** HOMEWORK. **

**
Assignment 1, due Tuesday, January 23, 2018, in class. **

Scenario 1: Suppose the price of Cisco stock on January 21 is $120 per share. This current price of the stock is called the spot price of the stock. The holder of the option will exercise it and make a net profit per share of $120 -$70 -$33 (spot price of stock on January 21 - price under exercise of option - option price) and hence a net profit of $1,700. This is a 1700/33 % = 51.5% profit on the $3,300 initial investment. On the other hand, if the $3,300 had been directly invested in stock, the investor could have bought 32 whole shares of stock and the profit would have been $18 times 32 = $576 on an investment of $ 102 times 32 = $3,264, which is a 57600/3264% = 17.6% profit.

Scenario 2: Suppose the price of Cisco stock on January 21 is $67 per share. The holder of the option will not exercise it and takes a loss of $33 per share (the cost of the option per share) and hence a net loss of $3,300. This is a 100% loss on the $3,300 initial investment. On the other hand, if the $3,300 had been invested directly in stock, the loss would have been $35 times 32 =$1,120 or a 34.3% loss on an investment of $3,264 in stock.

** 2. ** Suppose that a stock is currently selling for $50 per share.
A forward contract is to be written committing the holder of the long position in the contract
to buy 100 shares of
stock 3 months from now for $51 per share. Suppose that a bank
is charging interest on short term loans at the rate of 4% per annum (continuously compounded)
on a 3-month loan. Describe a strategy for trading in any or all of the forward contract,
the stock and a short term loan which creates an arbitrage
profit, and establish the amount of the profit.

** 3. ** A combination option called a strangle is obtained by taking a long position in a (European) call and a (European) put option with the same expiration date but differing strike prices, all based on the same underlying asset.
An investor who buys the strangle is betting that
there will be a large movement in the price of the underlying,
but is uncertain whether it will involve an increase or a decrease in the price.
Find a formula for the payoff for a strangle where the call has a strike price of K1 and the put has a strike price of K2 and K2 < K1. Draw a graph of this payoff as a function of the final price of the underlying asset. (Make sure to label your axes on the graph.)

From Chapter 2, Exercises 2 (part (d) is optional), 3 (part (d) is optional), 5 (note that you can use the result from Exercise 4 if you wish - there is a typo in the book at the end of Exercise 5, it should read "Exercise 4" rather than "Exercise 3").

One more problem (not optional): Consider the CRR model described in Exercise 2 of Chapter 2 as the model for a stock and a bond. A forward contract is to be offered under which the holder of a long position in the forward contract will buy 100 shares of stock at time T=2 for a fixed price F. (Here F is the total amount to be paid for the 100 shares). Remember that no money changes hands at time zero when a forward contract is written. What value should F take in order that there is no arbitrage opportunity for the investor who holds a long or a short position in the contract? Explain your reasoning fully (in particular, identify an associated European contingent claim and derive the value of F using arbitrage pricing for the contingent claim).

** Assignment 3, due Tuesday, February 20, 2018, in class. **

Exercises 6, 7 (except (d) parts) from Chapter 2, Exercise 2 from Chapter 3, and
the exercise in this pdf file, click here to access it.

** Assignment 4, due Thursday, March 1, 2018, in class. **

Exercises 3, 4 in Chapter 3.