Option Theory Problems

1. Suppose you want to speculate using call options. To do so, you form a long straddle by buying a call (Premium = $6) and buying a put (Premium = $3), where both options have the same 1-year maturity and the same $55 exercise price. a) Draw a graph showing the profits from the two-option portfolio as a function of the underlying asset's price. In particular, explicitly show the numerical profits for ST = 0 and ST = X.

2. Compute the price of a European call option with the following parameter values: S = $28, X = $30, r = 5% p.a., σ= 30%, T = 1 year. You may use the "normal" table, and use the closest value in the table to the number that you are looking for. In other words, you need not interpolate.

3. Compute the price of a European call option with the following parameter values: S = $28, X = $30, r = 5% p.a., σ= 30%, T = 2 years. You may use the "normal" table, and use the closest value in the table to the number that you are looking for. In other words, you need not interpolate.

4. What do problems 2 and 3 illustrate regarding the relationship between option prices and time to maturity?

5. Compute the price of a European put option with the following parameter values: S = $200, X = $200, r = 6% p.a., σ= 40%, T = 9 months. You may use the "normal" table, and use the closest value in the table to the number that you are looking for. In other words, you need not interpolate.

6. Compute the price of a European put option with the following parameter values: S = $200, X = $160, r = 6% p.a., σ= 40%, T = 9 months. You may use the "normal" table, and use the closest value in the table to the number that you are looking for. In other words, you need not interpolate.

7. What do problems 5 and 6 illustrate regarding the relationship between put option prices and strike price?

8. You buy a put option and sell the corresponding call option. Both options have an exercise price of $100. In addition, you also buy 1 share of IBM stock. What is the net payoff you receive from this 3-asset portfolio if at expiration the price of each share of IBM stock is a) $120; b) $12. You must draw the relevant graph.

9. Suppose you want to speculate using call options. To do so, you form a short straddle by selling a call (Premium = $9) and selling a put (Premium = $7), where both options have the same maturity (T=1 year) and the same exercise price (X=$100).

a) Draw a graph showing the profits from the two-option portfolio as a function of the underlying asset's price.

b) What are the numerical values of the profits for ST = 0 and ST = X?

c) Which price(s) of the underlying asset produce zero profits?

d) What's the minimum possible profit?

e) What's the maximum possible profit? (NOTE: Remember that profits can be positive or negative.)

10. You form a long butterfly spread by buying a call with an exercise price of X1 = $30 and a premium of C1 = $8. You continue by buying another call with an exercise price of X2 = $60 and a premium of C2 = $6. Finally, you sell two identical calls, each with an exercise price of X3 = $45 and a premium of C3 = $6.

Construct the graph of this speculative portfolio and, based on it, answer the following questions:

a) What is the profit if ST = 0?

b) What is the profit if ST = 23?

c) What is the profit if ST = 41?

d) What is the profit if ST = 55?

e) What is the profit if ST = 82?