Pricing Variance, Gamma and Corridor Swaps Using Multinomial Trees PDF Download
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Author: Honglei Zhao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This article introduces a new methodology to approximate the prices of variance, gamma and corridor swaps in a stochastic volatility framework applicable to any given tree structure. The efficiency of this tree method is based on the decomposing the payoff structure into nested conditional expectations which may be calculated using a single pass through the tree. The total number of calculations is commensurable with the number of tree nodes, making it substantially faster than Monte Carlo simulations. We exemplify the methodology using two different tree structures that approximate several types of stochastic volatility models. Furthermore, this methodology is general enough to be applied to any given tree structure. Extensive numerical tests show that the methodology introduced is fast, efficient and accurate. The method was applied to volatility instruments quoted on the CBOE.
Author: Honglei Zhao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This article introduces a new methodology to approximate the prices of variance, gamma and corridor swaps in a stochastic volatility framework applicable to any given tree structure. The efficiency of this tree method is based on the decomposing the payoff structure into nested conditional expectations which may be calculated using a single pass through the tree. The total number of calculations is commensurable with the number of tree nodes, making it substantially faster than Monte Carlo simulations. We exemplify the methodology using two different tree structures that approximate several types of stochastic volatility models. Furthermore, this methodology is general enough to be applied to any given tree structure. Extensive numerical tests show that the methodology introduced is fast, efficient and accurate. The method was applied to volatility instruments quoted on the CBOE.
Author: Honglei Zhao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In a recent study, we present a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model. This provides an efficient way of calculating the fair value of the strike for variance swaps. In this article, we expand the methodology to price nonlinear derivatives written on realized variance. Particularly we introduce a new option contract a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework, we also show how to value forward-start variance swaps, VIX futures and VIX options. Numerical tests show that the methodology introduced is efficient and accurate.
Author: Maria C. Mariani
Publisher: John Wiley & Sons
ISBN: 1118629965
Category : Business & Economics
Languages : en
Pages : 496
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Book Description
Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudo-algorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field. The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical Black-Scholes-Merton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are also discussed. Next, solutions to Partial Differential Equations (PDE), wavelets and Fourier transforms are presented. Several methodologies for pricing options namely, tree methods, finite difference method and Monte Carlo simulation methods are also discussed. We conclude this part with a discussion on stochastic differential equations (SDE’s). In the third part of this book, several new and advanced models from current literature such as general Lvy processes, nonlinear PDE's for stochastic volatility models in a transaction fee market, PDE's in a jump-diffusion with stochastic volatility models and factor and copulas models are discussed. In part four of the book, we conclude with a solid presentation of the typical topics in fixed income securities and derivatives. We discuss models for pricing bonds market, marketable securities, credit default swaps (CDS) and securitizations. Classroom-tested over a three-year period with the input of students and experienced practitioners Emphasizes the volatility of financial analyses and interpretations Weaves theory with application throughout the book Utilizes R and MATLAB software programs Presents pseudo-algorithms for readers who do not have access to any particular programming system Supplemented with extensive author-maintained web site that includes helpful teaching hints, data sets, software programs, and additional content Quantitative Finance is an ideal textbook for upper-undergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programs. It will also appeal to practitioners in the same fields.
Author: Christoph Burgard
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
We consider weighted variance contracts in which the realised variance is subjected to a spot dependent weighting function, a notable example of which is the corridor variance swap. Such payouts admit a quasi-static hedge involving European style options with expiries at all dates up to the maturity of the contract. This note proposes a method for over-hedging weighted variance using only a finite number of maturities. Moreover this approach is shown to have good convergence properties and allows one to treat dividends in a natural way. As an application the method is used to relate corridor variance with the variance implicit in the definition of the HSI volatility index.
Author: Jakub Drahokoupil
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Larry C. Holland
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Binomial pricing trees are often used to value options. However, binomial models can easily become very large and cumbersome. Multinomial option pricing trees can be constructed that produce results equivalent to binomial option pricing trees. The advantage of creating multinomial trees is that they are smaller and easier to construct than binomial trees. In this paper, trinomial and quintinomial option pricing trees are developed and compared to simple binomial trees, illustrating the similarities and differences. These multinomial pricing trees are much smaller and more compact because they require fewer calculations to produce results equivalent to binomial trees. Methods for valuing put and call options, European and American options, and accounting for dividends are also illustrated. Multinomial option pricing trees can be helpful to students in understanding how the models work and useful to practitioners in constructing simple option pricing models.
Author: Filippo Fiorani (t.d.-)
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Jens Ihlow
Publisher:
ISBN:
Category :
Languages : en
Pages : 104
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Book Description
Author: Andreas Horni
Publisher: Ubiquity Press
ISBN: 190918876X
Category : Technology & Engineering
Languages : en
Pages : 620
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Book Description
The MATSim (Multi-Agent Transport Simulation) software project was started around 2006 with the goal of generating traffic and congestion patterns by following individual synthetic travelers through their daily or weekly activity programme. It has since then evolved from a collection of stand-alone C++ programs to an integrated Java-based framework which is publicly hosted, open-source available, automatically regression tested. It is currently used by about 40 groups throughout the world. This book takes stock of the current status. The first part of the book gives an introduction to the most important concepts, with the intention of enabling a potential user to set up and run basic simulations. The second part of the book describes how the basic functionality can be extended, for example by adding schedule-based public transit, electric or autonomous cars, paratransit, or within-day replanning. For each extension, the text provides pointers to the additional documentation and to the code base. It is also discussed how people with appropriate Java programming skills can write their own extensions, and plug them into the MATSim core. The project has started from the basic idea that traffic is a consequence of human behavior, and thus humans and their behavior should be the starting point of all modelling, and with the intuition that when simulations with 100 million particles are possible in computational physics, then behavior-oriented simulations with 10 million travelers should be possible in travel behavior research. The initial implementations thus combined concepts from computational physics and complex adaptive systems with concepts from travel behavior research. The third part of the book looks at theoretical concepts that are able to describe important aspects of the simulation system; for example, under certain conditions the code becomes a Monte Carlo engine sampling from a discrete choice model. Another important aspect is the interpretation of the MATSim score as utility in the microeconomic sense, opening up a connection to benefit cost analysis. Finally, the book collects use cases as they have been undertaken with MATSim. All current users of MATSim were invited to submit their work, and many followed with sometimes crisp and short and sometimes longer contributions, always with pointers to additional references. We hope that the book will become an invitation to explore, to build and to extend agent-based modeling of travel behavior from the stable and well tested core of MATSim documented here.
Author: Mykel J. Kochenderfer
Publisher: MIT Press
ISBN: 0262331713
Category : Computers
Languages : en
Pages : 350
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Book Description
An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.
