1. slide no.: 1 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 1 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Equity Related Products Futures and Options Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics

2. slide no.: 2 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 2 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Futures

3. slide no.: 3 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 3 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Spot – Future - Parity Today, one (theoretical) Index-Future is sold at 4.090 € (1€ per Index-point). Long and Short-positions can be described by a profit and loss diagram: 4090 Index Profit Loss Long Future = Buyer Short Future = Seller If you are Long-Future, then you may claim for delivery of „one index“ at a price of 4090 € at the maturity of the index- future. That means, if the index at delivery is quoted at more than 4090, you will win from your futures position.

4. slide no.: 4 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 4 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Spot – Future - Parity You hold an Index-Portfolio, currently valued at 5,500 € (1 Index-point = 1 €). If the annual risk free rate r f is at 3.5 % and the expected dividends on your Index portfolio are at 100 € (d = 100/5,500), an Index – Future with one year to maturity has a fair price of: To prevent our Index-Portfolio from losses, we could hedge the price risk by taking a short – future position (selling a future at 5,592.40).

5. slide no.: 5 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 5 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Spot – Future - Parity AssetsPayoff 1 Payoff 2 Payoff 3 Payoff 4 Payoff 5 Stock Portfolio +4500,00+5000,00+5500,00+6000,00+6500,00 Dividends+100,00 Short Future+1092,40+592,40+92,40-407,60-907,60 Total+5692,40 The total expected payoffs from your portfolio will depend on the future state of the environment (see below payoffs 1-5). A decreasing stock market will be compensated by profits from the short future position, increasing stock prices will be outbalanced by losses due to payment obligations from the future. Loss Profit 5692,40 Index Short Future

6. slide no.: 6 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 6 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Spot – Future - Parity AssetsPayoff 1 Payoff 2 Payoff 3 Payoff 4 Payoff 5 Stock Portfolio+4500,0 0 +5000,00+5500,00+6000,00+6500,0 0 Dividends+100,00 Short Future+1092,4 0 +592,40+92,40-407,60-907,60 Total+5692,4 0 Initially you have paid 5,500 € for your stock portfolio. Taking the short future position, the final outcome of your portfolio will be 5,692,40 €, whatever the stock price will be, i.e. you will earn 192,40 which equals 3.5%. Obviously, this profit is riskless: Spot-Future- Parity

7. slide no.: 7 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 7 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Spot – Future - Parity Rising future prices will – due to arbitrage trading - induce rising spot prices. For example, a future traded at 6,000 € is clearly overpriced, when the stock portfolio remains unchanged at 5,500 €. In this case, „smart“ traders will make arbitrage profits of 407,50 € per contract and bring back the market to equilibrium: Actiont0t0 t1t1 Borrow money at r F (3,5%)+ 5,500.00- 5,692.50 Buy/Sell Stock Portfolio- 5,500.00+ Stock Sell/Buy Future at 6,0000+ 6,000.00 - Stock Total0+ 307,50 Note, that the arbitrage profit equals the difference between a fair- and mispriced future (6,000 – 5,592,40) plus Dividends. Higher Future prices will lead to massivly increased demand at spot markets until spot prices and futures are back to equilibrium.

8. slide no.: 8 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 8 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Spot – Future – Parity Financial Market Stability Spot Markets and Future (Forward) Markets are interlinked. Mispriced spot or future market instruments will affect both markets Future market speculations that drive futures prices will also drive spot market prices due to arbitrage trading (et vice versa) Speculation on futures markets, resulting in higher future prices will induce higher spot market prices due to arbitrage trading. Finally this may result in spot market bubbles that jeopardizes the allocation mechanism of real goods markets.

9. slide no.: 9 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 9 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Options

10. slide no.: 10 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 10 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Economic Benefits Provided by Options Derivative securities are instruments that derive their value from the value of other assets. Derivatives include options, futures, and swaps. Options and other derivative securities have several important economic functions: Help bring about a more efficient allocation of risk; Save transactions costs…sometimes it is cheaper to trade a derivative than the asset underlying it, and Permit investment strategies that would not otherwise be possible.

11. slide no.: 11 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 11 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Options Vocabulary Call option Gives the holder the right to purchase an asset at a specified price on or before a certain date Put option Gives the holder the right to sell an asset at a specified price on or before a certain date Strike price or exercise price: the price specified for purchase or sale in an option contract American or European option American options allow holders to exercise at any point prior to expiration European options allow holders to exercise only on the expiration date

12. slide no.: 12 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 12 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Options Vocabulary Neither trade usually has any connection to the underlying firm. Long position The buyer of an option has a long position, and has the right to exercise the option. Short position The seller (or writer) of an option has a short position, and must fulfill the contract if the buyer exercises. As compensation, the seller receives the option premium. Can trade options on an exchange (such as CBOE) or in the over-the-counter market.

13. slide no.: 13 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 13 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Moneyness of Options CallPut S>XIn-the-moneyOut-of-the- money S=XAt-the-money S<XOut-of-the- money In-the-money S = current stock price X = strike price

14. slide no.: 14 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 14 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Option Quotations 32.50 27.50 Strik e 3.831.55May30.00 3.240.85April30.00 1.233.91May30.00 0.673.26April30.00 PutCall Expire s Opti- Tech In-the-money calls Out-of-the-money puts In-the-money puts Out-of-the-money calls Option quotations The price per share for an option contract, which is a contract to buy or sell 100 shares of the underlying stock. CBOE options expire on the third Saturday of the expiration month.

15. slide no.: 15 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 15 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Intrinsic and Time Value of Options Intrinsic value For in the money options: the difference between the current price of the underlying asset and the strike price (S-X for calls and X-S for puts). For out of the money options: the intrinsic value is zero. Time value The difference between an option’s intrinsic value and its market price (premium) Consider the May call with $27.50 strike price from previous table: Intrinsic value = $30.00 - $27.50 = $2.50 Time value = $3.91 - $2.50 = $1.41

16. slide no.: 16 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 16 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Payoff Diagrams Shows value of an option on the expiration date Y-axis plots exercise value or “intrinsic value” X-axis plots price of underlying asset Use payoff diagrams for: Long and short positions Gross and net positions (the net positions subtract the option premium) Payoff: the price of the option at expiration date

17. slide no.: 17 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 17 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Long Call Option Payoffs Payoff at Expiration -8 stock price7583 slope = 1 Net payoff Payoff x = $75, premium = $8

18. slide no.: 18 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 18 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Short Call Option Payoffs x = $75, premium = $8 Payoff at expiration +8 stock price 75 slope = -1 83 Net payoff Payoff Both long and short positions have zero net payoff at a price of $83 On net basis, buyer of the call makes a profit when the price exceeds $ 83; seller of the call makes a profit when price is below $83.

19. slide no.: 19 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 19 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Long Put Option Payoffs Payoff at expiration -7 Price of stock 75 68 Net payoff Payoff x = 75, premium = $7

20. slide no.: 20 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 20 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Short Put Option Payoffs x = 75, premium = $7 Payoff at expiration 7 Stock price 75 68 -75 Net payoff Payoff

21. slide no.: 21 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 21 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Portfolios of Options Look at payoff diagrams for combinations of options rather than just one Shows the range of potential strategies made possible by options Some positions can be a form of portfolio insurance. Some strategies allow investor to speculate on the volatility (or lack thereof) of a stock rather than betting on which direction it will move.

22. slide no.: 22 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 22 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Portfolio Containing 1 Call and 1 Put (Long Straddle) Call x = 30, premium = $4.5, Put x = 30, premium = $3.5 30 38 22 -8 Net payoff Payoff Buy a put and a call on the same stock at the same strike price and the same expiration date Profits come with large price changes in either direction. Positive net payoff if the price rises above $38 or falls below $22

23. slide no.: 23 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 23 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Option Strategies (Straddle)

24. slide no.: 24 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 24 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Option Strategies (Strangle) Strangle - Long call and long put (at different exercise prices) Strategy for profiting from high volatility Share Price Position Value Strangle

25. slide no.: 25 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 25 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Option Strategies Synthetic Long Future Synthetic Long Future (Long Call & Short Put) Position Value Share Price Long Call Short Put Exercise Price (Strike)

26. slide no.: 26 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 26 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Synthetic Short Future(Short Call & Long Put) Position Value Share Price Short Call Long Put Exercise Price (Strike) Option Strategies Synthetic Short Future

27. slide no.: 27 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 27 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Option Strategies (Short Butterfly)

28. slide no.: 28 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 28 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Other Option Portfolio Payoffs Now look at portfolios containing options, stocks, and bonds: Looking at these payoffs will help lead us to an important option pricing relationship: put-call parity. Construct portfolios that include options, stocks and bonds: Stock and put options Bond and call options

29. slide no.: 29 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 29 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Gross Payoff of Stock + Put x x Stock price Payoff at expiration $X = strike price of put Position allows investor to profit if stock price rises above $X. If stock price falls below $X, portfolio provides protection: put option allows investor to sell at a price no lower than $X.

30. slide no.: 30 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 30 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Gross Payoff of Bond + Call x x stock price $X = strike price of call and face value of bond Payoff at expiration The bond assures a minimum payoff of $X The call allows for a higher payoff if the stock price rises This payoff diagram and the preceding one are identical!

31. slide no.: 31 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 31 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Put-Call Parity Future payoffs of “stock+put” are identical to payoffs of “bond+call” provided: Put and call have same exercise price and expiration date; Underlying stock pays no dividends during life of options; Put and call are European options; Bond is risk-free, zero-coupon, price at maturity = strike (X), Bond matures when options expire. If two assets A and B, have same future payoffs with certainty, then they should sell for the same price now Price of put + price of stock = Price of call + price of bond P + S = C + B

32. slide no.: 32 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 32 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Factors Affecting Option Prices (holding other factors equal) Price of underlying asset Asset price and call price are positively related. Asset price and put price are negatively related. Time to expiration More time usually makes options more valuable. Strike price Higher X means higher put price; lower X means higher call price. Interest rate Calls: higher rate means higher call value. Puts: higher rate reduces put value.

33. slide no.: 33 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 33 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Evaluation Framework Assume that a stock is currently quoted at 150 €. If nothing happens over the coming year, the stock‘s price will also be at 150 € in one year. The one-year risk free rate is at 10%. Under this assumptions, a Call – Option, maturing one year from now with a strike of 120 € is easy to value: 1 year Stock – price t 0 : 150 € Stock – price t 1 : 150 € Strike Call t 1 : 120 € = 120 X 2,7184 – 0,10 Strike Call t 0 ( PV): 108,58 € The Intrinsic Value of the Call (X-S) is 41,42 € !!

34. slide no.: 34 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 34 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Evaluation Framework Under this conditions, the Call Option Pricing Model is like: This price is a fair price, as it does not allow to gain risk-free profits from arbitrage-trading: One could also borrow money to buy the stock now. At a risk free rate of 10% p.a. the cost of borrowing over one year will add to ((150€ x (2,7184 0,10) - 1)) 15.7764 €. The other way round – borrowing money to buy the option - and one year later the stock leads to the same borrowing costs: Borrowing of 41,42 € at 10% means to pay back 41,42 x 2,7184 0,10 = 45,7764 € after one year. Netted with the profit from the option‘s exercise at a strike of 120 € (150 € - 120 € = 30 €), the costs add to 15.7764 €.

35. slide no.: 35 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 35 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Determinants of Option Prices VariableDirectionOption Price Strike...the higher the strike...the smaller the price Term to Exercise...the longer the duration...the higher the price Price of the Underlying...the higher the price Interest Rate...the higher the rate...the higher the price Volatility of the Underlying...the higher the volatility...the higher the price

36. slide no.: 36 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 36 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Price & Value Chart Strike Intrinsic Value Premium Option Price Intrinsic Value Time Value Stock Price Option Price Time Value in the money at the money Out of the money „Greeks“ show the sensitivity of the option price referring to:  = Delta: Call Price and Spot Price  = Gamma: Delta  = Theta: Call Price and Time to Expiration  = Kappa / Vega: Call Price and Volatility  = Rho: Call Price and Int. Rate

37. slide no.: 37 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics slide no.: 37 Prof. Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Factors Affecting Option Prices Volatility Suppose a stock now worth $40 might increase or decrease in value by $10: Call option with X = $40 will pay $10 or $0. Now suppose a stock worth $40 might increase or decrease in value by $20: Call option with X = $40 will pay $20 or $0. The 2nd call option is more valuable…upside is better, downside the same as the 1st option.