Chapter 5. Introduction to Financial instruments

Chapter 5 Introduction to Financial instruments

5.1 Introduction Securities ( 證券 ) = all financial instruments Assets/ Equities ( 資產 ) Stocks( 股票 ) ownership of the firm Commodities ( 商品 ) e.g. oil, gold, silver Debts ( 債務 ) Bonds( 債券 ) lend money to the firm

5.1 Introduction Financial market Exchange traded ( 交易所買賣 ) Trade at Hong Kong Exchanges and Clearing Limited ( 港交所 ) Contracts are standard Virtually no credit risk Over the counter ( 市場櫃檯買賣 ) Trade at private financial institutions/corporations Non-standard contracts More credit risk

5.1 Introduction Two Classes of financial instruments. Fundamental instruments Stocks( 股票 ) ownership of the firm Bonds( 債券 ) lend money to the firm Derivatives ( 衍生工具 ) Payoffs depends on fundamental instruments or other derivatives. 1. Forwards( 遠期交易 )/Futures( 期貨 ) 2. Options( 期權 ) / Warrants ( 窩輪 ) 3. Swaps( 掉期 )

5.2. Fundamental instruments Why do they exist? Raise money Stocks( 股票 ) ownership of the firm Share the earning If bankrupt, get the residuals after clearing the debts Limited liability: maximum possible loss = stock price Bonds( 債券 ) lend money to the firm fixed-income-security Credit/default risk US Treasury bond --- safe!

Stock

Bonds

5.3. Derivatives ( 衍生工具 ) A financial derivative is a security whose value depends on the value of other more elementary securities, like equity, bond and commodity. Examples Call Options on stock When you hold a call option, you have the option to buy a stock with $ K (strike price, 行使價 ) at time T (maturity, 到期日 ). Stock price = S, Strike price = K, term to maturity = T Payoff = Max(S T -K, 0)

5.3. Financial derivative 1) Forwards ( 遠期交易 )/Futures ( 期貨 ) Exchange asset with cash at a fixed time Forward: private agreements Future: standardized, trade in exchange market Buy asset long, Sell asset -- short

5.3. Financial derivative 1) Futures Forwards ( 遠期交易 )-private agreements, unregulated Mark is leaving HK next month. He has a car Tony will buy Mark s car for $2000 next month Futures ( 期貨 ) - standardized, traded in the exchange market Contractor can t afford a hike in metal price. Long metal futures at future price $K Purchase metal at $K in the future. free from fluctuation of metal price. Performance is guaranteed by Clearing house ( 結算所 )

5.3. Financial derivative 1) Futures Payoff of Forward/Futures Future price: K price of the underlying securities at maturity: S Long position Payoff = S-K Short position Payoff = K-S Long position Short position Payoff Payoff 45 o -45 o K price at maturity S K price at maturity S

5.3 Financial derivative 2) Options Options ( 期權 ) Call ( 認購 ) Put ( 認沽 )

5.3 Financial derivative 2) Options

Example Draw the payoff of a long call with strike K=40 with call price c=2 Draw the profit/loss of a short put with strike K=50 and put price p=3.

Example Draw the payoff of a long call with strike Payoff K=40 with c=2 45 o Draw the profit/loss of a short put with strike K=50 and put price p=3. Profit/loss 40 price at maturity S 3 50-45 o price at maturity S

5.3 Financial derivative 2) Options Options styles European( 歐式 ): exercise on expiration day American( 美式 ): can exercise anytime Barrier( 界限 ): the right to exercise depends on a given barrier level Asian( 亞洲式 ): Average-value option

Barrier options Barrier: the right to exercise depends on a given barrier level B Up and out. S o <B, if S>B before T, then contract is void. Down and out S o >B, if S<B before T, then contract is void. Up and in S o <B, if S>B before T, then contract is activated. Down and in S o >B, if S<B before T, then contract is activated.

Bull( 牛市 ) and bear( 熊市 ) market

Callable Bull/Bear Contracts ( 牛熊證 ) CBBC The contract is Called back when S hits B. Callable Bear ( 熊證, 看淡 ) expect S to fall S o <B, if S>B before T, then contract is void. Up-and-out put option. Callable Bull ( 牛證, 看好 ) expect S to rise S o >B, if S<B before T, then contract is void. Down-and-out call option. Strike price K = 行使價 Call price B = 回收價

Example Beginning time=04 Maturity time T=02 Find the payoff for a) A Call option with strike K=64. b) A put option with strike price 65. c) A down-and-out call option with strike price 50 and Barrier 55 d) An up-and-in put option with strike price 85 and Barrier 83 e) A Callable Bull contract with Strike price strike price 75 and Barrier 78

Example Beginning time=04 Maturity time T=02 Find the payoff for a) A Call option with strike K=64. payoff=65.3-64=1.3 b) A put option with strike price 65. payoff=0 c) A down-and-out call option with strike price 50 and Barrier 55 payoff=65.3-50=15.3 d) An up-and-in put option with strike price 85 and Barrier 83 payoff=85-65.3=19.7 e) A Callable Bull contract with Strike price strike price 75 and Barrier 78 Contract is called back, payoff=0

Buying Options

Asian options A(T) = 1 T T i 1 S i

5.3 Financial derivative 2) Options Warrant( 窩輪 / 認股證 ) Has the same function as an call option Written by a company on its own stock Issuance of new shares of stock.

5.3. Financial derivative 3) Swaps Swaps Two parties exchanges financial instruments. E.g. Currency swap (both parties avoid exchange rate risk)

5.3. Financial derivative 3) Swaps Swaps Two parties exchanges financial instruments. E.g. Interest rate swap Party 1 expects LIBOR drops. Party 2 expects LIBOR rises

5.3. Financial derivative 3) Swaps Example If you are party 1 (who expects LIBOR drops), then what is your accumulated gain/loss at the maturity? (assume that you can invest in LIBOR rate for the gain/loss)

5.4. Option Strategies Question: Can you find a trading strategy with probability of winning bigger than 50%?

5.4 Option Strategies Straddle long call and put, same strike and maturity Strangle long call and put, same maturity, Bull spread buy call with, sell call with Bear spread buy call with, sell call with Butterfly

5.4 Option Strategies Straddle long call and put with same strike and maturity

5.4 Option Strategies Straddle long call and put with same strike and maturity long position: gain if option fluctuates short position: gain if option stays

5.4 Option Strategies Strangle long call and put, same maturity, similar to straddle, but wider range

5.4 Option Strategies Bull spread buy call with, sell call with gain if stock rises, less premium, limited profit

5.4 Option Strategies Bear spread buy call with, sell call with gain if stock falls, less premium, limited profit

5.4 Option Strategies Butterfly long position: gain if stock price stays

Can you find a trading strategy with probability of winning bigger than 50%? yes, you can: consider a strangle But don t forget the severity win a little, lose a lot ( 嬴粒糖, 輸間廠 )

Examples Call options on a stock are available with strike price 15, 17.5 and 20. Their prices are $4, 2, 0.5 respectively. Create a bear spread Create a butterfly spread

Examples Call options on a stock are available with strike price 15, 17.5 and 20. Their prices are $4, 2, 0.5 Profit/loss respectively. Create a bear spread Profit: If S T <15, profit= 3.5 If S T >20, profit= -1.5-0.5 4 15 20 Create a butterfly spread Profit: If S T <15, profit= -0.5 If S T >20, profit= -0.5 If S T =17.5, profit = 2 Profit/loss 4 15-0.5 20

5.5 Clearinghouse ( 結算所 ) and margin( 孖展 ) Clearinghouse a corporation that ensures that future contracts trade smoothly Guarantees that traders fulfill their obligations Margin is the fund deposited by traders to ensure that they fulfill the obligations Initial margin amount deposit at the beginning Maintenance margin a barrier If the margin fund fall below maintenance margin, need additional deposit If no additional deposit, the clearinghouse will sell the contract i.e. cut position ( 斬倉 ) Variation margin = additional deposit ( 補倉 )

5.5. Margin for future Future: 200 ounces of gold, $400/ounce,($ 80000) Initial margin = 4000, maintenance margin= 3000 If future contract < $395 and no additional deposit is made, the bank can sell the future contract and secure $80000

5.5. Margin for stock Stock price=$100 You purchase the stock: invest $20, borrow $80 from bank Initial Margin=20, Maintenance Margin=10 If stock <$90, the bank can sell the stock, retain $80

Why buy the margin for stock Stock selling $100, take $20, borrow $80 from bank Initial Margin=20, Maintenance Margin=10 If stock>$120, you can sell the stock, return $80 to bank Invest $20, get $40. If you buy stock, you need to invest $100 to get $120. Higher risk = Higher possible return

Importance of Derivatives Market completeness ( 完整市場 ) In a complete market For any financial instrument/derivative, its payoff can be obtained (replicated) by trading other securities available in the market. Speculation ( 投機 ) Allows traders to expose themselves to well-understood risks in pursuit of profit. Prediction for commodity price, interest/exchange rate e.g. expensive call option means the stock price may rise Risk management Derivatives can help risk managers to hedge the risks.

Hedging examples A US company will pay 10 million for imports from Britain in 3 months hedge using a long position in a forward contract on. You father owns 800 HSBC shares currently worth $70 per share. He need $50000 in the coming Sep to pay for your school fees. buy put option with strike $62.5.

Arbitrage ( 套戥 ) There will be a match of Team A vs Team B. Jerry: A must win tonight. I ll bet $400 with your $100. Henry: A and B must draw tonight. I ll bet $400 with your $100. Terry: B must win tonight. I ll bet $400 with your $100. What would you do?

Arbitrage = Free lunch Arbitrage involves locking in a riskless profit by constructing a portfolio with 100% chance of non-negative income. Intuitively, arbitrage means you can earn money for sure.

How to take Arbitrage opportunity The only rule: Buy low, sell high Example S 0 =85, T=1 yr, i=0 Strike K Price Call 1 75 11 Call 2 80 5 Which is low, which is high?

How to take Arbitrage opportunity The only rule: Buy low, sell high Example S 0 =85, T=1 yr, i=0 Buy Call 2, Sell Call 1 Time 0: payoff = -5 +11=+6 Time 1: Strike K Price Call 1 75 11 Call 2 80 5 If S 1 <75: payoff = 0 If 75<S 1 <80: payoff = -(S 1-75) > - 5 If S 1 >80: payoff = -(S 1-75) +(S 1-80) = -5 Profit is at least 6-5 = 1 for any case Arbitrage!

More examples in No-arbitrage S 0 =100, T=1 yr, i=0.1, K=110 Call price: c = 2 Put price: p = 1

More examples in No-arbitrage S 0 =100, T=1 yr, i=0.1, K=110 Call price: c = 2 Put price: p = 1 Buy put, sell call Time 0: payoff = -1 +2= +1 Time 1: If S 1 <110: payoff = 110-S 1 If S 1 >110: payoff = -(S 1-110) Need to hold stock Borrow money to buy Stock!

More examples in No-arbitrage S 0 =100, T=1 yr, i=0.1, K=110 Call price: c = 2 Put price: p = 1 Buy put, sell call, borrow 100 to buy Stock Time 0: payoff = -1 +2-100 + 100 = +1 Time 1: If S 1 <110: payoff = (110-S 1 ) + S 1-100x1.1 = 0 If S 1 >110: payoff = -(S 1-110) + S 1-100x1.1 = 0 Profit Time 0: 1 Time 1: 0 for all cases Arbitrage!

No Arbitrage From: http://bwog.com/tag/free-food/

No Arbitrage principle Arbitrage opportunities cannot last for long We assume no arbitrage opportunity exists in financial markets. The market is called efficient ( 效率市場 ) if no arbitrage opportunity exists. No-arbitrage principle is important for pricing The price should not lead to arbitrage. construct a replicating portfolio that mimic the payoff structure of a derivative at maturity. $ of derivative = $ of portfolio now

1) Bond pricing Bonds - P +cf +cf +cf +(1+c)F Price Replicating portfolio: deposit k ( 1 i) for k periods (1 c) F and deposit for T periods (1 i) T Bond price = current value of the replicating portfolio: cf c c c 1 c P F 2 T i i i 1 (1 ) (1 ) (1 ) (1 i) T k=1,2..t-1

2) Futures Pricing Long a future Payoff = S T -K Expected present value present value?= S 0 K/(1+r) In fact, price = S 0 K/(1+r) where r is the interest rate for the whole period

2) Futures Pricing Long a future Payoff = S T K price=value of the contract now Pricing by replicating portfolio Replicating portfolio Hold the stock + borrow K/(1+r) Payoff at maturity = S T -K current value = S 0 -K/(1+r) price of future = current value of Rep. portfolio = S 0 - K/(1+r)

2) Futures Pricing Short Selling Selling securities that you do not own Your broker borrows the securities from another client and sells them in the market in the useful way At some later time, you have to buy the securities so they can be returned to the client. e.g. S 0 =120. You expect S drops. Borrow 500 shares and sell it. Time 0 Borrow 500 & sell +60000 Time 1 S pay 500 dividend - 500 Time 0 Borrow 500 & sell +60000 Time 1 S pay 500 dividend - 500 Time 2 S T =100, buy stock and return -50000 Time 2 S T =130, buy stock and return -65000 +9500-5500 Scenario 1 Scenario 2

2) Futures Pricing Alternative method to prove the price (prove by contradiction) Find arbitrage opportunity if price > S 0 K/(1+r) Find arbitrage opportunity if price < S 0 K/(1+r) S 0 =40, K=39.9, r=0.05, price = S 0 K/(1+r)=40-39.9/(1.05)=2

3) Option pricing Simple case Binomial Tree r=0.12, Call option with K=21 What is the price of the call, c?

3) Binomial Tree r=0.12, Call option with K=21 Call option payoff: Case 1: Stock goes up: $+1 Case 2: Stock goes down: $ 0 Replicating portfolio X units of Stocks Y units of bank deposit Case 1: Stock goes up: 22X+1.12Y Case 2: Stock goes down: 18X+1.12Y Find the replicating portfolio = Solve for

3) Binomial Tree Solve for X=0.25, Y=-4.017857 Hold 0.25 shares of stock +borrow $4.0178 At maturity Payoff of option = Payoff of replicating portfolio At the beginning Call price c = Value of replicating portfolio = 20X+Y=0.982

3) Option pricing If there are sunlight, water and carbon dioxide, trees grow... 2-step Binomial Tree r=0.12, Call option with K=21 What is the price of the call, c?

3) 2-step Binomial Tree r=0.12, Call option with K=21 What is the price of the call, c?