Tid: 20 december 1999 kl 1515-1600
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Föredragshållare: Pontus Lidbrink och Gustav Fyring
Titel: Valuing and hedging Asian Basket options
The main objectives of this thesis is to evaluate a closed approximation formula for Asian Basket options and construct a hedge of a portfolio containing over 100 Asian Basket options. The approximation formula is based on a moment matching method where we try to match the first two moments of the pay-off variable to a log-normal distribution. The formula is verified with Monte-Carlo simulation and has proven to be very precise. We also show how to match a reciprocal gamma function to the pay-off variable, but simulations indicate that the log-normal distribution better replicates the empirical distribution.
Our suggested hedge, which is based on multiple linear regression, uses two or three equity index futures with the aim to minimize the variance of the total position. Two strategies have been implemented, one that uses S&P 500 and Nikkei 225 futures and one that also includes DAX 30 index futures. The hedge that uses three index futures has proven to work much better than the one using only two, and on our sample portfolio it reduces the variance up to over 14 times.
During the preparation of this report one problem was to access and process the large amount of data that is necessary to conduct the calculations. A large database in Microsoft Access has been built for this purpose, a database that communicates with the FAME database where the historical data of all equities along with interest rates and spot exchange rates are stored. At the same time the Access database contains Visual Basic based macros that takes care of all calculations.
To the list of seminars