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Please determine the payoff for the following knock-in put option, based on the price path summary below: Starting price of underlying (at inception): $101.32 Maximum traded price of underlying: $114.84 Minimum traded price of underlying: $98.35 Terminal price of underlying (at maturity): $103.16 Strike rate, K: $106.47 Barrier, H: $112.86 (Assume continuous price observations)

Question

Please determine the payoff for the following knock-in put option, based on the price path summary below: Starting price of underlying (at inception): 101.32Maximumtradedpriceofunderlying:101.32 Maximum traded price of underlying: 114.84 Minimum traded price of underlying: 98.35Terminalpriceofunderlying(atmaturity):98.35 Terminal price of underlying (at maturity): 103.16 Strike rate, K: 106.47Barrier,H:106.47 Barrier, H: 112.86 (Assume continuous price observations)

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Solution

The payoff for a knock-in put option depends on whether the price of the underlying asset hits the barrier level during the life of the option. If the price hits the barrier, the option is "knocked in," or activated, and the payoff is the maximum of zero or the difference between the strike price and the terminal price of the underlying asset. If the price does not hit the barrier, the option is not activated and the payoff is zero.

In this case, the maximum traded price of the underlying asset is 114.84,whichisabovethebarrierlevelof114.84, which is above the barrier level of 112.86. Therefore, the option would be knocked in.

The payoff would then be the maximum of zero or the difference between the strike price (106.47)andtheterminalpriceoftheunderlyingasset(106.47) and the terminal price of the underlying asset (103.16). Since 106.47isgreaterthan106.47 is greater than 103.16, the payoff would be 106.47106.47 - 103.16 = $3.31.

So, the payoff for this knock-in put option would be $3.31.

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