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American call option American put option arbitrage assumed calculated cash Chapter commodity Consider continuously compounded default delivery derivative security dividend yield equal estimate European call option European option European put option ex-dividend date Example exchange rate exercise price expected growth rate expected return Figure Financial Economics financial institution finite difference method follows foreign currency forward contract forward price futures contract futures option futures price gamma holder implied volatility interest-rate swap investor Journal of Financial lambda LIBOR loan long position market price maturity months non-dividend-paying stock normal distribution open int option price parameters payment payoff portfolio insurance price of risk rate of interest risk-free interest rate risk-free rate risk-neutral valuation risk-neutral world riskless Section short position standard deviation stochastic process stock index stock price Suppose term structure traded option traded security Treasury bill underlying asset underlying variable vol Wed Wed vol Wiener process zero