Question

1. American options can be valued using a binomial tree by?

1. Checking whether early exercise is optimal at the final nodes.
2. Increasing the number of time steps on the tree
3. Checking whether early exercise is optimal at the penultimate nodes a the final nodes.
4. Checking whether early exercise is optimal at all nodes where the option is in the money.

  

1. The Black-Scholes-Merton model assumes

1. The return from the stock in a short period of time is lognormal
2. The stock price at a future time is lognormal
3. The stock price at a future time is normal
4. None of the above

  

Answer 1

A. INCORRECT : Checking whether early exercise is optimal at all the nodes and not just the final nodes, where the option is in the money. If the option is out of the money, it will not be exercised.
B. INCORRECT : The number of time steps on the tree is same for both American and European options. American option do not increase the number of time steps on the tree.
C : INCORRECT : Checking whether early exercise is optimal at the penultimate nodes and the final notes only when the option is in the money. If the option is out of the money, it will not be exercised.
D : CORRECT : For an American option it must be checked whether exercising will be better than non exercising at each node when the option is in the money. Therefore checking for early exercise is optimal at all nodes where the option is in the money.

Option D is correct.

A. INCORRECT : Black-Scholes-Merton Model assumes that stock returns are normally distributed. It assumes market volatility is constant over time.
B. CORRECT : The Black-Scholes-Merton Model assumes that stock prices follow a lognormal distribution implying that asset price cannot take a negative value.
C. INCORRECT : The Black-Scholes-Merton Model assumes that stock prices follow a lognormal distribution implying that asset price cannot take a negative value.
D. INCORRECT : Option B. is correct.

Option B is correct. The stock price at a future time is lognormal.