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Recovery of Time-Dependent Parameters of a Black-Scholes-Type Equation: An Inverse Stieltjes Moment Approach

Marianito R. Rodrigo, Rogemar S. Mamon
2007 Journal of Applied Mathematics  
We show that the problem of recovering the time-dependent parameters of an equation of Black-Scholes type can be formulated as an inverse Stieltjes moment problem.  ...  An application to the problem of implied volatility calculation in the case when the model parameters are time varying is provided and results of numerical simulations are presented.  ...  Acknowledgment The first author wishes to acknowledge the support of the Asociaci ón Mexicana de Cultura, A.C.  ... 
doi:10.1155/2007/62098 fatcat:r4tivr2c7bbmzcr2s4fn3km7by

On Neural Differential Equations [article]

Patrick Kidger
2022 arXiv   pre-print
This doctoral thesis provides an in-depth survey of the field.  ...  The conjoining of dynamical systems and deep learning has become a topic of great interest.  ...  If the SDE is simple enough -for example the analytically tractable Black-Scholes model -then equation (4.2) can often be computed explicitly [BS73] .  ... 
arXiv:2202.02435v1 fatcat:vglknmvlgfeddoe2cxohubauxm

Review Paper. A survey of mathematical finance

D. Hobson
2004 Proceedings of the Royal Society A  
In this survey we begin with the simplest possible financial model, and then give an account of the Black-Scholes option pricing formula, in which the key ideas are the replication of option pay-offs and  ...  analysis and partial differential equations can bring to bear experiences and results from their own fields to problems of real world interest.  ...  This equation can be viewed as an example of a backward stochastic differential equation (BSDE) (see Mania et al . 2003) .  ... 
doi:10.1098/rspa.2004.1386 fatcat:jzqrznsukzck7droowts4flxum

Parametric Inference and Dynamic State Recovery From Option Panels

Torben G. Andersen, Nicola Fusari, Viktor Todorov
2015 Econometrica  
In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying risk premia of extreme events, i.e., jumps, as well as a more  ...  (cross-sectional) dimension, but with a fixed time span.  ...  The only issue is whether the inverse mapping from a given value of model prices, expressed in Black-Scholes implied volatilities, κ(k, τ, S t , θ), back into the parameter and state vector, θ and S t  ... 
doi:10.3982/ecta10719 fatcat:2ysfgktisvh4rhl332uvgh35du

A Comparative Analysis of 30 Bonus-Malus Systems

Jean Lemaire, Hongmin Zi
1994 ASTIN Bulletin: The Journal of the International Actuarial Association  
Principal components analysis is used to define an "Index of Toughness" for all systems.  ...  AbstractThe automobile third party insurance merit-rating systems of 22 countries are simulated and compared, using as main tools the stationary average premium level, the variability of the policyholders  ...  ACKNOWLEDGMENTS I would like to thank Professor RAGNAR NORBERG and Professor HANS BOHLMANN for their helpful comments on an earlier version of this paper.  ... 
doi:10.2143/ast.24.2.2005071 fatcat:ctuwdoi63vetpkaijfy6btkkeu

Credit Risk Modeling [chapter]

Tomasz R. Bielecki
2015 Encyclopedia of Systems and Control  
Finance as a discipline has been growing rapidly. The numbers of researchers in academy and industry, of students, of methods and models have all proliferated in the past decade or so.  ...  Titles in this series will be scholarly and professional books, intended to be read by a mixed audience of economists, mathematicians, operations research scientists, financial engineers, and other investment  ...  n V ) from S t 0 , . . . , S t N using the inverse of the Black-Scholes formula viewed as a function of the value of the underlying asset. (2) Estimate σ n+1 V by thinking of V t 0 (σ n V ), . . . , V  ... 
doi:10.1007/978-1-4471-5058-9_43 fatcat:p26hb5ljunegpc46ysmroqzd7q

Extreme Events and the Copula Pricing of Commercial Mortgage-Backed Securities

Zhan Yong Liu, Gang-Zhi Fan, Kian Guan Lim
2008 Journal of real estate finance and economics  
It is also important to sufficiently consider complex default dependence structure and the likelihood of extreme events occurring in pricing various CMBS bonds.  ...  Default on underlying commercial mortgages within a pool is a crucial risk associated with CMBS transactions.  ...  developed by Black and Scholes (1973) .  ... 
doi:10.1007/s11146-008-9156-9 fatcat:mat5vemsovey3izwdtx4gpkab4

PAPERS FROM ACTUARIAL JOURNALS WORLDWIDE

2015 Annals of Actuarial Science  
Members of the Institute and Faculty of Actuaries can also access these journals directly by registering for the eLibrary. A password is available on request.  ...  Single copies of the papers listed here can be obtained, subject to copyright law, by contacting the libraries. There may be a charge for this service.  ...  In a classical Black-Scholes market, we establish a connection between two seemingly different approaches to continuous-time utility optimization.  ... 
doi:10.1017/s1748499515000044 fatcat:tichq2o465bchfbulibdedq7du

Fractional Models to Credit Risk Pricing

Arturo Leccadito, Giovanni Urga
2010 Social Science Research Network  
Long Range Dependence in Finance Although introduction of the Geometric Brownian motion-based Black-Scholes formulation of vanilla options by Black, Scholes, and Merton marked the advent of mathematical  ...  The price of the bond can be derived using the corresponding Black-Scholes formulae.  ... 
doi:10.2139/ssrn.1571583 fatcat:nnrxwm53bjdohmxoh2hmq7jqyi

A multiple-curve Lévy forward rate model in a two-price economy

Ernst Eberlein, Christoph Gerhart
2017 Quantitative finance (Print)  
A multiple-curve Heath-Jarrow-Morton (HJM) forward rate model driven by time-inhomogeneous Lévy processes (a multiple-curve Lévy term structure model) is presented.  ...  In this thesis, we combine and merge the multiple-curve approach and the two-price theory based on acceptability indices in a Lévy interest rate model.  ...  He introduced me to the topic of Lévy term structure models and aroused my interest for the multiple-curve approach and the two-price theory.  ... 
doi:10.1080/14697688.2017.1384558 fatcat:qr27m2yu3zexpcuuqvc4d7r4ja

Hedging of Defaultable Claims [chapter]

Tomasz R. Bielecki, Monique Jeanblanc, Marek Rutkowski
2004 Lecture notes in mathematics  
After time τ , the market reduces to a standard Black-Scholes model, and thus the solution to the corresponding optimization problem is well known.  ...  Default-Free Market Consider an economy in continuous time, with the time parameter t ∈ R + .  ...  Recall that the process Z depends on the choice of a contingent claim X, as well as on the model's parameters , σ and ν.  ... 
doi:10.1007/978-3-540-44468-8_1 fatcat:jxw7kjxtf5h7hgkhzbo5ecck7i

Stochastic Correlation for Asset Pricing and Credit Derivative Products

Ashish Kumar, László Márkus
2020
First of all, I would like to express my sincere gratitude to my supervisor, Prof. László Márkus. His support and guidance were vital throughout my PhD studies.  ...  This model is an extension of the Black-Scholes model in order to manage the two interest rates, one domestic and one foreign.  ...  Having this in mind, the dynamics of the mean-reverting fOU process is given by a Langevin-type stochastic differential equation (SDE) driven by a fBm W H = {W H (t),t ≥ 0} of Hurst parameter H ∈ (0, 1  ... 
doi:10.15476/elte.2020.179 fatcat:btxssdsfengplafrzuko3glxde

Stochastic models for valuation and risk management of credit-sensitive hybrid derivatives

Nicola Pede, Damiano Brigo
2019
In particular, we applied results from Analytically Tractable First–Passage (AT1P) model — a model belonging to the family of structural approaches — to the pricing of Contingent Conversion bonds and a  ...  With respect to the former problem, we proposed a method to incorporate regulatory capital information into an AT1P–based model.  ...  (B.25) and the evaluation of an European call option under the classic Black-Scholes framework. We used a set of parameters calibrated to the relevant market prices and such that B = 0.  ... 
doi:10.25560/65699 fatcat:olfddb5ew5bvliauoiatfgmqe4

Credit portfolio modelling with elliptically contoured distributions - approximation, pricing, dynamisation [article]

Clemens Prestele, Universität Ulm, Universität Ulm
2016
We will provide a diligent study on the impact of our modelling framework to the pricing of Collateralized Debt Obligations and apply this to the valuation of iTraxx tranches.  ...  The aim of this thesis is to introduce a new set of factor models for the pricing of portfolio credit derivatives, which match the observations on the derivatives markets better than the standard Gaussian  ...  Ss the payment to the equity holder is exactly the payoff to a long position in a European call, one can employ the Black-Scholes options pricing theory.  ... 
doi:10.18725/oparu-1071 fatcat:w7vjyu4bevdrphjufzw54dlmqu

Information-Based Jumps, Asymmetry and Dependence in Financial Modelling

Levent Ali Menguturk, Mark Davis, Ozyegin Universitesi
2013
We focus on a special type of GLPs that we call Archimedean Survival Processes (ASPs). The terminal value of an ASP has an [Symbol appears here.  ...  The terminal values of GLPs have generalised multivariate Liouville distributions, and GLPs can model a wide spectrum of information-driven dependence structures between assets.  ...  To construct a GLP, we start with a master LRB {L t } 0≤t≤un where L un has marginal law ν for u n ∈ N + and n ≥ 2. We assume that ν has no continuous singular part (see Sato, 1999) .  ... 
doi:10.25560/10953 fatcat:zmgymsp7gzba5ikcrnrdqmungi