Question

A stock index is currently 1,500. Its volatility is $18 \%$. The risk-free rate is $4 \%$ per annum (continuously compounded) for all maturities and the dividend yield on the index is $2.5 \%$. Calculate values for $u, d$, and $p$ when a 6 -month time step is used. What is the value a 12 -month American put option with a strike price of 1,480 given by a two-step binomial tree.

   A stock index is currently 1,500. Its volatility is $18 \%$. The risk-free rate is $4 \%$ per annum (continuously compounded) for all maturities and the dividend yield on the index is $2.5 \%$. Calculate values for $u, d$, and $p$ when a 6 -month time step is used. What is the value a 12 -month American put option with a strike price of 1,480 given by a two-step binomial tree.

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 13, Problem 17

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Step 1

The up factor \( u \) and down factor \( d \) in a binomial model are calculated using the volatility \( \sigma \) and the time step \( \Delta t \). The formulas are: \[ u = e^{\sigma \sqrt{\Delta t}} \] \[ d = e^{-\sigma \sqrt{\Delta t}} \] Given: - Volatility Show more…

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A stock index is currently 1,500. Its volatility is $18 \%$. The risk-free rate is $4 \%$ per annum (continuously compounded) for all maturities and the dividend yield on the index is $2.5 \%$. Calculate values for $u, d$, and $p$ when a 6 -month time step is used. What is the value a 12 -month American put option with a strike price of 1,480 given by a two-step binomial tree.

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