sergio scarlatti - Academia.edu (original) (raw)
Papers by sergio scarlatti
Quantum Probability and Applications II, 1985
ABSTRACT Without Abstract
European Journal of Operational Research, 2021
We consider the problem of computing the Value Adjustment of European contingent claims when defa... more We consider the problem of computing the Value Adjustment of European contingent claims when default of either party is considered, possibly including also funding and collateralization requirements. As shown in Brigo et al. ([12], [13]), this leads to a more articulate variety of Value Adjustments (XVA) that introduce some nonlinear features. When exploiting a reducedform approach for the default times, the adjusted price can be characterized as the solution to a possibly nonlinear Backward Stochastic Differential Equation (BSDE). The expectation representing the solution of the BSDE is usually quite hard to compute even in a Markovian setting, and one might resort either to the discretization of the Partial Differential Equation characterizing it or to Monte Carlo Simulations. Both choices are computationally very expensive and in this paper we suggest an approximation method based on an appropriate change of numeraire and on a Taylor's polynomial expansion when intensities are represented by means of affine processes correlated with the asset's price. The numerical discussion at the end of this work shows that, at least in the case of the CIR intensity model, even the simple first-order approximation has a remarkable computational efficiency.
SSRN Electronic Journal, 2020
In this paper we present a simple, but new, approximation methodology for pricing a call option i... more In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black & Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching technique applied to a conditional Black & Scholes formula, is quite general and it applies to various models, whether affine or not. To check its accuracy and computational time, we implement it for the CIR interest rate model correlated with the underlying, using the Monte Carlo simulations as a benchmark. The method's performance turns out to be quite remarkable, even when compared with analogous results obtained by the affine approximation technique presented in [9] and by the expansion formula introduced in [11], as we show in the last section.
Annals of Operations Research, 2019
We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in pr... more We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.
SSRN Electronic Journal, 2019
In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment)... more In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment) for a vulnerable option, that is an option subject to some default event, concerning the solvability of the issuer. CVA is needed to evaluate correctly the contract and it is particularly important in presence of WWR (Wrong Way Risk), when a credit deterioration determines an increase of the claim's price. In particular, we are interested in evaluating the CVA in stochastic volatility models for the underlying's price (which often fit quite well the market's prices) when admitting correlation with the default event. By cunningly using Ito's calculus, we provide a general representation formula applicable to some popular models such as SABR, Hull & White and Heston, which explicitly shows the correction in CVA due to the processes correlation. Later, we specialize this formula and construct its approximation for the three selected models. Lastly, we run a numerical study to test the formula's accuracy, comparing our results with Monte Carlo simulations.
Seminar on Stochastic Analysis, Random Fields and Applications, 1999
A new class of infinite dimensional Laplacians is presented and its main properties are highlight... more A new class of infinite dimensional Laplacians is presented and its main properties are highlighted. We also discuss some specific example and refer to [11] for the general theory.
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
A Mathematical Introduction to String Theory
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
A Mathematical Introduction to String Theory
ABSTRACT Classical string theory is concerned with the propagation of classical one-dimensional c... more ABSTRACT Classical string theory is concerned with the propagation of classical one-dimensional curves, i.e. "strings", and has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras has been used for such quantization. In this book, the authors give an introduction to global analytic and probabilistic aspects of string theory, bringing together and making explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.
SSRN Electronic Journal, 2015
We introduce a natural generalization of the forward-starting options, first discussed by M. Rubi... more We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein ([28]). The main feature of the contract presented here is that the strikedetermination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options Random Time Forward Starting (RTFS). We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.
Advances in Analysis, Probability and Mathematical Physics, 1995
ABSTRACT We discuss non-trivial singular traces on the compact operators, extending some results ... more ABSTRACT We discuss non-trivial singular traces on the compact operators, extending some results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states using tools of non-standard analysis.
Review of Derivatives Research, 2009
Efficient valuation of exchange options with random volatilities while challenging at analytical ... more Efficient valuation of exchange options with random volatilities while challenging at analytical level, has strong practical implications: in this paper we present a new approach to the problem which allows for extensions of previous known results. We undertake a route based on a multi-asset generalization of a methodology developed in Antonelli and Scarlatti (Finan Stoch 13:269-303, 2009) to handle simple European one-asset derivatives with volatility paths described by Ito's diffusive equations. Our method seems to adapt rather smoothly to the evaluation of Exchange options involving correlations among all the financial quantities that specify the model and it is based on expanding and approximating the theoretical evaluation formula with respect to correlation parameters. It applies to a whole range of models and does not require any particular distributional property. In order to test the quality of our approximation numerical simulations are provided in the last part of the paper.
Mathematical Social Sciences, 2008
We consider a repeated game where at each stage players simultaneously choose one of two rooms. T... more We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.
Journal of Functional Analysis, 1996
The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also estab... more The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Some results on the allowed functional calculus for closed derivations on Hilbert algebras are obtained. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.
Quantum Probability and Applications II, 1985
ABSTRACT Without Abstract
European Journal of Operational Research, 2021
We consider the problem of computing the Value Adjustment of European contingent claims when defa... more We consider the problem of computing the Value Adjustment of European contingent claims when default of either party is considered, possibly including also funding and collateralization requirements. As shown in Brigo et al. ([12], [13]), this leads to a more articulate variety of Value Adjustments (XVA) that introduce some nonlinear features. When exploiting a reducedform approach for the default times, the adjusted price can be characterized as the solution to a possibly nonlinear Backward Stochastic Differential Equation (BSDE). The expectation representing the solution of the BSDE is usually quite hard to compute even in a Markovian setting, and one might resort either to the discretization of the Partial Differential Equation characterizing it or to Monte Carlo Simulations. Both choices are computationally very expensive and in this paper we suggest an approximation method based on an appropriate change of numeraire and on a Taylor's polynomial expansion when intensities are represented by means of affine processes correlated with the asset's price. The numerical discussion at the end of this work shows that, at least in the case of the CIR intensity model, even the simple first-order approximation has a remarkable computational efficiency.
SSRN Electronic Journal, 2020
In this paper we present a simple, but new, approximation methodology for pricing a call option i... more In this paper we present a simple, but new, approximation methodology for pricing a call option in a Black & Scholes market characterized by stochastic interest rates. The method, based on a straightforward Gaussian moment matching technique applied to a conditional Black & Scholes formula, is quite general and it applies to various models, whether affine or not. To check its accuracy and computational time, we implement it for the CIR interest rate model correlated with the underlying, using the Monte Carlo simulations as a benchmark. The method's performance turns out to be quite remarkable, even when compared with analogous results obtained by the affine approximation technique presented in [9] and by the expansion formula introduced in [11], as we show in the last section.
Annals of Operations Research, 2019
We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in pr... more We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.
SSRN Electronic Journal, 2019
In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment)... more In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment) for a vulnerable option, that is an option subject to some default event, concerning the solvability of the issuer. CVA is needed to evaluate correctly the contract and it is particularly important in presence of WWR (Wrong Way Risk), when a credit deterioration determines an increase of the claim's price. In particular, we are interested in evaluating the CVA in stochastic volatility models for the underlying's price (which often fit quite well the market's prices) when admitting correlation with the default event. By cunningly using Ito's calculus, we provide a general representation formula applicable to some popular models such as SABR, Hull & White and Heston, which explicitly shows the correction in CVA due to the processes correlation. Later, we specialize this formula and construct its approximation for the three selected models. Lastly, we run a numerical study to test the formula's accuracy, comparing our results with Monte Carlo simulations.
Seminar on Stochastic Analysis, Random Fields and Applications, 1999
A new class of infinite dimensional Laplacians is presented and its main properties are highlight... more A new class of infinite dimensional Laplacians is presented and its main properties are highlighted. We also discuss some specific example and refer to [11] for the general theory.
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
A Mathematical Introduction to String Theory
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
Variational Problems, Geometric and Probabilistic Methods
A Mathematical Introduction to String Theory
ABSTRACT Classical string theory is concerned with the propagation of classical one-dimensional c... more ABSTRACT Classical string theory is concerned with the propagation of classical one-dimensional curves, i.e. "strings", and has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras has been used for such quantization. In this book, the authors give an introduction to global analytic and probabilistic aspects of string theory, bringing together and making explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.
SSRN Electronic Journal, 2015
We introduce a natural generalization of the forward-starting options, first discussed by M. Rubi... more We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein ([28]). The main feature of the contract presented here is that the strikedetermination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options Random Time Forward Starting (RTFS). We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.
Advances in Analysis, Probability and Mathematical Physics, 1995
ABSTRACT We discuss non-trivial singular traces on the compact operators, extending some results ... more ABSTRACT We discuss non-trivial singular traces on the compact operators, extending some results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states using tools of non-standard analysis.
Review of Derivatives Research, 2009
Efficient valuation of exchange options with random volatilities while challenging at analytical ... more Efficient valuation of exchange options with random volatilities while challenging at analytical level, has strong practical implications: in this paper we present a new approach to the problem which allows for extensions of previous known results. We undertake a route based on a multi-asset generalization of a methodology developed in Antonelli and Scarlatti (Finan Stoch 13:269-303, 2009) to handle simple European one-asset derivatives with volatility paths described by Ito's diffusive equations. Our method seems to adapt rather smoothly to the evaluation of Exchange options involving correlations among all the financial quantities that specify the model and it is based on expanding and approximating the theoretical evaluation formula with respect to correlation parameters. It applies to a whole range of models and does not require any particular distributional property. In order to test the quality of our approximation numerical simulations are provided in the last part of the paper.
Mathematical Social Sciences, 2008
We consider a repeated game where at each stage players simultaneously choose one of two rooms. T... more We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.
Journal of Functional Analysis, 1996
The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also estab... more The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Some results on the allowed functional calculus for closed derivations on Hilbert algebras are obtained. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.