Currency Option Valuation using Esscher and Fourier Transforms
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Date
2019Author
Kamau, Simon Muoria
Type
ThesisLanguage
enMetadata
Show full item recordAbstract
The size and volatility of the exchange rate market warrants the use of currency options
in order to hedge the exchange rate risk. This study sought to build a robust pricing model
that takes into account some of the stylized facts of exchange rates reported in literature.
The normal inverse Gaussian distribution is chosen to model the exchange rate returns
as: one, its higher order moments exist, thus can capture skewness and excess kurtosis
unlike the two-parameter normal distribution; and two, since it is a normal mixture, the
aggregational Gaussianity property holds. To price options written on these exchange
rates under the risk-neutral measure, a change of measure is required as this proposed
model renders the market incomplete, which implies the existence of a range of equivalent
martingale measures (by the fundamental theorem of asset pricing). To choose a unique
martingale measure, we apply the Esscher measure. Pricing equations are, thus, derived as
the expected discounted value of the payo s with respect to this risk-neutral measure. The
fast Fourier transform is then applied to compute option prices due to its computational
e ciency. From the results presented herein, the NIG distribution results in a better t
of the empirical distribution of the exchange rate returns and the corresponding option
pricing model, the Esscher-NIG model, outperforms the Black-Scholes model in pricing
performance.
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Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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