2 edition of simple binomial no-arbitrage model of the term structure found in the catalog.
simple binomial no-arbitrage model of the term structure
Thomas J. O"Brien
by New York University Salomon Center, Leonard N. Sterm School of Business in New York, N.Y
Written in English
Includes bibliographical references (p. 58-61).
|Statement||by Thomas J. O"Brien.|
|Series||Monograph series in finance and economics -- monograph 1991-4|
|LC Classifications||HG4637 .O24 1991|
|The Physical Object|
|Pagination||65 p. :|
|Number of Pages||65|
The field of financial mathematics has developed tremendously over the past thirty years, and the underlying models that have taken shape in interest rate markets and bond markets, being much richer in structure than equity-derivative models, are particularly fascinating and complex. This book introduces the tools required for the arbitrage-free modelling of the dynamics of these markets. Lecture 6: Option Pricing Using a One-step Binomial Tree Friday, Septem because of no-arbitrage, we must have • The natural way to extend is to introduce the multiple step binomial model: S= S= S=90 S= S=95 S= A B C Friday, Septem File Size: 1MB.
forward PD model under the Merton model framework. In section 3, we show how a PD term structure can be derived based on forward PDs and how loss can be evaluated over a multi-period scenario using the PD term structure. In section 4, we determine the log-likelihood function for observing the term default frequency. the terminal time.) Existence of a no arbitrage price depends on the existence of a so-called risk neutral probability and uniqueness depends on there being a replicating strategy for the contingent claim. Binomial or CRR Model The CRR model is a simple discrete time model for a nancial market. There are nitely many trading timest=0;1;;T File Size: KB.
In a binomial option model, if we take the uptick as 6%, downtick as 5% (assume equally probable), and RFR of 6% (continuous compounding), then we have a violation of $0 model at all? Is no-arbitrage one of the required assumptions? Binomial Option Pricing 1 Arbitrage Binomial trees are a no arbitrage model. S0 = $20 Call option strike = $21 Rf = 12% Stock price in 3 months will be either $22 or $
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Next present the five most important no-arbitrage term-structure models: • Ho–Lee Model. This model was the first no-arbitrage term-structure model.
It assumes constant and identical volatility for all spot and forward rates and does not incorporate mean reversion. • Hull–White Model. This model extends the Ho–Lee model to allow for mean reversion. A simple binomial no-arbitrage model of the term structure: with applications to the valuation of interest-sensitive options and interest-rate swaps Author: Thomas J O'Brien.
A simple binomial no-arbitrage model of the term structure with applications to the valuation of interest-sensitive options and interest-rate swaps Author: Thomas J O'Brien ; Salomon Brothers Center for the Study of Financial Institutions.
Previously, we analyzed the Vasicek () model of the default-free term structure of interest rates. That model assumed speciﬁc parametric forms for the dynamics of the short-term interest rate and for the market price of interest rate risk.
Based on these structural assumptions and the assumption of no arbitrage opportunities, it derived the prices of bonds of any particular maturities. Arbitrage-Free Binomial Models of the Term Structure Earlier, in our discussion of martingale pricing theory, we showed that the absence of arbi-trage implied that the date t price of any asset, f(t),satisﬁes: f(t)=B(t)E˜t f(T) 1 B(T) ¸ = E˜ t h e− R T t rs dsf(T) i (1)File Size: KB.
An Arbitrage-Free Two-Factor Model of the Term Structure of Interest Rates: A Multivariate Binomial Approach NYU Working Paper No. FIN Number of pages: 40 Posted: 11 Nov Cited by: 1. Ingersoll-Ross ] model may not match the current term structure.
The Black-Derman-Toy (BDT) and Black-Karasinksi models discussed in this article are important examples of models in which the current term structure can always be replicated.
BINOMIAL INTEREST RATE MODELS Before introducing these models, we give a short intro-File Size: KB. Binomial models for the term structure of interest 1 The conventional binomial model for shares and currency: and 7 and which plays a dominant role for the construction of discrete time term structure models.
This model works well for an arbitrary number of periods. It File Size: KB. No-arbitrage constraints2 instead force us to substitute the risk-neutral probability ˇfor the true probability p.
Accordingly, we may view the binomial model as the discounted expected payo of the option in a risk-neutral world: C= 1 rn n E ˇ h max(0;ukdn kS K) i = 1 rn n E ˇ[P]: Note that the binomial model is contingent upon model File Size: KB.
Binomial Model Hull, Chapter 11 + Sections and The very simple binomial model already contains many of the features of more general models. Risk-neutral probabilities (risk-neutral probability measure) exist if and only if there are no arbitrage opportunities in the model (this statement is known as The First Fundamental Theorem File Size: KB.
A New Simple Proof of the No-arbitrage Theorem for Multi-period Binomial Model. Liang Hong, ASA, Ph.D. Assistant Professor of Mathematics and Actuarial science, Department of Mathematics, Bradley University, West Bradley Avenue, Peoria, ILUSA. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We build a no-arbitrage model of the term structure, using two stochastic factors on each date, the short-term interest rate and the premium of the forward rate over the short-term interest rate.
The model can be regarded as an extension to two factors of the lognormal interest rate model of Black-Karasinski. A afﬁne term structure models An afﬁne term structure model hypothesizes that interest rates, at any point in time, are a time-invariant linear function of a small set of common factors.
This class of models has proven to be a remarkably ﬂexible structure for examining the dynamics of default-risk free bonds, and as a result afﬁneFile Size: 98KB.
The Discrete Binomial Model for Option Pricing Rebecca Stockbridge Program in Applied Mathematics University of Arizona Abstract This paper introduces the notion of option pricing in the context of ﬁnancial markets. The discrete time, one-period binomial model is explored and generalized to the multi-period bi-nomial Size: KB.
A binomial option pricing model is an options valuation method that uses an iterative procedure and allows for the node specification in a set : Marshall Hargrave.
Jeff Sauro, James R. Lewis, in Quantifying the User Experience (Second Edition), Criticisms of the binomial model for problem discovery. In the early s, there were a number of published criticisms of the use of the binomial model for problem discovery.
For example, Woolrych and Cockton () pointed out that a simple point estimate of p might not be sufficient for estimating the.
Exploring Arbitrage Opportunities in the Binomial Tree Ophir Gottlieb 10/11/ 1 Set Up We use the same set up as described in the previous article in which we derived the expressions for the risk neutral probabilities and delta. The single step setup is repeated below for convenience.
We let S t be the stock price at time t. In this simple. Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance.
model the prices of the interest rate securities as functions of one or a few state variables, say, spot interest rate, long-term interest rate, spot forward rate, etc.
In the so called no arbitrage or term structure interest rate models, the consistencies with the observed initial term structures of interest rates. Binomial Term Structure models Pricing bond options with the Black Scholes model, or its binomial approximation, as done in chap does not always get it example, it ignores the fact that at the maturity of the bond, the bond volatility is zero.
The mathematical chapters begin with the simple binomial model that introduces many core ideas. But the main chapters work their way systematically through all of the main developments in continuous-time interest rate modelling.
The book describes fully the broad range of approaches to interest rate modelling: short-rate models, no-arbitrage.We derive a no-arbitrage model of the term structure in which any two futures rates act as factors. The term structure shifts and tilts as the factor rates vary.Author of A simple binomial no-arbitrage model of the term structure, An Advanced Catechism Of Catholic Faith And Practice, International financial economics, A compendium of the history of Ireland by way of question and answer designed principally for the use of schools, West Nile, Corporate measurement of economic exposure to foreign exchange risk, Applied International Finance, Applied .