Economics 434 Theory of Financial Markets

1. Economics 434Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

2. Three Main Types of Derivatives • Options • Futures (Forwards) • Swaps

3. Options • Calls and Puts • Originially for stocks • Now calls and puts for everything: options on futures, options on bonds, options on ? • What determines the price of a call? • Volatility (standard deviation of stock price) • Risk free rate • Plus (current stock price, exercise price, maturity)

4. Cox-Ross Example • Consider the following portfolio • Short 3 calls with ex price of 50 • Long 2 shares of stock • Borrow $ 40 at 25 % interest rate • What is the liquidation value of this portfolio? • At $ 100 per share • Pay $ 150 on short calls • Receive $ 200 on sale of 2 shares of stock • Pay $ 50 to lender • At $ 25 per share • Calls worth zero • Sell shares; receive $ 50 • Pay $ 50 to lender • Zero liquidation value regardless of outcome • Current price is $ 50, then calls must be $ 20 each

5. Future • Suppose gold is $ 1600 per troy ounce • What is a three month future worth (assume no storage or security costs)? • Need to know risk free rate. Suppose 12 % per annum or 3 % per three months • Buy gold, sell future should earn 3 %. Thus future price = 1.03 times 1600 = 1648 • So buy 100 at 1648

6. You now own 100 3 month gold futures at 1648 • What do you pay? • Nothing. Instead you have to put up “good faith collateral” to ensure that, when the time comes, you will pay the $ 164,800 that you owe. Let’s suppose you have to put up $ 25,000 as good faith collateral. • If price of gold goes up, the future price will go up as well. Suppose price goes up to 1748. • You’ve made $ 10,000. The exchange will credit you with $ 10,000 cash. (Wow 40 % profit on your $ 25,000!)

7. Is there another side? • Yes, • Suppose future price falls to 1548 • Margin call of $ 10,000 (immediately)

8. The End