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The Swap Market Model with Local Stochastic Volatility
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Ränteswap marknadsmodellen med lokal stokastisk volatilitet (Swedish)
Abstract [en]

Modeling volatility is an intricate part of all financial models and the pricing of derivative contracts. And while local volatility has gained popularity in equity and FX models, it remained neglected in interest rates models. In this thesis, using spot starting swaps, the goal is to build a swap market model with non-parametric local volatility functions and stochastic volatility scaling factors. The local stochastic volatility formula is calibrated through a particle algorithm to match the market’s swaption volatility smile. Numerical experiments are conducted for different currencies to compute the local stochastic volatility at different expiry dates, swap tenors and strike values. The results of the simulation show the high quality calibration of the algorithm and the efficiency of local stochastic volatility in interest rate smile building.

Abstract [sv]

Att modellera volatilitet är en invecklad del av alla finansiella modeller och prissättning av derivatkontrakt. Medan lokala volatilitet har fått stor popularitet på aktie- och FX-modeller, har de förblivit försummade i räntemodeller. I detta examensarbete är målet att bygga en ränteswapmarknads-modell med en icke-parametrisk lokal volatilitetsfunktion och en stokastisk volatilitets skalningsfaktor. Den lokala stokastiska volatiliteten kalibreras genom en partikelalgoritm för att matcha marknadens swaptions- volatilitetsleenden. För olika valutor utförs numeriska experiment för att beräkna den lokal stokastiska volatilitet för olika utgångsdatum, swap-tenorer och lösenräntor. Resultaten av simuleringen visar att kalibreringen med den presenterade algoritmen är av hög kvalitet och effektiviteten i användandet av lokal stokastisk volatilitet vid återskapning av ränteleende.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:048
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249561OAI: oai:DiVA.org:kth-249561DiVA, id: diva2:1307407
External cooperation
Kidbrooke Advisory
Subject / course
Mathematical Statistics
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Examiners
Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-04-26Bibliographically approved

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CiteExportLink to record
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