University of Illinois at Urbana-Champaign Department of Economics
Aram Grigoryan
Project 2
ECON426 – Monetary Economics Due April 13th
1. (25 points) During the class we derived the payo for Call and Put Op- tions. Write a program that calculates the payo for the buyer and the seller of each option given the price, strike price, exercise date and the interest rate.
(a) Plot the payo for the buyer of the European call option with strike price $100 and option price $5. Exercise date is 3 months from now and the interest rates in the economy are 6% yearly.
(b) Consider the case where you bought a call option for $5 and you can sell a similar call option for $4 and strike price $102. Plot your payo with dierent spot prices.
2. (25 points)Assume the futures prices for oil are as given in Table 1
Table 1: Futures prices per barrel
Calculate the net convenience yield for each period.
3. (25 points) Suppose the spot price of company A’s share is $80 in the market. It can change ±20% in a month with equal probabilities. How much is the price of European call option with strike price of $80, given the annual risk free interest rate is 5%? How the price will change if the likely changes are now ±10%.
4. (25 points)(python is not required) Akerlof’s model for the adverse selec- tion. Recall our adverse selection model we discussed in class. Suppose the seller tries to sell a car that has quality of q. The seller gets utility of 1.1q from holding the car and wants to sell the car for 12000. Buyers treat the quality of any car to be greater than 4000 and drawn from a uniform
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Maturity
October
December
June (2019)
December (2019)
Futures price
117.5
119.6
122.66
123.49
Risk free rates
0.0415
0.05
0.0514
0.0507
distribution. Find the highest possible marginal utility from the quality of the potential buyer that agreed to buy the car and explain why there are ineciencies in trade in such markets.
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