清华大学：《期权、期货衍生产品》（英文版） Chapter3 ForwardandFuturesPrices

3. Forward and futures prices Summary Short selling The repo rate Forward Contracts Forward Price vs, Futures price Stock index Futures Forward and futures contracts on currencies Charles cao

1 Charles Cao 3. Forward and Futures Prices ◼ Summary ◼ Short Selling ◼ The Repo Rate ◼ Forward Contracts ◼ Forward Price vs. Futures Price ◼ Stock Index Futures ◼ Forward and Futures Contracts on Currencies

Short Selling Selling securities that you do not own and buying them back later Yield a profit if the price of a security goes down Yield a loss if the price of a security goes up a Real world application Charles cao 2

2 Charles Cao Short Selling ◼ Selling securities that you do not own and buying them back later ◼ Yield a profit if the price of a security goes down ◼ Yield a loss if the price of a security goes up ◼ Real world application

Short Selling: Example You call your broker and instruct him to short 100 shares of att He will borrow 100 shares of att from another client Sell them in the open market at $50 per share Deposit the cash in your account Charles cao 3

3 Charles Cao Short Selling: Example ◼ You call your broker and instruct him to short 100 shares of ATT ◼ He will borrow 100 shares of ATT from another client ◼ Sell them in the open market at $50 per share ◼ Deposit the cash in your account

Short Selling: Example a You instruct your broker to close out the position 10 days later. He will buy 100 shares of att and return them to the client If the price is $48 the profit is $200 If the price is $51, the loss is $100 Charles cao

4 Charles Cao Short Selling: Example ◼ You instruct your broker to close out the position 10 days later. He will buy 100 shares of ATT, and return them to the client ◼ If the price is $48, the profit is $200 ◼ If the price is $51, the loss is $100

Short Selling Shares can only be sold on an uptick (price increases) a Margin requirement Some brokers pay interest on margin accounts Dividends and interest received by the investor will be transferred to the client from whom the shares were borrowed Charles cao

5 Charles Cao Short Selling ◼ Shares can only be sold on an uptick (price increases) ◼ Margin requirement ◼ Some brokers pay interest on margin accounts ◼ Dividends and interest received by the investor will be transferred to the client from whom the shares were borrowed

The Repo rate The risk-free rate available to investors is the repo rate repurchase agreement You sell securities to another investor Buy them back at a higher price The difference between the two prices is the interest earned by the counterparty Charles cao

6 Charles Cao The Repo Rate ◼ The risk-free rate available to investors is the repo rate, repurchase agreement ◼ You sell securities to another investor ◼ Buy them back at a higher price ◼ The difference between the two prices is the interest earned by the counterparty

The Repo rate Repo is slightly higher than the t-bi rate Overnight repo term repo Charles cao

7 Charles Cao The Repo Rate ◼ Repo is slightly higher than the T-bill rate ◼ Overnight repo, term repo

Forward contracts Notations. expiration day current time T-t: the life of the contract(in years) price of asset underlying forward contract at t Charles cao

8 Charles Cao Forward Contracts ◼ Notations: T : expiration day t : current time T-t : the life of the contract (in years) St : price of asset underlying forward contract at t T

Forward contracts Notations:(cont St: price of asset underlying forward contract at T F: forward price at t r: risk-free rate per year k: delivery price in forward contract f: value of a long forward contract Charles cao

9 Charles Cao Forward Contracts ◼ Notations: (cont.) ST : price of asset underlying forward contract at T F : forward price at t r : risk-free rate per year K: delivery price in forward contract f : value of a long forward contract

Forward contracts a Forward contracts on a security that provides no income Determine today's forward price using no arbitrage argument Charles cao

10 Charles Cao Forward Contracts ◼ Forward contracts on a security that provides no income ◼ Determine today’s forward price using no￾arbitrage argument