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Financial Pricing Models in Continuous Time and Kalman Filtering

  • Book
  • © 2001

Overview

Authors:
  1. B. Philipp Kellerhals

    1. Gesellschaft für Wertpapieranlagen mbH, Deutscher Investment-Trust, Frankfurt am Main, Germany

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Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 506)

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XIV
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  2. Overview of the Study

    1. Overview of the Study

      • B. Philipp Kellerhals
      Pages 1-3

  3. Modeling and Estimation Principles

    1. Front Matter

      Pages 5-5
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    2. Stochastic Environment

      • B. Philipp Kellerhals
      Pages 7-9

    3. State Space Notation

      • B. Philipp Kellerhals
      Pages 11-14

    4. Filtering Algorithms

      • B. Philipp Kellerhals
      Pages 15-27

    5. Parameter Estimation

      • B. Philipp Kellerhals
      Pages 29-33

  4. Pricing Equities

    1. Front Matter

      Pages 35-35
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    2. Introduction

      • B. Philipp Kellerhals
      Pages 37-41

    3. Valuation Model

      • B. Philipp Kellerhals
      Pages 43-53

    4. First Empirical Results

      • B. Philipp Kellerhals
      Pages 55-70

    5. Implications for Investment Strategies

      • B. Philipp Kellerhals
      Pages 71-81

    6. Summary and Conclusions

      • B. Philipp Kellerhals
      Pages 83-84

  5. Term Structure Modeling

    1. Front Matter

      Pages 85-85
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    2. Introduction

      • B. Philipp Kellerhals
      Pages 87-96

    3. Term Structure Model

      • B. Philipp Kellerhals
      Pages 97-103

    4. Initial Characteristic Results

      • B. Philipp Kellerhals
      Pages 105-127

    5. Risk Management and Derivatives Pricing

      • B. Philipp Kellerhals
      Pages 129-145

    6. Calibration to Standard Instruments

      • B. Philipp Kellerhals
      Pages 147-173

    7. Summary and Conclusions

      • B. Philipp Kellerhals
      Pages 175-176
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Keywords

About this book

Straight after its invention in the early sixties, the Kalman filter approach became part of the astronautical guidance system of the Apollo project and therefore received immediate acceptance in the field of electrical engineer­ ing. This sounds similar to the well known success story of the Black-Scholes model in finance, which has been implemented by the Chicago Board of Op­ tions Exchange (CBOE) within a few month after its publication in 1973. Recently, the Kalman filter approach has been discovered as a comfortable estimation tool in continuous time finance, bringing together seemingly un­ related methods from different fields. Dr. B. Philipp Kellerhals contributes to this topic in several respects. Specialized versions of the Kalman filter are developed and implemented for three different continuous time pricing models: A pricing model for closed-end funds, taking advantage from the fact, that the net asset value is observable, a term structure model, where the market price of risk itself is a stochastic variable, and a model for electricity forwards, where the volatility of the price process is stochastic. Beside the fact that these three models can be treated independently, the book as a whole gives the interested reader a comprehensive account of the requirements and capabilities of the Kalman filter applied to finance models. While the first model uses a linear version of the filter, the second model using LIBOR and swap market data requires an extended Kalman filter. Finally, the third model leads to a non-linear transition equation of the filter algorithm.

Authors and Affiliations

  • Gesellschaft für Wertpapieranlagen mbH, Deutscher Investment-Trust, Frankfurt am Main, Germany

    B. Philipp Kellerhals

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