Practice problems in this post reinforce the following blog post on multiperiod binomial option pricing calculation:

found in this companion blog.

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**Practice Problems**

*Practice Problem 1*

The following gives the information on a particular stock.

- The current stock price is $40.
- The stock is non-dividend paying.
- The annual standard deviation of the stock return is 0.3.
- The annual risk-free interest rate is 5%.

Price a 6-month European put option on this stock using a 2-period binomial tree. The strike price of the option is $45. Include the replicating portfolio on each node in the binomial tree.

*Practice Problem 2*

Calculate the price of a 6-month European call option on a certain stock with the following characteristics:

- The initial stock price is $60.
- Strike price of the call option is $55.
- The stock is non-dividend paying.
- The annual standard deviation of the stock return is 0.3.
- The annual risk-free interest rate is 4%.

Use a 2-period binomial tree. Include the replicating portfolio on each node in the binomial tree.

*Practice Problem 3*

The following gives the information on a 3-month European put option:

- The initial stock price is $40.
- Strike price of the call option is $45.
- The stock is non-dividend paying.
- The annual standard deviation of the stock return is 0.3.
- The annual risk-free interest rate is 5%.

Price this put option using a 3-period binomial tree. Include the replicating portfolio on each node in the binomial tree.

*Practice Problem 4*

The following gives the information on a 2-year European call option:

- The initial stock price is $50.
- Strike price of the call option is $60.
- The stock pays dividends at the annual continuous rate of 5%.
- The annual standard deviation of the stock return is 0.3.
- The annual risk-free interest rate is 2%.

Price this call option using a 3-period binomial tree. Include the replicating portfolio on each node in the binomial tree.

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**Answers**

**Practice Problem 1 – pricing 6-month European put**

**Practice Problem 2 – pricing 6-month European call**

**Practice Problem 3 – pricing 3-month European put**

**Practice Problem 3 – pricing 3-month European put – Replicating portfolios**

**Practice Problem 4 – pricing 2-year European call**

**Practice Problem 4 – pricing 2-year European call – Replicating portfolios**

For more information on how to calculate the option prices for these practice problems, refer to The binomial option pricing model, part 4.

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