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Efficient Monte Carlo Simulation for Counterparty Credit Risk Modeling
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
Effektiv Monte Carlo-simulering för modellering av motpartskreditrisk (Swedish)
Abstract [en]

In this paper, Monte Carlo simulation for CCR (Counterparty Credit Risk) modeling is investigated. A jump-diffusion model, Bates' model, is used to describe the price process of an asset, and the counterparty default probability is described by a stochastic intensity model with constant intensity. In combination with Monte Carlo simulation, the variance reduction technique importance sampling is used in an attempt to make the simulations more efficient. Importance sampling is used for simulation of both the asset price and, for CVA (Credit Valuation Adjustment) estimation, the default time. CVA is simulated for both European and Bermudan options. It is shown that a significant variance reduction can be achieved by utilizing importance sampling for asset price simulations. It is also shown that a significant variance reduction for CVA simulation can be achieved for counterparties with small default probabilities by employing importance sampling for the default times. This holds for both European and Bermudan options. Furthermore, the regression based method least squares Monte Carlo is used to estimate the price of a Bermudan option, resulting in CVA estimates that lie within an interval of feasible values. Finally, some topics of further research are suggested.

Abstract [sv]

I denna rapport undersöks Monte Carlo-simuleringar för motpartskreditrisk. En jump-diffusion-modell, Bates modell, används för att beskriva prisprocessen hos en tillgång, och sannolikheten att motparten drabbas av insolvens beskrivs av en stokastisk intensitetsmodell med konstant intensitet. Tillsammans med Monte Carlo-simuleringar används variansreduktionstekinken importance sampling i ett försök att effektivisera simuleringarna. Importance sampling används för simulering av både tillgångens pris och, för estimering av CVA (Credit Valuation Adjustment), tidpunkten för insolvens. CVA simuleras för både europeiska optioner och Bermuda-optioner. Det visas att en signifikant variansreduktion kan uppnås genom att använda importance sampling för simuleringen av tillgångens pris. Det visas även att en signifikant variansreduktion för CVA-simulering kan uppnås för motparter med små sannolikheter att drabbas av insolvens genom att använda importance sampling för simulering av tidpunkter för insolvens. Detta gäller både europeiska optioner och Bermuda-optioner. Vidare, används regressionsmetoden least squares Monte Carlo för att estimera priset av en Bermuda-option, vilket resulterar i CVA-estimat som ligger inom ett intervall av rimliga värden. Slutligen föreslås några ämnen för ytterligare forskning.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:081
Keywords [en]
CCR, OTC derivatives, European option, Bermudan option, CVA, jump-diffusion model, stochastic intensity model, Monte Carlo, variance reduction, importance sampling, least squares Monte Carlo
Keywords [sv]
CCR, OTC-derivat, europeisk option, Bermuda-option, CVA, jump-diffusion-modell, stokastisk intensitetsmodell, Monte Carlo, variansreduktion, importance sampling, least squares Monte Carlo
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-252566OAI: oai:DiVA.org:kth-252566DiVA, id: diva2:1319685
External cooperation
Cinnober Financial Technology
Subject / course
Mathematical Statistics
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2019-06-04 Created: 2019-06-03 Last updated: 2019-06-11Bibliographically approved

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