Perpetual American Options and ImpliedVolatility

Abstract: This thesis analyzes perpetual American options and in particular aimsto identify what kind of behavior the implied volatility of perpetual Americanput options display. Using two different approaches, we derive the valuefunction for the American put option. Moreover, by assuming the volatilityfunction of the underlying model to be decreasing we find that this inducesan implied volatility skew. Furthermore, this claim is illustrated with numericalcalculations.