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Calibrating the Hull-White model using Adjoint Algorithmic Differentiation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Kalibrering av Hull-White modellen genom adjungerad algoritmisk differentiering (Swedish)
Abstract [en]

This thesis includes a brief introduction to Adjoint Algorithmic Differentiation (AAD), accompanied by numerical examples, step-by-step explanations and runtime comparisons to a finite difference method. In order to show the applicability of AAD in a stochastic setting, it is also applied in the calculation of the arbitrage free price and partial derivatives of a European call option, where the underlying stock has Geometric Brownian motion dynamics.

Finally the Hull-White model is calibrated using a set of zero coupon bonds, and a set of swaptions. Using AAD, the partial derivatives of the model are found and used in a Newton-Raphson method in order to find the market's implied volatility. The end result is a Monte Carlo simulated short rate curve and its derivatives with respect to the calibration parameters, i.e. the zero coupon bond and swaption prices.

Abstract [sv]

Denna uppsats innehåller en introduktion till Adjungerad Algoritmisk Differentiering (AAD), tillsammans med numeriska exempel, steg-för-steg beskrivningar samt körtidsjämförelser med en finit differensmetod. För att illustrera applicerbarheten av AAD i ett stokastiskt ramverk, tillämpas metoden i beräkningen av det arbitragefria priset och de partiella derivatorna av en europeisk köp-option, där den underliggande aktien har geometrisk Brownsk dynamik.

Slutligen kalibreras Hull-White-modellen genom ett antal nollkupongsobligationer och swap-optioner. Via AAD beräknas de partiella derivatorna för modellen som sedan används i Newton-Raphsons metod för att finna markandens implicita volatilitet. Slutresultatet är en Monte Carlo-simulerad räntekurva och dess derivator med avseende på kalibreringsparametrarna, dvs. nollkupongs- och swap-optionspriserna.

Place, publisher, year, edition, pages
2017.
Series
TRITA-MAT-E ; 2017:57
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-214031OAI: oai:DiVA.org:kth-214031DiVA, id: diva2:1147858
Subject / course
Financial Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2017-10-09 Created: 2017-10-09 Last updated: 2017-10-09Bibliographically approved

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