The Market Model of Interest Rate Dynamics
TLDR
In this paper, a class of term structure models with volatility of lognormal type is analyzed in the general HJM framework, and a two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.Abstract:
A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.read more
Citations
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Arbitrage Theory in Continuous Time
TL;DR: In this article, the Martingale Approach to Arbitrage theory is used to model the Binomial Model and the Stochastic Optimal Control (SOC) model for short-term interest rates.
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Alternative models for stock price dynamics
TL;DR: In this article, the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions is evaluated.
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LIBOR and swap market models and measures
TL;DR: Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitrage-free model with such volatility specification.
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The Term Structure of Interest Rates
TL;DR: This article reviewed the term structure of interest rates literature relating to the arbitrage-free pricing and hedging of interest rate derivatives and emphasized term structure theory, including the HJM model, forward and futures contracts, the expectations hypothesis, and pricing of caps/floors.
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Closed Form Solutions for Term Structure Derivatives with Log‐Normal Interest Rates
TL;DR: In this paper, a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds was derived.
References
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Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
Posted Content
Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation
TL;DR: In this article, a unifying theory for valuing contingent claims under a stochastic term structure of interest rates is presented, based on the equivalent martingale measure technique.
Journal ArticleDOI
Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation'
TL;DR: In this article, the authors present a unifying theory for valuing contingent claims under a stochastic term structure of interest rates, based on the equivalent martingale measure technique.
Journal ArticleDOI
Closed Form Solutions for Term Structure Derivatives with Log‐Normal Interest Rates
TL;DR: In this paper, a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds was derived.