The question relates to calculating the price of a European call option with discrete dividends using a binomial tree and determining the replicating strategy. It involves constructing a binomial model, accounting for dividends, and applying the risk-neutral valuation method, then finding the trades in the underlying stock and the risk-free asset that will replicate the option payoffs.
- The question asks us to calculate the price of a European call option with discrete dividends using a two-step binomial tree, and find the replicating strategy at time 0 and time 1.
- This involves discounting the expected cash flows from the option back to the present value at the given risk-free interest rate, then using this information to determine the appropriate trading strategy in the option and the underlying stock at the initial time and after one period.
How to Calculate the Call Option Price
- To calculate the call option price, we need to construct a two-step binomial tree, account for the dividends, and apply the risk-neutral valuation method which involves discounting the option payoffs at the risk-free rate.
- Let's break down the steps needed for this calculation and consider an example where the present values of future cash flows from a bond or a stock are determined under different discount rates.
Finding the Replicating Strategy
- Once we have the option price, we move on to find the replicating strategy at time 0 and time 1.
- This involves determining the number of shares of the stock to hold and the amount of borrowing or lending required so that the portfolio replicates the payoffs of the option at each step of the binomial tree.