# Capped Option

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## Capped Option

An option contract that establishes a maximum profit for the holder. Capped options contain a provision stating that the option is automatically exercised if the underlying security closes on a trading day above (for a call) or below (for a put) some established price. This means that if the underlying security moves in a direction disadvantageous for the writer, there is a maximum amount the writer can lose. A capped option is also called a capped-style option.
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In Section 2 we introduce capped options. In Sections 3 and 4 we introduce how to use capped options to improve the traditional binomial tree method and LSM.
Turnbull, "Pricing and Hedging Capped Options," Journal of Futures Markets, vol.
Capped option is a conventional option with a predefined profit cap written into the contract.
In this paper we use the American capped option with the closed-form formula given by Broadie and Detemple  to improve the binomial tree approach for pricing American call options.
In this section, how to use American capped option in improving binomial tree method is introduced.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the real value of American call option (see Broadie and Detemple ), which means that the value of capped option is much closer to the true American option than the European option, it is more accurate to replace [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Broadie and Detemple  used capped option as a tool to obtain the lower bond [L.sup.*] of American call option as shown in Figure 2, where the solid line [B.sup.*] is the optimal exercise boundary for an American call option.
Broadie and Detemple  only proved formula (1) for the capped option with lower dividend rates.
Use capped option as a tool to improve CRR model with parameters: S0 = 100; [delta] = 0.07; r = 0.03; [sigma] = 0.2; T = 0.5; t = 0; K = 100.
Use capped option as a tool to improve CRR model with parameters: S0 = 100; [delta] = 0.03; r = 0.03; [sigma] = 0.2; T = 0.5; t = 0; K = 100.
And capped option does a better job in improving the CRR binomial tree method for the higher dividend and lower dividend CRR model than the CRR model with dividend being equal to risk free rate according to Tables 1-3.
The following example tests the capped option as a tool to improve the traditional binomial tree method in Tian model .

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