{"id":{"repo_id":"milano","oai_identifier":"oai:air.unimi.it:2434/150559"},"canonical_url":"https://search.dev.ndltd.org/etd/milano/oai:air.unimi.it:2434/150559","repository":{"repo_id":"milano","name":"Università degli Studi di Milano","base_url":"https://air.unimi.it/oai/request"},"display":{"title":"ADIABATIC CONDITIONS FOR FINANCIAL SYSTEMS","abstract":"In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is possible to get a new fitting procedure of the volatility smile that considers also the exponential decay of the real PDF of returns observed in the financial markets. In addiction, we show that this approach based on a volatility smile leads to relative minima for the distribution function (\"bad\" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring \"adiabatic\" conditions on the volatility smile. Our study finds application in the Risk Management activities where the tails characterization of financial returns PDF has a central role for the risk estimation.","abstract_html":"In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is possible to get a new fitting procedure of the volatility smile that considers also the exponential decay of the real PDF of returns observed in the financial markets. In addiction, we show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile. Our study finds application in the Risk Management activities where the tails characterization of financial returns PDF has a central role for the risk estimation.","abstract_has_math":false,"creators":["L. 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We show that, considering a scaling law derived from data, it is possible to get a new fitting procedure of the volatility smile that considers also the exponential decay of the real PDF of returns observed in the financial markets. In addiction, we show that this approach based on a volatility smile leads to relative minima for the distribution function (\"bad\" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring \"adiabatic\" conditions on the volatility smile. Our study finds application in the Risk Management activities where the tails characterization of financial returns PDF has a central role for the risk estimation."]},{"key":"dc:title","label":"Title","values":["ADIABATIC CONDITIONS FOR FINANCIAL SYSTEMS"]}]}],"canonical_facts":{"dc:contributor":["tutore: Fausto Borgonovi ; coordinatore: Marco Bersanelli","L. Spadafora","BERSANELLI, MARCO RINALDO FEDELE"],"dc:creator":["L. Spadafora"],"dc:date":["2011-01-21"],"dc:description":["In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is possible to get a new fitting procedure of the volatility smile that considers also the exponential decay of the real PDF of returns observed in the financial markets. In addiction, we show that this approach based on a volatility smile leads to relative minima for the distribution function (\"bad\" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring \"adiabatic\" conditions on the volatility smile. Our study finds application in the Risk Management activities where the tails characterization of financial returns PDF has a central role for the risk estimation."],"dc:identifier":["http://hdl.handle.net/2434/150559","10.13130/spadafora-luca_phd2011-01-21"],"dc:language":["eng"],"dc:publisher":["Università degli Studi di Milano"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:subject":["Settore FIS/03 - Fisica della Materia"],"dc:title":["ADIABATIC CONDITIONS FOR FINANCIAL SYSTEMS"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-27T20:19:15Z"}