... option[*]
The name is derived from the fact that Bermuda is between America and Europe! 
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... value[*]
This will be shown later 
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... Dividends[*]
This derivation is taken from Hull[2] 
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... time)[*]
In theoretical finance, it is always assumed that the interest is continuously compounded 
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... Parity[*]
We will later show that this fact can be shown using the fact that $e^{-rt}S$ is a martingale in a risk-neutral world 
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... infinity[*]
This was a problem with Einstein's original theory of Brownian motion. Since then many alternative processes have been proposed which reduce to Einstein's theory for large $\tau$ and do not have this problem, the most famous among them being the Ornstein-Uhlenbeck process discussed in some detail in section 1.8 of Roepstorff[5] 
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... process[*]
The theory has its origin in a fundamental paper by N. Wiener in 1923 [6]. 
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...$W = \dot{X_t}$[*]
this, of course, is merely a formal object 
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...Steineq)[*]
We can include this process if we add a term of the form $\gamma V^{1/2}$ to the drift term 
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... this[*]
For example, see Poterba and Summers[22], Stein[23] and Merville and Pieptea[24] 
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...$-1 < \rho < 1$[*]
In fact, as we will see, the solution for zero correlation is trivial 
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... choose[*]
This is not a realistic process as $P(V<0)>0$ while $V$ is obviously non-negative. However, it might be a reasonable approximation for relatively short times for which $P(V<0)$ is negligible. 
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...Stein[*]
The original solution for simple Brownian motion was obtained way back in 1944 by Cameron and Martin[26] 
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... 1998[*]
The data was obtained from Bloomberg which I was able to access with the kind permission of Dr. Lawrence Ma 
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... decreasing[*]
The simulations for non-zero correlation show more interesting behaviour but we are interested only in the behaviour for strike prices close to the underlying security price as these are the only kind of options traded in the market 
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