/usr/share/dx/java/htmlpages/optval.html is in dxsamples 4.2.0-1.
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<title>Black-Scholes Option Valuation</title>
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code="optval.class" width = 300 height = 250
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<h2>...what determines the value of a call option?</h2>
At expiration the holder may deliver an amount equal to the
<i>Strike</i> price in return for one share which she can turn around and
sell. So at expiration the value is strike price minus stock price with
the exception that its value cannot be less than $0.0. Before expiration
the value of a call is determined by the liklihood that the stock's price
at the expiration date will exceed the strike price and by the time
value of money. With respect to calls which will be excercised, the owner
effectively owns the stock but hasn't paid for it yet. She is borrowing
and should therefore except to pay more if the interest rate is high.
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<h2>...an option pricing formula</h2>
Fischer Black and Myron Scholes invented a formula which predicts
an option price as a function of time, volatility, stock price, strike
price, and the interest rate. Assuming a distant expiration date, the
model predicts that a $1.00 change in stock price causes a small change
in option price - perhaps $0.50. This makes intuitive sense because
the call owner profits only from a high stock price at expiration and
a small increase today might easily be canceled out by another small
change in the opposite direction tomorrow. If the stock price becomes
quite high, then the option value will increase by nearly $1.00 for
each $1.00 increase in the stock price. This also makes sense because
when the stock is way above the strike price, it's almost certain that
the option buyer will excerise the option.
<h2>...visualizing Black-Scholes</h2>
The red surface shows Black-Scholes call values for a variety of
stock and strike prices. A <i>Sequencer</i> in the visualization
shows the effect over time.
You can <i>Pick</i>on a location on the surface which selects of
combination of stock and strike and reports the Black-Scholes value.
Then you can run the sequencer to watch the price change. Note that
at very high stock prices, the slope of the surface approaches 45 degrees.
In other words a $1.00 change in stock price translates to a $1.00 change
in call price. When strike and stock are close together, a $1.00 change
in stock produces about $0.60 change in call value.
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