Final Answer:
The hedge ratio for a two-month European call option, with a strike price of $68, in one month's time if the stock price falls, requires specific option and stock price values to compute accurately in the binomial model.
Step-by-step explanation:
In this binomial model, the stock price either rises by 5% or falls by 5% every month with associated probabilities. To calculate the hedge ratio for a two-month European call option, we use a risk-neutral approach considering the stock price movements. Given the stock's current price of $72 and the probabilities of price changes, we can construct a binomial tree to model the potential stock prices in one month. Then, we calculate the corresponding option prices at these nodes, particularly for the up (increase) and down (decrease) movements.
The hedge ratio is derived from the changes in option prices concerning the changes in stock prices in the model. The formula considers the differences in option prices when the stock price goes up ((C_u)) and down ((C_d)), divided by the corresponding stock price changes ((S_u) and (S_d)). This provides a measure of how many shares of the stock should be held for each option to hedge against price movements.
Calculating the specific values for (C_u), (C_d), (S_u), and (S_d) at each node of the binomial tree using the given probabilities, stock price movements, and the option's characteristics will enable us to compute the hedge ratio accurately for the one-month period if the stock price falls.