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The Calibration of the Hull-White Model and Its Application for the Interest Rate Derivatives Pricing

Student: Klimachev Aleksej

Supervisor: Alexey S. Shvedov

Faculty: Faculty of Economic Sciences

Educational Programme: Bachelor

Year of Graduation: 2014

<p>In this paper the calibration of the Hull &ndash; White interest rate model is studied. A common application of the Hull &ndash; White model is the option pricing. With the help of calibration one can receive estimates of the volatility and the parameter of mean reversion. The purpose of this paper is to study different approaches to the calibration of the Hull-White model and the possibilities of the application of this model for the interest rate derivatives pricing and hedging. The main problem studied in this paper is to perform calculations connected with the interest rate derivatives pricing with the help of the Hull &ndash; White model. In the chapter &ldquo;The Hull &ndash; White model&rdquo; there is a description of the Hull &ndash; White model and a technique of the interest rate instruments pricing. In the chapter &ldquo;The calibration of the Hull &ndash; White model&rdquo; there is a literature review on the topic of the calibration of the Hull &ndash; White model. The chapter &ldquo;The calculations by the Monte &ndash; Carlo method&rdquo; is an numerical example based on the simulated data that demonstrates one of the ways of the calibration of the Hull &ndash; White model.</p><p>The paper is structured in the following way. In the chapter &ldquo;Some types of the financial instruments&rdquo; the definitions of financial instruments are given. In the chapter &ldquo;An example of delta-hedging European call/put bond options&rdquo; the application of the delta-hedging strategy for constructing a portfolio with a guaranteed profit is shown.</p><p>The calculations are performed on the simulated data. The programs written on the programming languages Python and R are used for the calculations. There are the results of the calculations performed with the help of the Hull-White model and the calculations that demonstrate the calibration of the Hull &ndash; White model. The results indicate that the application of the Hull &ndash; White model with the calibration procedure can be performed on the market data.</p>

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