Question

A special type of one-year put option is written on a certain asset. The current price of the asset is 40 pesos and the current exercise price is 40 pesos. At month 6, if the price of the asset is below 35 pesos, the price of exercise is reduced to 35 pesos; if not, it remains unchanged. The interest rate risk free is 5 percent per year; the volatility of the asset is 35 percent hundred per year. 1. Use a 2-period binomial tree with the usual selection of u and d to value the

option.
i. Use a 2-period binomial tree with the usual selection of u and d to value the
ii. Now use a 4-period binomial tree to value the option.
iii. What is the difficulty in valuing this type of option?

Answer 1

To value a put option on an asset using a binomial tree model, one must use up and down factors to build the tree, calculate the option's value at each node, and discount these values to the present using the risk-free rate. This valuation becomes complex when the exercise price can change, as in the described case where it adjusts based on the asset's price at month 6.

The valuation of a one-year put option with a changing exercise price using a binomial tree model involves a step-by-step approach. The asset current price is 40 pesos, with an exercise price of 40 pesos, modifying to 35 pesos if the asset's price is below this threshold at month 6. With a risk-free interest rate of 5% per year and a volatility of 35%, a 2-period and a 4-period binomial tree are used to value the option.

For a 2-period binomial tree:

1. Calculate the up and down factors using the volatility (u, d).
2. Build the binomial tree, pricing the asset at the end of each period.
3. Calculate the value of the option at each node based on the exercise price.
4. Discount the option value back to the present using the risk-free rate.

For a 4-period binomial tree, repeat the steps but with additional periods to accommodate more precise estimations.

Valuing this option is difficult because the exercise price can change during the life of the option, adding complexity to the model.