This study proposes an analysis of the main drawbacks emerged when adopting the traditional short rate dynamics under extreme market conditions such as under negative interest rates. In fact, this condition has led to invalidate the use of the majority of the most popular stochastic differential equations (SDE) reported in the scientific literature. The first part of the paper makes an overall introduction to the problem, analyzing it from different perspectives. Given that the author dealt with these topics in previous research items, the objective of the paper is to focus on only one of these aspects which was not scrutinized before and to examine it in full detail. As a result, the most popular stochastic dynamics are shown in the second part and the problems raised by their numerical integration are then discussed. Starting from the equations for which it is feasible to implement a numerical scheme for their solution, the problem thus becomes how to find a reasonable estimation for the SDE parameters. The third section deals with the problems occurred in the application of Maximum Likelihood Estimation (MLE) caused by the negative interest rates during the implementation of the well-established approaches. For every analyzed dynamics a real market case is provided. The paper highlights the appropriateness of the Hull-White model which can be considered a feasible and reliable solution for simulating short rates also under extreme market conditions.
{"title":"Critical analysis of the most widespread methodologies for the simulation of the short rate dynamics under extreme market conditions","authors":"P. Giribone, Banca Carige","doi":"10.47473/2020rmm0076","DOIUrl":"https://doi.org/10.47473/2020rmm0076","url":null,"abstract":"This study proposes an analysis of the main drawbacks emerged when adopting the traditional short rate dynamics under extreme market conditions such as under negative interest rates. In fact, this condition has led to invalidate the use of the majority of the most popular stochastic differential equations (SDE) reported in the scientific literature. The first part of the paper makes an overall introduction to the problem, analyzing it from different perspectives. Given that the author dealt with these topics in previous research items, the objective of the paper is to focus on only one of these aspects which was not scrutinized before and to examine it in full detail. As a result, the most popular stochastic dynamics are shown in the second part and the problems raised by their numerical integration are then discussed. Starting from the equations for which it is feasible to implement a numerical scheme for their solution, the problem thus becomes how to find a reasonable estimation for the SDE parameters. The third section deals with the problems occurred in the application of Maximum Likelihood Estimation (MLE) caused by the negative interest rates during the implementation of the well-established approaches. For every analyzed dynamics a real market case is provided. The paper highlights the appropriateness of the Hull-White model which can be considered a feasible and reliable solution for simulating short rates also under extreme market conditions.","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126055607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-30DOI: 10.1101/2020.05.28.20115790
Fabio Verachi, L. Trussoni, Luciano Lanzi
The objective of this paper is to evaluate the potential costs deriving from the adoption of the CoViD-19 epidemic management strategy. For this purpose, we developed a specific methodology that combines an epidemiological model, known in the literature as "SIR" (Susceptible - Infected - Recovered), and a probabilistic state model, also known as "multi-state". The model thus conceived was then parameterized using the dataset published by the Italian Government through the Civil Protection and the Istituto Superiore di Sanita. We therefore estimated the duration of the disease and the related costs, with reference to the strategy currently under discussion between government institutions and social organizations involved. Given the flexibility of the adopted approach, the tool will also be able to provide useful indications in relation to any alternative strategies that the Government could adopt in the near future, as well as being the starting point of an analysis of the epidemic indirect costs such as losses of GDP fractions.
{"title":"CoViD-19 in Italy: a mathematical model to analyze the epidemic containment strategy and the economic impacts","authors":"Fabio Verachi, L. Trussoni, Luciano Lanzi","doi":"10.1101/2020.05.28.20115790","DOIUrl":"https://doi.org/10.1101/2020.05.28.20115790","url":null,"abstract":"The objective of this paper is to evaluate the potential costs deriving from the adoption of the CoViD-19 epidemic management strategy. For this purpose, we developed a specific methodology that combines an epidemiological model, known in the literature as \"SIR\" (Susceptible - Infected - Recovered), and a probabilistic state model, also known as \"multi-state\". The model thus conceived was then parameterized using the dataset published by the Italian Government through the Civil Protection and the Istituto Superiore di Sanita. We therefore estimated the duration of the disease and the related costs, with reference to the strategy currently under discussion between government institutions and social organizations involved. Given the flexibility of the adopted approach, the tool will also be able to provide useful indications in relation to any alternative strategies that the Government could adopt in the near future, as well as being the starting point of an analysis of the epidemic indirect costs such as losses of GDP fractions.","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124390978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-Performing Exposures of banks: impatient diktats and national solutions vs patient management and Asset Management Companies at European level","authors":"R. Masera","doi":"10.47473/2020rmm0009","DOIUrl":"https://doi.org/10.47473/2020rmm0009","url":null,"abstract":"","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115371763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anna Bottasso, Pier Giuseppe Giribone, Matilde Martorana
{"title":"Analisi e progettazione di un sistema di misure quantitative per il monitoraggio dei rischi finanziari delle Garanzie d’Origine","authors":"Anna Bottasso, Pier Giuseppe Giribone, Matilde Martorana","doi":"10.47473/2020rmm0027","DOIUrl":"https://doi.org/10.47473/2020rmm0027","url":null,"abstract":"","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123699962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fintech, Distristributed Ledgers Tecnology (DLT), blockchain, machine learning, algorithmic trading and High Frequency Trading (HFT), are among the most disruptive digital innovations that are transforming the structure of any industrial sector, including the financial industry. Together with the positive spillovers of the introduction of these new technologies (i.e. reducing transaction costs, reducing operating costs, improving speed and security of the transactions, ...), we should be aware of the potential new risks that may involve the financial system, whose activity is guaranteed by the trust of the operators. Regulators and supervisors should therefore extend their understanding of the new technologies, both to assess their potential impact on banks' business models and to address risks arising with due caution. Similarly, banks operating within the new technological framework, must rethink their own business models and consider the upcoming challenges, which require specific knowledge and skills.
{"title":"New frontiers in financial markets: from machine learning to algorithmic trading","authors":"Valentina Lagasio","doi":"10.47473/2020rmm0025","DOIUrl":"https://doi.org/10.47473/2020rmm0025","url":null,"abstract":"Fintech, Distristributed Ledgers Tecnology (DLT), blockchain, machine learning, algorithmic trading and High Frequency Trading (HFT), are among the most disruptive digital innovations that are transforming the structure of any industrial sector, including the financial industry. Together with the positive spillovers of the introduction of these new technologies (i.e. reducing transaction costs, reducing operating costs, improving speed and security of the transactions, ...), we should be aware of the potential new risks that may involve the financial system, whose activity is guaranteed by the trust of the operators. Regulators and supervisors should therefore extend their understanding of the new technologies, both to assess their potential impact on banks' business models and to address risks arising with due caution. Similarly, banks operating within the new technological framework, must rethink their own business models and consider the upcoming challenges, which require specific knowledge and skills.","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123060265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Il risk appetite framework: una «teoria del tutto» per le banche?","authors":"Giacomo Vadi","doi":"10.47473/2020rmm0024","DOIUrl":"https://doi.org/10.47473/2020rmm0024","url":null,"abstract":"","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125535738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Towards the Reform of the European Financial Supervisory Authorities on Intermediaries and Financial Markets: some Notes for a Discussion. The dynamics that are blurring the borders between old and new financial intermediation practices, partly induced by fintech, call for a significant move to enhance a light regulation, supported by a proactive risk based supervision. That implies an update of the European and National Competent Authorities’ architectures to serve the tasks they are committed to, by effectively implementing market conduct and prudential supervision across processes, activities and platforms. The paper concludes with some drill-down on the steps that could be appropriate to re-address the hybrid Italian twin-peaks for a more coherent set-up. 1. Le lezioni della crisi La segnalazione di carenze regolamentari e di vigilanza, a valle dell’irrompere della crisi finanziaria, ha portato le istituzioni europee a sottolineare con insistenza, nel corso degli ultimi dieci anni, l’importanza che gli interventi riparatori su questi due fronti fossero finalizzati a: (1) prevenire crisi sistemiche, (2) garantire l’integrità e l’ordinato funzionamento dei mercati finanziari, (3) rafforzare le tutele per gli investitori, in particolare di quelli retail. Le strade percorse per tradurre in prassi queste finalità (overarching principles) si sono dispiegate lungo due direttrici: il ridisegno del sistema delle Autorità europee, accompagnato da un pervasivo sforzo di revisione e completamento del quadro normativo e regolamentare ad integrazione del “single rule book”. In risposta alle emergenze poste dall’irrompere della crisi finanziaria, la Commissione Europea ha finalizzato le raccomandazioni del High Level Group presieduto da Jaques de Lerosière, avviando un percorso che ha portato alla istituzione nel 2010 dell’European Systemic Risk Board (ESRB), a cui sono stati affidati i presidi macroprudenziali necessari per prevenire/mitigare il rischio sistemico. A completamento del European System of Financial Supervision (ESFS), nel gennaio del 2011 vengono istituite tre Autorità di settore EBA, EIOPA ed ESMA (rispettivamente per banche, assicurazioni e fondi pensione, strumenti finanziari e mercati) per i profili microprudenziali 2 . Nel novembre del 2014 la BCE assume le competenze di vigilanza sugli enti creditizi dell’area euro ad integrazione dell’attività svolta dalle autorità di settore nazionali; una scelta che si è rivelata appropriata ed efficace alla luce delle implicazioni sistemiche di alcune problematiche legate al mondo del credito. Alle nuove Autorità europee sono stati affidati ruoli in ambito prevalentemente regolamentare, lasciando così a lungo la vigilanza su ampi settori dell’industria finanziaria tra le competenze delle Autorità dei singoli paesi (NCA), che hanno fatto prevalere nel tempo le prassi nazionali sulle ripetute sollecitazioni della Commissione a convergere. Scelte che, di fatto, hanno contribuito a cristallizzare preval
欧洲金融监管机构对中介机构和金融市场的改革:一些讨论要点。部分由金融科技引起的新旧金融中介实践之间界限模糊的动态，要求采取重大举措，加强宽松监管，并辅以积极主动的基于风险的监管。这意味着更新欧洲和国家主管当局的架构，通过有效地实施市场行为和跨流程、活动和平台的审慎监管，为他们承诺的任务服务。这篇论文总结了一些关于步骤的深入研究，这些步骤可能适合重新解决意大利混合双峰问题，以获得更连贯的设置。1. 金融危机的解决方案，金融危机的解决方案，欧洲机构的解决方案，最终解决方案的解决方案，干预方案的解决方案的解决方案，最终解决方案的解决方案，最终解决方案的解决方案。(1)预防危机系统;(2)保证金融市场的“整合”和“协调”功能;(3)保障投资者，特别是散户投资者的利益。按贸易惯例执行的总体原则(总体原则)是指在适当的指导下执行的原则:欧洲行政管理制度的总体原则和普遍原则;修订、完善、管理和统一的“单一规则手册”。在金融危机爆发后的紧急情况下，欧洲委员会最终通过了一项决议，即由雅克·德·勒罗西特(jacques de lerosiire)担任高级小组主席，并于2010年由欧洲系统风险委员会(ESRB)担任预防/缓解金融危机爆发所必需的宏观审慎主席。1 .欧洲金融监管体系(ESFS)的完善，2011年12月1日发布的《欧洲金融监管体系(ESFS)》，EIOPA和ESMA(银行监管、养老金监管、工具金融和商业监管)，以及微观审慎。2014年11月1日起，欧盟委员会将承担欧洲地区和欧洲一体化委员会的责任，并承担欧洲地区和欧洲一体化委员会的责任。unselta che si è rivelata appropriata Ed effices all luce delle implizioni sistemiche di calcalproblem leglegalmondo del credit。新欧洲自治当局在雄心和普遍的管理方面的国家地位的确立，新欧洲自治当局在雄心和普遍的管理方面的地位的确立，新欧洲自治当局在雄心和普遍的管理方面的地位的确立，新欧洲自治当局的地位的确立，新欧洲自治当局的地位的确立，新欧洲自治当局的地位的确立，新欧洲自治当局的地位的确立，新欧洲自治当局的地位的确立。我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲，我的父亲。“单一规则手册”不可能è不可能实现。在“不同质性”和“不同质性”方面，我们提出了“商业、金融、多样化”和“劳动、媒体、经济、经济、经济、经济”这两个概念。cio si e aggiunta l 'oggettiva difficolta di declinare标准adatte一presidiare efficacemente le主trasformazioni格瓦拉在questi安妮汉诺ridisegnato le modalita di produzione prestazione e fruizione一些servizi finanziari。在所有的规则中，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则，所有的规则都是规则。问题是，在管理当局的管理方面，必须有明确和有效的监管目标，必须有明确和有效的监管，必须有明确的总体原则，必须有明确的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标，必须有严格的监管目标。1 2018年12月6日，意大利米兰。《经济与社会》，2018，第3期。在2002年和2004年的机构间委员会中:CEBS (bancaria民团)、CEIOPS (assicurazioni e pension民团)、CESR (regamentazionone valori mobilii)。3 V。孔蒂:《从危机中吸取教训的监管与监督反思》，《保罗·巴菲中心研究论文丛刊》，2011年第1期(http://ssrn.com/abstract=1918765)。
{"title":"The Margin of Conservatism (MoC) in the IRB approach: defining and measuring the general estimation error","authors":"Franco Varetto, S. Cuneo","doi":"10.47473/2020rmm0031","DOIUrl":"https://doi.org/10.47473/2020rmm0031","url":null,"abstract":"Towards the Reform of the European Financial Supervisory Authorities on Intermediaries and Financial Markets: some Notes for a Discussion. The dynamics that are blurring the borders between old and new financial intermediation practices, partly induced by fintech, call for a significant move to enhance a light regulation, supported by a proactive risk based supervision. That implies an update of the European and National Competent Authorities’ architectures to serve the tasks they are committed to, by effectively implementing market conduct and prudential supervision across processes, activities and platforms. The paper concludes with some drill-down on the steps that could be appropriate to re-address the hybrid Italian twin-peaks for a more coherent set-up. 1. Le lezioni della crisi La segnalazione di carenze regolamentari e di vigilanza, a valle dell’irrompere della crisi finanziaria, ha portato le istituzioni europee a sottolineare con insistenza, nel corso degli ultimi dieci anni, l’importanza che gli interventi riparatori su questi due fronti fossero finalizzati a: (1) prevenire crisi sistemiche, (2) garantire l’integrità e l’ordinato funzionamento dei mercati finanziari, (3) rafforzare le tutele per gli investitori, in particolare di quelli retail. Le strade percorse per tradurre in prassi queste finalità (overarching principles) si sono dispiegate lungo due direttrici: il ridisegno del sistema delle Autorità europee, accompagnato da un pervasivo sforzo di revisione e completamento del quadro normativo e regolamentare ad integrazione del “single rule book”. In risposta alle emergenze poste dall’irrompere della crisi finanziaria, la Commissione Europea ha finalizzato le raccomandazioni del High Level Group presieduto da Jaques de Lerosière, avviando un percorso che ha portato alla istituzione nel 2010 dell’European Systemic Risk Board (ESRB), a cui sono stati affidati i presidi macroprudenziali necessari per prevenire/mitigare il rischio sistemico. A completamento del European System of Financial Supervision (ESFS), nel gennaio del 2011 vengono istituite tre Autorità di settore EBA, EIOPA ed ESMA (rispettivamente per banche, assicurazioni e fondi pensione, strumenti finanziari e mercati) per i profili microprudenziali 2 . Nel novembre del 2014 la BCE assume le competenze di vigilanza sugli enti creditizi dell’area euro ad integrazione dell’attività svolta dalle autorità di settore nazionali; una scelta che si è rivelata appropriata ed efficace alla luce delle implicazioni sistemiche di alcune problematiche legate al mondo del credito. Alle nuove Autorità europee sono stati affidati ruoli in ambito prevalentemente regolamentare, lasciando così a lungo la vigilanza su ampi settori dell’industria finanziaria tra le competenze delle Autorità dei singoli paesi (NCA), che hanno fatto prevalere nel tempo le prassi nazionali sulle ripetute sollecitazioni della Commissione a convergere. Scelte che, di fatto, hanno contribuito a cristallizzare preval","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123950688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Simone Fioribello, Pier Giuseppe Giribone, Banca Carige
Al fine di valorizzare opzioni su valuta si ricorre tendenzialmente al framework di pricing di Garman – Kohlhagen, che costituisce un’estensione di quello tradizionale di Black-Scholes-Merton. Tali modelli di valutazione hanno in comune la definizione di un’equazione alle derivate parziali rappresentativa, sotto alcune ipotesi, della possibile evoluzione futura del valore del derivato, nota come PDE fondamentale. La specifica del tipo di opzione avviene mediante la definizione delle condizioni iniziali (IC – Initial Conditions) e delle condizioni al contorno di Dirichlet del problema (BC – Boundary Conditions), che dipendono strettamente dal pay-off dell’opzione. Qualora questo sia semplice la PDE ammette una soluzione in forma chiusa, altrimenti è necessario ricorrere ad una metodologia numerica di pricing. La discretizzazione avviene tipicamente impiegando i metodi delle differenze finite (FDM – Finite Difference Method) o degli elementi finiti (FEM – Finite Elements Method). Negli ultimi anni l’ingegneria finanziaria si sta concentrando su una metodologia innovativa per la valorizzazione di opzioni, che pone i suoi fondamenti teorici sulle funzioni a base radiale (RBF – Radial Basis Functions). Il fine del presente studio è quello di presentare i principi di funzionamento di tale tecnica e di fornire, dopo aver condotto un’accurata validazione del codice, un esempio di applicazione nella valutazione di un’opzione esotica digitale scritta su valuta. Garman – Kohlhagen framework, which is an extension of the most popular Black-Scholes-Merton model, is often used by financial institutions in order to price options with a currency as underlying. These pricing techniques have in common the definition of a partial differential equation used for the definition of the future value of the derivative, called Fundamental PDE. The financial instruments characterization depends on the derivative pay-off and it is realized through the specification of the initial conditions (IC) and the Dirichlet’s boundary conditions (BC). For standard contracts, called plain-vanilla derivatives, and for a few class of non-standard instruments, called exotic derivatives, this problem can be solved analytically reaching a theoretical fair value through a closed formula (CF) valuation, otherwise a numerical method must be used. Classical numerical integration schemes, which have been implemented for this purpose, are Finite Difference Method (FDM) and Finite Elements Method (FEM). In the last ten years, financial engineering has focused on an innovative methodology for option pricing which has its foundations on Radial Basis Functions (RBF). This paper aims to examine how this technique works in the financial field and how this method can be applied to the fair-value determination of vanilla and exotic Forex options.
{"title":"La determinazione del fair value di opzioni su valuta impiegando funzioni a base radiale: un’applicazione al framework di pricing di Garman-Kohlhagen","authors":"Simone Fioribello, Pier Giuseppe Giribone, Banca Carige","doi":"10.47473/2020rmm0032","DOIUrl":"https://doi.org/10.47473/2020rmm0032","url":null,"abstract":"Al fine di valorizzare opzioni su valuta si ricorre tendenzialmente al framework di pricing di Garman – Kohlhagen, che costituisce un’estensione di quello tradizionale di Black-Scholes-Merton. Tali modelli di valutazione hanno in comune la definizione di un’equazione alle derivate parziali rappresentativa, sotto alcune ipotesi, della possibile evoluzione futura del valore del derivato, nota come PDE fondamentale. La specifica del tipo di opzione avviene mediante la definizione delle condizioni iniziali (IC – Initial Conditions) e delle condizioni al contorno di Dirichlet del problema (BC – Boundary Conditions), che dipendono strettamente dal pay-off dell’opzione. Qualora questo sia semplice la PDE ammette una soluzione in forma chiusa, altrimenti è necessario ricorrere ad una metodologia numerica di pricing. La discretizzazione avviene tipicamente impiegando i metodi delle differenze finite (FDM – Finite Difference Method) o degli elementi finiti (FEM – Finite Elements Method). Negli ultimi anni l’ingegneria finanziaria si sta concentrando su una metodologia innovativa per la valorizzazione di opzioni, che pone i suoi fondamenti teorici sulle funzioni a base radiale (RBF – Radial Basis Functions). Il fine del presente studio è quello di presentare i principi di funzionamento di tale tecnica e di fornire, dopo aver condotto un’accurata validazione del codice, un esempio di applicazione nella valutazione di un’opzione esotica digitale scritta su valuta. Garman – Kohlhagen framework, which is an extension of the most popular Black-Scholes-Merton model, is often used by financial institutions in order to price options with a currency as underlying. These pricing techniques have in common the definition of a partial differential equation used for the definition of the future value of the derivative, called Fundamental PDE. The financial instruments characterization depends on the derivative pay-off and it is realized through the specification of the initial conditions (IC) and the Dirichlet’s boundary conditions (BC). For standard contracts, called plain-vanilla derivatives, and for a few class of non-standard instruments, called exotic derivatives, this problem can be solved analytically reaching a theoretical fair value through a closed formula (CF) valuation, otherwise a numerical method must be used. Classical numerical integration schemes, which have been implemented for this purpose, are Finite Difference Method (FDM) and Finite Elements Method (FEM). In the last ten years, financial engineering has focused on an innovative methodology for option pricing which has its foundations on Radial Basis Functions (RBF). This paper aims to examine how this technique works in the financial field and how this method can be applied to the fair-value determination of vanilla and exotic Forex options.","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129275158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Appunti sul riassetto delle Autorità su intermediari e mercati finanziari","authors":"Vittorio Conti","doi":"10.47473/2020rmm0029","DOIUrl":"https://doi.org/10.47473/2020rmm0029","url":null,"abstract":"","PeriodicalId":296057,"journal":{"name":"Risk Management Magazine","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115150008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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