Convergence Of Discrete Time Option Pricing Models Under Stochastic Interest Rates
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Discrete-Time Valuation of American Options with Stochastic Interest Rates
Author | : Kaushik I. Amin |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : |
ISBN | : |
We develop an arbitrage-free discrete time model to price American-style claims for which domestic term structurerisk, foreign term structure risk and currency risk are important. This model combines a discrete version of the Heath, Jarrow, Morton (1992) term structure model with the binomial model of Cox, Ross, and Rubinstein (1979). It converges (weakly) to the continuous time models in Amin and Jarrow (1991, 1992). The general model is quot;path dependentquot; and can be implemented with arbitrary volatility functions to value claims with maturity up to five years. The model is illustrated with applications to long-dated American currency warrants and a cross-rate swap from the quanto class.
Weak Convergence of Financial Markets
Author | : Jean-Luc Prigent |
Publisher | : Springer Science & Business Media |
Total Pages | : 432 |
Release | : 2013-03-14 |
Genre | : Business & Economics |
ISBN | : 3540248315 |
A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
Martingale Methods in Financial Modelling
Author | : Marek Musiela |
Publisher | : Springer Science & Business Media |
Total Pages | : 521 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662221322 |
A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.
Discrete-Time Approximations and Limit Theorems
Author | : Yuliya Mishura |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 222 |
Release | : 2021-10-25 |
Genre | : Mathematics |
ISBN | : 3110652994 |
The De Gruyter Series in Probability and Stochastics is devoted to the publication of high-level monographs and specialized graduate texts in any branch of modern probability theory and stochastics, along with their numerous applications in other parts of mathematics, physics and informatics, in economics and finance, and in the life sciences. The aim of the series is to present recent research results in the form of authoritative and comprehensive works that will serve the probability and stochastics community as basis for further research. Editorial Board Itai Benjamini, Weizmann Institute of Science, Israel Jean Bertoin, Universität Zürich, Switzerland Michel Ledoux, Université de Toulouse, France René L. Schilling, Technische Universität Dresden, Germany
Risk-Neutral Valuation
Author | : Nicholas H. Bingham |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1447138562 |
This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.
Dynamic Asset Pricing Theory
Author | : Darrell Duffie |
Publisher | : Princeton University Press |
Total Pages | : 488 |
Release | : 2010-01-27 |
Genre | : Business & Economics |
ISBN | : 1400829208 |
This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.
Fixed Income Modelling
Author | : Claus Munk |
Publisher | : Oxford University Press |
Total Pages | : 573 |
Release | : 2011-06-30 |
Genre | : Business & Economics |
ISBN | : 0199575088 |
A large number of securities related to various interest rates are traded in financial markets. Traders and analysts in the financial industry apply models based on economics, mathematics and probability theory to compute reasonable prices and risk measures for these securities. This book offers a unified presentation of such models and securities.
Stochastic Dominance and Option Pricing in Discrete and Continuous Time
Author | : Ioan Mihai Oancea |
Publisher | : |
Total Pages | : 48 |
Release | : 2007 |
Genre | : |
ISBN | : |
This paper examines option pricing in a universe in which it is assumed that markets are incomplete. It derives multiperiod discrete time option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution, discrete or continuous. It then considers the limit behavior of these bounds for special categories of such distributions as trading becomes progressively more dense, tending to continuous time. It is shown that these bounds nest as special cases most, if not all, existing arbitrage- and equilibrium-based option pricing models. Thus, when the underlying asset follows a generalized diffusion both bounds converge to a single value. For jump-diffusion processes, stochastic volatility models, and GARCH processes the bounds remain distinct and define several new option pricing results containing as special cases the arbitrage-based results.