Question

Future prices of a stock are modelled with a 2-period binomial tree, each period being one year. You are given the following information: (i) The tree is constructed based on forward prices. (ii) The stock’s initial price is 50. (iii) The continuously compounded risk-free rate of interest is 3%. (iv) The stock pays continuous dividends proportional to its price at a rate of 6%. (v) σ = 0.3. An American call option on the stock expiring in 2 years has strike price 60. Determine the price of the call option.

Answer 1

The price of the call option can be determined using the binomial option pricing model.

Step-by-step explanation:

The price of an American call option on the stock can be determined using the binomial option pricing model. In this model, the stock's future prices are represented by a binomial tree, with two periods of one year each.

First, we need to calculate the parameters of the model. Given that the stock's initial price is $50, the risk-free rate of interest is 3%, the stock pays continuous dividends at a rate of 6%, and the stock's volatility is 0.3, we can calculate the up and down factors of the tree. The up factor is calculated as e^(σ√T), where σ is the volatility and T is the time period, and the down factor is calculated as e^(-σ√T).

With these parameters, we can construct the binomial tree and calculate the prices of the stock at each node of the tree. Then, we can calculate the option prices at each node using the formula max(0, S - K), where S is the stock price and K is the strike price. Finally, we can work backwards through the tree to determine the price of the call option at the initial node.