werpapierprospekgesez Frankfur School of Finance & Managemen

14 73. Dickler, Rober A. / Schalas, Chrisoph Disressed Deb in Germany: Wha s Nex? Possible Innovaive Exi Sraegies Belke, Ansgar / Pollei, Thorsen How he ECB and he US Fed se ineres raes Heidorn, Thomas / Hoppe, Chrisian / Kaiser, Dieer G. Heerogeniä von Hedgefondsindizes Baumann, Sefan / Löchel, Hors The Endogeneiy Approach of he Theory of Opimum Currency Areas - Wha does i mean for ASEAN + 3? Heidorn, Thomas / Traumann, Alexandra Niederschlagsderivae Heidorn, Thomas / Hoppe, Chrisian / Kaiser, Dieer G. Möglichkeien der Srukurierung von Hedgefondsporfolios Belke, Ansgar / Pollei, Thorsen (How) Do Sock Marke Reurns Reac o Moneary Policy? An ARDL Coinegraion Analysis for Germany Daynes, Chrisian / Schalas, Chrisoph Akuelle Rechsfragen des Bank- und Kapialmarksrechs II: Disressed Deb - Invesing in Deuschland Gerdesmeier, Dieer / Pollei, Thorsen Measures of excess liquidiy Becker, Gerno M. / Harding, Perham / Hölscher, Luise Financing he Embedded Value of Life Insurance Porfolios Schalas, Chrisoph Modernisierung der Wasserwirschaf im Spannungsfeld von Umwelschuz und Webewerb Brauch Deuschland eine Rechsgrundlage für die Vergabe von Wasserversorgungskonzessionen? 62. Bayer, Marcus / Cremers, Heinz / Kluß, Norber Wersicherungssraegien für das Asse Managemen Löchel, Hors / Pollei, Thorsen A case for money in he ECB moneary policy sraegy Richard, Jörg / Schalas, Chrisoph / Schanz, Kay-Michael Unernehmen im Prime Sandard - Saying Public oder Going Privae? - Nuzenanalyse der Börsennoiz Heun, Michael / Schlink, Torsen Early Warning Sysems of Financial Crises - Implemenaion of a currency crisis model for Uganda Heimer, Thomas / Köhler, Thomas Auswirkungen des Basel II Akkords auf öserreichische KMU Heidorn, Thomas / Meyer, Bernd / Pierowiak, Alexander Performanceeffeke nach Direcors Dealings in Deuschland, Ialien und den Niederlanden Gerdesmeier, Dieer / Roffia, Barbara The Relevance of real-ime daa in esimaing reacion funcions for he euro area Barhel, Erich / Gierig, Rauno / Kühn, Ilmhar-Wolfram Unerschiedliche Ansäze zur Messung des Humankapials Anders, Diemar / Binder, Andreas / Hesdahl, Ralf / Schalas, Chrisoph / Thöne, Thomas Akuelle Rechsfragen des Bank- und Kapialmarkrechs I : Non-Performing-Loans / Faule Kredie - Handel, Work-Ou, Ousourcing und Securiisaion Pollei, Thorsen The Slowdown in German Bank Lending Revisied Heidorn, Thomas / Siragusano, Tindaro Die Anwendbarkei der Behavioral Finance im Devisenmark Schüze, Daniel / Schalas, Chrisoph (Hrsg.) Wider die Verschleuderung von Unernehmen durch Pfandverseigerung Gerhold, Mirko / Heidorn, Thomas Invesiionen und Emissionen von Converible Bonds (Wandelanleihen) Chevalier, Pierre / Heidorn, Thomas / Krieger, Chrisian Temperaurderivae zur sraegischen Absicherung von Beschaffungs- und Absazrisiken Becker, Gerno M. / Seeger, Norber Inernaionale Cash Flow-Rechnungen aus Eigner- und Gläubigersich Boenkos, Wolfram / Schmid, Wolfgang M. Noes on convexiy and quano adjusmens for ineres raes and relaed opions Frankfur School of Finance & Managemen

15 46. Hess, Dieer Deerminans of he relaive price impac of unanicipaed Informaion in U.S. macroeconomic releases 45. Cremers, Heinz / Kluß, Norber / König, Markus Incenive Fees. Erfolgsabhängige Vergüungsmodelle deuscher Publikumsfonds Heidorn, Thomas / König, Lars Invesiionen in Collaeralized Deb Obligaions Kahler, Holger / Seeger, Norber Bilanzierung von Unernehmenszusammenschlüssen nach US-GAAP Beiräge von Sudierenden des Sudiengangs BBA 012 uner Begleiung von Prof. Dr. Norber Seeger Rechnungslegung im Umbruch - HGB-Bilanzierung im Webewerb mi den inernaionalen Sandards nach IAS und US-GAAP 41. Overbeck, Ludger / Schmid, Wolfgang Modeling Defaul Dependence wih Threshold Models Balhasar, Daniel / Cremers, Heinz / Schmid, Michael Porfolioopimierung mi Hedge Fonds uner besonderer Berücksichigung der Risikokomponene Heidorn, Thomas / Kanwill, Jens Eine empirische Analyse der Spreadunerschiede von Fessazanleihen zu Floaern im Euroraum und deren Zusammenhang zum Preis eines Credi Defaul Swaps Böcher, Henner / Seeger, Norber Bilanzierung von Finanzderivaen nach HGB, EsG, IAS und US-GAAP Moormann, Jürgen Terminologie und Glossar der Bankinformaik Heidorn, Thomas Bewerung von Krediproduken und Credi Defaul Swaps Heidorn, Thomas / Weier, Sven Einführung in die fundamenale Akienanalyse Seeger, Norber Inernaional Accouning Sandards (IAS) Moormann, Jürgen / Sehling, Frank Sraegic Posiioning of E-Commerce Business Models in he Porfolio of Corporae Banking Sokolovsky, Zbynek / Srohhecker, Jürgen Fi für den Euro, Simulaionsbasiere Euro-Maßnahmenplanung für Dresdner-Bank-Geschäfssellen Roßbach, Peer Behavioral Finance - Eine Alernaive zur vorherrschenden Kapialmarkheorie? Heidorn, Thomas / Jaser, Oliver / Willeiner, Ulrich Even Risk Covenans Biswas, Ria / Löchel, Hors Recen Trends in U.S. and German Banking: Convergence or Divergence? Eberle, Güner Georg / Löchel, Hors Die Auswirkungen des Übergangs zum Kapialdeckungsverfahren in der Renenversicherung auf die Kapialmärke Heidorn, Thomas / Klein, Hans-Dieer / Siebrech, Frank Economic Value Added zur Prognose der Performance europäischer Akien Cremers, Heinz Konvergenz der binomialen Opionspreismodelle gegen das Modell von Black/Scholes/Meron Löchel, Hors Die ökonomischen Dimensionen der New Economy Frank, Axel / Moormann, Jürgen Grenzen des Ousourcing: Eine Exploraion am Beispiel von Direkbanken Heidorn, Thomas / Schmid, Peer / Seiler, Sefan Neue Möglichkeien durch die Namensakie Böger, Andreas / Heidorn, Thomas / Graf Waldsein, Philipp Hybrides Kernkapial für Krediinsiue Heidorn, Thomas Enscheidungsorieniere Mindesmargenkalkulaion Wolf, Birgi Die Eigenmielkonzepion des 10 KWG Frankfur School of Finance & Managemen

16 19. Cremers, Heinz / Robé, Sophie / Thiele, Dirk Bea als Risikomaß - Eine Unersuchung am europäischen Akienmark Cremers, Heinz Opionspreisbesimmung Cremers, Heinz Value a Risk-Konzepe für Markrisiken Chevalier, Pierre / Heidorn, Thomas / Rüze, Merle Gründung einer deuschen Srombörse für Elekriziäsderivae Deiser, Daniel / Ehrlicher, Sven / Heidorn, Thomas CaBonds Jochum, Eduard Hoshin Kanri / Managemen by Policy (MbP) Heidorn, Thomas Krediderivae Heidorn, Thomas Kredirisiko (CrediMerics) Moormann, Jürgen Terminologie und Glossar der Bankinformaik Löchel, Hors The EMU and he Theory of Opimum Currency Areas Löchel, Hors Die Geldpoliik im Währungsraum des Euro Heidorn, Thomas / Hund, Jürgen Die Umsellung auf die Sückakie für deusche Akiengesellschafen Moormann, Jürgen Sand und Perspekiven der Informaionsverarbeiung in Banken Heidorn, Thomas / Schmid, Wolfgang LIBOR in Arrears Jahresberich Ecker, Thomas / Moormann, Jürgen Die Bank als Bereiberin einer elekronischen Shopping-Mall Jahresberich Cremers, Heinz / Schwarz, Willi Inerpolaion of Discoun Facors Moormann, Jürgen Lean Reporing und Führungsinformaionssyseme bei deuschen Finanzdiensleisern 1995 FRANKFURT SCHOOL / HFB WORKING PAPER SERIES CENTRE FOR PRACTICAL QUANTITATIVE FINANCE No. Auhor/Tile Year 09. Wysup, Uwe Foreign Exchange Symmeries Becker, Chrisoph / Wysup, Uwe Was kose eine Garanie? Ein saisischer Vergleich der Rendie von langfrisigen Anlagen Schmid, Wolfgang Defaul Swaps and Hedging Credi Baskes Kilin, Fiodor Acceleraing he Calibraion of Sochasic Volailiy Models Griebsch, Susanne/ Kühn, Chrisoph / Wysup, Uwe Insalmen Opions: A Closed-Form Soluion and he Limiing Case Boenkos, Wolfram / Schmid, Wolfgang M. Ineres Rae Convexiy and he Volailiy Smile 2006 Frankfur School of Finance & Managemen

17 03. Becker, Chrisoph/ Wysup, Uwe On he Cos of Delayed Currency Fixing Boenkos, Wolfram / Schmid, Wolfgang M. Cross currency swap valuaion Wallner, Chrisian / Wysup, Uwe Efficien Compuaion of Opion Price Sensiiviies for Opions of American Syle 2004 HFB SONDERARBEITSBERICHTE DER HFB - BUSINESS SCHOOL OF FINANCE & MANAGEMENT No. Auhor/Tile Year 01. Nicole Kahmer / Jürgen Moormann Sudie zur Ausrichung von Banken an Kundenprozessen am Beispiel des Inerne (Preis: 120,--) 2003 Prined ediion: shipping Download: hp:// Order address / conac Frankfur School of Finance & Managemen Sonnemannsr D Frankfur/M. Germany Phone: +49 (0) Fax: +49 (0) m.biemer@frankfur-school.de Furher informaion abou Frankfur School of Finance & Managemen may be obained a: hp:// Frankfur School of Finance & Managemen