This practice problem reinforces the concept of the hedge ratio discussed in the following post

found in this companion blog.

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**Practice Problems**

The stock prices in the following problems are modeled by a 1-year binomial tree with 1.2 and 0.8. The current stock price is $50. The stock is non-dividend paying. The annual risk-free interest rate is 5%.

*Practice Problem 1*

A market maker has just sold a 1-year call option with strike price $55. Determine the replicating portfolio that has the same payoff as this call option. What is the price of this call option?

*Practice Problem 2*

Repeat Problem 1 for the initial stock prices $55, $60, $65, and $70. What is the pattern of the hedge ratio as initial stock price goes from $50 to $70? Explain this pattern.

*Practice Problem 3*

A market maker has just sold a 1-year put option with strike price $45. Determine the replicating portfolio that has the same payoff as this call option. What is the price of this call option?

*Practice Problem 4*

Perform the same calculation for Problem 3 for the initial stock prices $45, $40, $35, and $30. What is the pattern of the hedge ratio as initial stock price increases? Explain this pattern.

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**Answers**

*Practice Problem 2*

**Call option hedge ratio when initial stock prices are increasing**

*Practice Problem 4*

**Put option hedge ratio when initial stock prices are decreasing**

Refer to The binomial option pricing model, part 3 for the explanation.

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