2. (30 points) During the class we derived the payoff for Call and Put Options. Write a program that calculates the payofffor the buyer and the seller of each option given the price, strike price, exercise date and the interest rate. (Python)

(a) Plot the payoff 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 payoff with different spot prices.

3. (20 points)Assume the futures prices for oil are as given in Table 1

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

Table 1: Futures prices per barrel Calculate the net convenience yield for each period.

4. (30 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%. What will happen to the price of the call option if the probability of decrease in price is 1/3 instead of 1/2.

2. (30 points) During the class we derived the payoff for Call and Put Op tions. Write a program that calculates the payoff for the buyer and the seller of each option given the price, strike price, exercise date and the interest rate (a) Plot the payoff 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 payoff with different spot prices. 3. (20 points) Assume the futures prices for oil are as given in Table 1 Maturity Futures price June (2019) December (2019) October December 117.5 119.6 122.66 123.49 Risk free rates 0.0514 0.0415 0.05 0.0507 Table 1 Futures prices per barrel Calculate the net convenience yield for each period. 4. (30 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%. What will happen to the price of the call option if the probability of decrease in price is 1/3 instead of 1/2. 2. (30 points) During the class we derived the payoff for Call and Put Op tions. Write a program that calculates the payoff for the buyer and the seller of each option given the price, strike price, exercise date and the interest rate (a) Plot the payoff 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 payoff with different spot prices. 3. (20 points) Assume the futures prices for oil are as given in Table 1 Maturity Futures price June (2019) December (2019) October December 117.5 119.6 122.66 123.49 Risk free rates 0.0514 0.0415 0.05 0.0507 Table 1 Futures prices per barrel Calculate the net convenience yield for each period. 4. (30 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%. What will happen to the price of the call option if the probability of decrease in price is 1/3 instead of 1/2