## American Put OptionsAn American put option gives its owner the right to sell a share of stock at a given specified price on or before a given date. This book provides a detailed comparison of recent works on the American put option from both theoretical and computational approaches. |

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American options American put option American put value asset assume assumption Bachelier Bachelier's Black and Scholes Black-Scholes boundary conditions bounded Brennan and Schwartz Brennan-Schwartz algorithm call option coercive commodity option compute continuous function converges critical stock price decreasing define denotes distribution European option European put option exercise price expected return expiration formula geometric Brownian motion Geske and Johnson hedge ratio Hence implies inequality inf{s instantaneous integral interest rate Jacka Jaillet Karatzas 28 Lamberton Lemma lognormal martingale matrix Merton 44 nondecreasing Note obtain optimal stopping option pricing p(St partial derivative partial differential equation payoff portfolio PROOF Proposition put price respect risk-free risk-free interest rate riskless satisfies Sc(t solving standard Brownian motion stochastic differential equation stock price changes stock price process Theorem theory tion tridiagonal matrix underlying stock uniformly variance vector volatility XB(T zero