Question

discounted call payoff = \left[ S(T) - \min_{j=0,...,d} S(jT/d) \right] e^{-rT} \\ or \left[ S(T) - \min_{0<t<T} S(t) \right] e^{-rT} \\ discounted put payoff = \left[ \max_{j=0,...,d} S(jT/d) - S(T) \right] e^{-rT} \\ or \left[ \max_{0<t<T} S(t) - S(T) \right] e^{-rT}

          discounted call payoff = \left[ S(T) - \min_{j=0,...,d} S(jT/d) \right] e^{-rT} \\ or \left[ S(T) - \min_{0<t<T} S(t) \right] e^{-rT} \\ discounted put payoff = \left[ \max_{j=0,...,d} S(jT/d) - S(T) \right] e^{-rT} \\ or \left[ \max_{0<t<T} S(t) - S(T) \right] e^{-rT}

discounted call payoff = [ S(T) - minj=0,...,d S(jT/d) ] e^-rT
or [ S(T) - min0<t<T S(t) ] e^-rT
discounted put payoff = [ maxj=0,...,d S(jT/d) - S(T) ] e^-rT
or [ max0<t<T S(t) - S(T) ] e^-rT

Added by Benjamin C.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Jason Horton

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(Computer problem) Consider the problem of pricing lookback options for a stock modeled by a geometric Brownian motion with an initial price of $100, a volatility of 40%, and zero interest rate. Let the expiry time be 24 weeks in the future (considering 52 weeks a year), and let the monitoring frequency be weekly. a) Use the GAIL software to find the price of both the put and call options to the nearest $0.1. b) The lookback put option should have a higher price based on the definition. Could you think about the reason? Discounted call payoff = IS(T) - min S(jT/d) j=0,...,d or S(T) - min S(t) 1>>r Discounted put payoff = max S(jT/d) - S(T) j=0,...,d or max S(t) - S(T) 1>>r