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Pricing a basket option when volatility is capped using affinejump-diffusion models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2013 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This thesis considers the price and characteristics of an exotic option called the Volatility-Cap-Target-Level(VCTL) option. The payoff function is a simple European option style but the underlying value is a dynamic portfolio which is comprised of two components: A risky asset and a non-risky asset. The non-risky asset is a bond and the risky asset can be a fund or an index related to any asset category such as equities, commodities, real estate, etc.

The main purpose of using a dynamic portfolio is to keep the realized volatility of the portfolio under control and preferably below a certain maximum level, denoted as the Volatility-Cap-Target-Level (VCTL). This is attained by a variable allocation between the risky asset and the non-risky asset during the maturity of the VCTL-option. The allocation is reviewed and if necessary adjusted every 15th day. Adjustment depends entirely upon the realized historical volatility of the risky asset.

Moreover, it is assumed that the risky asset is governed by a certain group of stochastic differential equations called affine jump-diffusion models. All models will be calibrated using out-of-the money European call options based on the Deutsche-Aktien-Index(DAX).

The numerical implementation of the portfolio diffusions and the use of Monte Carlo methods will result in different VCTL-option prices. Thus, to price a nonstandard product and to comply with good risk management, it is advocated that the financial institution use several research models such as the SVSJ- and the Seppmodel in addition to the Black-Scholes model.

Keywords: Exotic option, basket option, risk management, greeks, affine jumpdiffusions, the Black-Scholes model, the Heston model, Bates model with lognormal jumps, the Bates model with log-asymmetric double exponential jumps, the Stochastic-Volatility-Simultaneous-Jumps(SVSJ)-model, the Sepp-model.

Place, publisher, year, edition, pages
2013. , 82 p.
Series
TRITA-MAT-E, 2013:27
Keyword [en]
Exotic option, basket option, risk management, greeks, affine jumpdiffusions, the Black-Scholes model, the Heston model, Bates model with lognormal jumps, the Bates model with log-asymmetric double exponential jumps, the Stochastic-Volatility-Simultaneous-Jumps(SVSJ)-model, the Sepp-model
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-123395OAI: oai:DiVA.org:kth-123395DiVA: diva2:631612
External cooperation
Carnegie
Subject / course
Mathematical Statistics
Educational program
Master of Science in Engineering -Engineering Physics
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2013-06-22 Created: 2013-06-07 Last updated: 2013-06-22Bibliographically approved

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