calculate the theoretical prices of different options with 6 months to maturity. The current USD risk-free rate
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calculate the theoretical prices of different options with 6 months to maturity. The current USD risk-free rate (continuously compounded, annualized) is 3%. The dividend yield (continuously compounded, annualized) of the S&P 500 index is 1%. The estimated variance of daily log returns of the S&P 500 index is 0.000128572. The current S&P 500 index level is 4000.
The company also offers shout put options. Let K be the strike price of the option. The option holder can choose to "shout" prior to maturity.1 The payoff at maturity of the option is max{0,K ST ,K S } where ST is the underlying asset price at maturity and S is the underlying asset price when the option holder "shouts". For this question, assume for simplicity that the option can only be "shouted" at nodes in the binomial tree. Calculate the price of a shout put option with strike price 3700 (round to 4 decimal places).
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