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Integral Representation of Vega for American Put Options

There is an inaccurate formula in Huang et al. (1996). In fact, a substantial term is missing in their equation (14) for computing the value of an important option hedging parameter, i.e., the vega. We fix it in this note by providing its correct form and characterizing an associated (new) integral equation. Some related explanations and arguments are also corrected.