Consider the European put option with the automatic strike reset feature, where the strike price is reset

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Consider the European put option with the automatic strike reset feature, where the strike price is reset to the prevailing asset price on a prespecified reset date if the option is out-of-the-money on that date. The strike price at expiry is not known a priori, rather it depends on the actual realization of the asset price on those prespecified reset dates. Construct the FSG scheme that prices the strike reset put option (Kwok and Lau, 2001a). 

Let t, ℓ = 1, 2, ··· ,m be the prespecified reset dates, and let X denote the strike price reset at t. Explain why

Xe = max(X, Xe1, S(t)),

where X is the original strike price and S(tℓ) denotes the asset price at t.

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