KTH Matematik  

Matematisk Statistik

Tid: 14 juni 2013 kl 13.00-13.45.

Seminarierummet 3721, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!

Föredragshållare: Daniel Krebs

Titel: Pricing a basket option when volatility is capped using affine jump-diffusion models. (Examensarbete - Master thesis).

Abstract 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 non-standard 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 Sepp-model in addition to the Black-Scholes model.

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Sidansvarig: Filip Lindskog
Uppdaterad: 25/02-2009