Products related to Calculus:
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Malliavin Calculus in Finance : Theory and Practice
Malliavin Calculus in Finance: Theory and Practice, Second Edition introduces the study of stochastic volatility (SV) models via Malliavin Calculus. Originally motivated by the study of the existence of smooth densities of certain random variables, Malliavin calculus has had a profound impact on stochastic analysis.In particular, it has been found to be an effective tool in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. This book aims to bridge the gap between theory and practice and demonstrate the practical value of Malliavin calculus.It offers readers the chance to discover an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces.It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. FeaturesIntermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative financeIncludes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scriptsCovers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text.The library has been implemented so that the users can re-use the numerical code for building their examples.The repository can be accessed here: https://bit.ly/2KNex2Y. New to the Second EditionIncludes a new chapter to study implied volatility within the Bachelier framework. Chapters 7 and 8 have been thoroughly updated to introduce a more detailed discussion on the relationship between implied and local volatilities, according to the new results in the literature.
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Elementary Stochastic Calculus, With Finance In View
Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance.However, stochastic calculus is based on a deep mathematical theory.This book is suitable for the reader without a deep mathematical background.It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory.Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived.The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.
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Malliavin Calculus in Finance : Theory and Practice
Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems.In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. The objective of this book is to offer a bridge between theory and practice.It shows that Malliavin calculus is an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces.It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. Features Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text.The library has been implemented so that the users can re-use the numerical code for building their examples.The repository can be accessed here: https://bit.ly/2KNex2Y.
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Introduction to Stochastic Calculus Applied to Finance
Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods.Maintaining the lucid style of its popular predecessor, Introduction to Stochastic Calculus Applied to Finance, Second Edition incorporates some of these new techniques and concepts to provide an accessible, up-to-date initiation to the field.New to the Second EditionComplements on discrete models, including Rogers' approach to the fundamental theorem of asset pricing and super-replication in incomplete markets Discussions on local volatility, Dupire's formula, the change of numéraire techniques, forward measures, and the forward Libor model A new chapter on credit risk modeling An extension of the chapter on simulation with numerical experiments that illustrate variance reduction techniques and hedging strategies Additional exercises and problemsProviding all of the necessary stochastic calculus theory, the authors cover many key finance topics, including martingales, arbitrage, option pricing, American and European options, the Black-Scholes model, optimal hedging, and the computer simulation of financial models.They succeed in producing a solid introduction to stochastic approaches used in the financial world.
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What is the difference between calculus and advanced calculus?
Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities. It includes topics such as limits, derivatives, and integrals. Advanced calculus, on the other hand, delves deeper into these concepts and explores more advanced topics such as multivariable calculus, vector calculus, and differential equations. Advanced calculus typically requires a stronger mathematical background and is more theoretical and abstract compared to basic calculus.
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Struggling with calculus?
If you are struggling with calculus, don't worry, you are not alone. Many students find calculus to be a challenging subject due to its complex concepts and problem-solving techniques. It's important to seek help from your teacher, classmates, or a tutor to clarify any doubts and practice regularly to improve your understanding and skills in calculus. Remember, with dedication and perseverance, you can overcome the challenges and succeed in mastering calculus.
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What is calculus?
Calculus is a branch of mathematics that deals with the study of rates of change and accumulation. It is divided into two main branches: differential calculus, which focuses on the concept of the derivative and rates of change, and integral calculus, which deals with the concept of the integral and accumulation of quantities. Calculus is widely used in various fields such as physics, engineering, economics, and computer science to solve problems involving continuous change and motion.
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Is calculus difficult?
Calculus can be difficult for some people, as it involves complex concepts and requires a strong understanding of algebra and trigonometry. However, with dedication and practice, many students are able to grasp the concepts and excel in calculus. It is important to seek help from teachers, tutors, or online resources if you are struggling with calculus, as it is a foundational subject for many fields of study, including engineering, physics, and economics.
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Stochastic Calculus for Finance II : Continuous-Time Models
Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance.The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability.The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided.The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties.Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time. Master's level studentsand researchers in mathematical finance and financial engineering will find this book useful.
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Stochastic Calculus for Finance II : Continuous-Time Models
Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance.The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability.The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided.The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties.Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time. Master's level studentsand researchers in mathematical finance and financial engineering will find this book useful.
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Pre-Calculus, Calculus, and Beyond
This is the last of three volumes that, together, give an exposition of the mathematics of grades 9–12 that is simultaneously mathematically correct and grade-level appropriate.The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K–12 as a totally transparent subject. This volume distinguishes itself from others of the same genre in getting the mathematics right.In trigonometry, this volume makes explicit the fact that the trigonometric functions cannot even be defined without the theory of similar triangles.It also provides details for extending the domain of definition of sine and cosine to all real numbers.It explains as well why radians should be used for angle measurements and gives a proof of the conversion formulas between degrees and radians. In calculus, this volume pares the technicalities concerning limits down to the essential minimum to make the proofs of basic facts about differentiation and integration both correct and accessible to school teachers and educators; the exposition may also benefit beginning math majors who are learning to write proofs.An added bonus is a correct proof that one can get a repeating decimal equal to a given fraction by the “long division” of the numerator by the denominator.This proof attends to all three things all at once: what an infinite decimal is, why it is equal to the fraction, and how long division enters the picture. This book should be useful for current and future teachers of K–12 mathematics, as well as for some high school students and for education professionals.
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Calculus
Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis.His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote.Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort.Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.
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Why does calculus work?
Calculus works because it provides a precise and systematic way to analyze and understand change. By using concepts such as limits, derivatives, and integrals, calculus allows us to model and solve real-world problems involving rates of change, accumulation, and optimization. Its rigorous mathematical framework enables us to make accurate predictions and calculations in various fields such as physics, engineering, economics, and biology.
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What is vector calculus?
Vector calculus is a branch of mathematics that deals with vector fields and their derivatives. It involves studying functions that have both a magnitude and a direction, such as velocity and force. Vector calculus is used in various fields such as physics, engineering, and computer science to analyze and solve problems involving quantities that have both magnitude and direction. It includes operations like gradient, divergence, curl, and line integrals, which help in understanding the behavior of vector fields in three-dimensional space.
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What is integral calculus?
Integral calculus is a branch of calculus that deals with the concept of integration, which is essentially the reverse process of differentiation. It involves finding the integral of a function, which represents the area under the curve of the function. This area can be used to calculate quantities such as displacement, velocity, and acceleration. Integral calculus is widely used in various fields such as physics, engineering, economics, and statistics to solve problems involving continuous quantities.
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What is differential calculus?
Differential calculus is a branch of mathematics that deals with the study of rates at which quantities change. It involves the concept of derivatives, which represent the rate of change of a function at a given point. Differential calculus is used to solve problems involving motion, optimization, and many other real-world applications where understanding how quantities change over time is important. It is a fundamental tool in mathematics and is essential in fields such as physics, engineering, economics, and biology.
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