The Binomial Distribution

The binomial distribution makes these assumptions:

The probability, p, of success is constant for all trials.

The trials are independent.

[Practice Problems] A stock is priced at $100.00 and follows a one-period binomial process with an up move that equals 1.05 and a down move 0.97. If 1 million Bernoulli trials are conducted, and the average terminal stock price is $102.00, the probability of an up move (p) is closest to:

A.  0.375.

B.  0.500.

C.  0.625.

[Practice Problems] A call option on a stock index is valued using a three-step binomial tree with an up move that equals 1.05 and a down move that equals 0.95. The current level of the index is $190, and the option exercise price is $200. If the option value is positive when the stock price exceeds the exercise price at expiration and $0 otherwise, the number of terminal nodes with a positive payoff is:

A. one. B. two.  C. three.