Problem Set 2

Problem Set 2 – FIN 400 (Due date: November 4, Monday)

Name:                                                           Student ID Number:

1. Consider the case of European IBM call and put options that have an exercise price of $115 and expire in two. The price of the call is $3, and the price of the put is $6. Assume IBM is expected to pay no dividend in the next two months. Suppose also that the current price of IBM stock is $109.30 and the bond-equivalent yield on a two-month T- bill is 6.0 per cent nonannualized.

1-1. (2 points) Cost of Strategies A & B today?

Strategy A = $112.3
Strategy B = $108.49

1-2. (1 point) A profitable arbitrage strategy is to long/buy (1) and short/sell (2) this year and hold this position until next year. Choose the correct strategies (Strategy A or Strategy B) in each blank (1) and (2).

(1) Strategy B
(2) Strategy A

2. CEO of Company X has 30 million shares of stocks and 30 million shares of options (of Company X). The stock return volatility (𝜎) is 0.50, dividend yield (d) is 0.0, risk-free rate (r) is 0.05, and maturity (T) is five years. The following table shows the stock price of Company X during

Suppose that options were granted at the money on February 2016.

2-1. (2 points) Find the option’s delta (change in one share of the option due to a $1 increase in stock price) as of December 2016.

2-2. (2 points) Find an increase in CEO wealth for a $1 increase in Company X’s stock price as of December 2016.

$57.47 Million

3. (3 points) The Federal Crop Insurance Corporation (FCIC) protect farmers against crop losses caused by the vagaries of weather: If farmers default, FCIC pays back any debt borrowed from a bank on behalf of the defaulted farmer. FCIC has relatively few inspectors to inspect individual claims. A farmer in Arizona can choose between planting water-hungry crops or hardy crops. Both crops cost $50. The gross returns on these plants depend on the annual rainfall. For water-hungry scraps, the gross return is $100 if the annual rainfall exceeds 12 inches (50% probability) and $0 if the annual rainfall is less than 12 inches (50% probability). For hardy crops, the gross return is

$60 if the annual rainfall exceeds 12 inches (50% probability), and $50 if the annual rainfall is less than 12 inches (50% probability).

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Suppose a farmer borrows debt (pay back the borrowed amount, or everything he has if the cash flow is smaller than the borrowed amount) from a bank to finance the cost of planting crops. In case of a farmer’s default, the bank gets paid by FCIC. Which plant will the farmer choose? Why (show farmers’ profit for each crop).

Hardy crop

Hardy crop: 0.5(60-50) + 0.5(50-50) = $5

Water hungry crop: 0.5*(100-50) + 0.5*(0-50) = $0

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Problem Set 2 – FIN 400 (Due date: November 4, Monday)

Name:                                                           Student ID Number:

Problem Set 2

1. Consider the case of European IBM call and put options that have an exercise price of $115 and expire in two. The price of the call is $3, and the price of the put is $6. Assume IBM is expected to pay no dividend in the next two months. Suppose also that the current price of IBM stock is $109.30 and the bond-equivalent yield on a two-month T- bill is 6.0 per cent nonannualized.

1-1. (2 points) Cost of Strategies A & B today?

Strategy A:

Strategy B:

1-2. (1 point) A profitable arbitrage strategy is to long/buy (1) and short/sell (2) this year and hold this position until next year. Choose the correct strategies (Strategy A or Strategy B) in each blank (1) and (2).

2. CEO of Company X has 30 million shares of stocks and 30 million shares of options (of Company X). The stock return volatility (𝜎) is 0.50, dividend yield (d) is 0.0, risk-free rate (r) is 0.05, and maturity (T) is five years. The following table shows the stock price of Company X during

Suppose that options were granted at the money on February 2016.

2-1. (2 points) Find the option’s delta (change in one share of the option due to a $1 increase in stock price) as of December 2016.

2-2. (2 points) Find an increase in CEO wealth for a $1 increase in Company X’s stock price as of December 2016.

3. (3 points) The Federal Crop Insurance Corporation (FCIC) protect farmers against crop losses caused by the vagaries of weather: If farmers default, FCIC pays back any debt borrowed from a bank on behalf of the defaulted farmer. FCIC has relatively few inspectors to inspect individual claims. A farmer in Arizona can choose between planting water-hungry crops or hardy crops. Both crops cost $50. The gross returns on these plants depend on the annual rainfall. For water-hungry crops, the gross return is $100 if the annual rainfall exceeds 12 inches (50% probability) and $0 if the annual rainfall is less than 12 inches (50% probability). For hardy crops, the gross return is $60 if the annual rainfall exceeds 12 inches (50% probability) and $50 if the annual rainfall is less than 12 inches (50% probability).

Suppose a farmer borrows debt (pay back the borrowed amount, or everything he has if the cash flow is smaller than the borrowed amount) from a bank to finance the cost of planting crops. In case of a farmer’s default, the bank gets paid by FCIC. Which plant will the farmer choose? Why (show farmers’ profit for each crop).

Problem Set 2 FIN400