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Pricing American Options with the Lower-Upper Bound Approximation (LUBA) Method
Pricing American Options with the Lower-Upper Bound Approximation (LUBA) Method
This Demonstration shows the lower and upper bound approximation methods [3] for an American call option.
The upper graph shows the lower approach (t) (red line) for the early exercise boundary (t), and its approximation using Kim's method (black dashed line). For the American call's holder, the early exercise becomes optimal when the asset price exceeds (t), where the intrinsic value of the option becomes greater than its holding value. An American capped call option is automatically exercised if the underlying asset rises above a predetermined price, which is called the "cap price".
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L
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B
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B
The lower graph locates the cap price that maximizes the payoff function of an American capped call and shows the approximations that correspond to the top table. The blue curve represents the payoff function of the American capped call depending on the cap price [1]. The horizontal black line is the reference for the American call, according to Mathematica's built-in function FinancialDerivative.
Adjust the "zoom out" level accordingly, in order to achieve the best visualization.