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The Pricing of Power Options under the Generalized Black-Scholes ModelWu, Yi-Yun 08 August 2011 (has links)
A closed-form pricing formula of European options is obtained by Fischer Black and Myron Scholes (1973). In such a European option, the payoff depends `linearly' on the underlying asset price at the expiration time. An
power option has a payoff which depends nonlinearly on the underlying asset price at the expiration time by raising a certain exponent. In the Black-Scholes model, a closed-form formula of a power option is obtained by Esser (2004). This paper extends Esser's result to the generalized Black-
Scholes model. That is, we derive a closed-form pricing formula of a power option in the case when both the interest rate and the stock volatility are time-dependent.
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The technique of measure and numeraire changes in optionShi, Chung-Ru 10 July 2012 (has links)
A num¡¦eraire is the unit of account in which other assets are denominated.
One usually takes the num¡¦eraire to be the currency of a country.
In some applications one must change the num¡¦eraire due to the finance considerations.
And sometimes it is convenient to change the num¡¦eraire because
of modeling considerations. A model can be complicated or simple, depending
on the choice of thenum¡¦eraire for the method.
When change the num¡¦eraire, denominating the asset in some other unit of account,
it is no longer a martingale under ˜P . When we change the num¡¦eraire,
we need to also change the risk-neutral measure in order to maintain risk
neutrality.
The details and some applications of this idea developed in this thesis.
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