Options dan Futures DWITYAPOETRA S. BESAR MATA KULIAH : ANALISIS INVESTASI DAN MANAJEMEN RISIKO PROG STUDI MAGISTER MANAJEMEN UNIVERSITAS TRISAKTI

Transcription

1 Options dan Futures DWITYAPOETRA S. BESAR MATA KULIAH : ANALISIS INVESTASI DAN MANAJEMEN RISIKO 2013 PROG STUDI MAGISTER MANAJEMEN UNIVERSITAS TRISAKTI

2 Bahan Bodie, Kane, and Marcus (BKM), 2009, Investments, 8 th (global) edition, McGraw-Hill / Irwin. Kuliah sesi ini: BKM, Bab 20, 21 dan 22 Soal:

3 Outline Bagian 1: Pasar Opsi Bagian 2: Valuasi Opsi Bagian 3: Pasar Futures

4 Bagian 1: Pasar Opsi

5 Terminologi Opsi Buy - Long Sell - Short Call Put Key Elements Exercise atau Strike Price Premium atau Price Maturity atau Expiration

6 Pasar Opsi Hubungan harga pasar dan eksekusi In the Money - exercise of the option would be profitable Call: market price>exercise price Put: exercise price>market price Out of the Money - exercise of the option would not be profitable Call: market price<exercise price Put: exercise price<market price At the Money - exercise price and asset price are equal

7 Opsi Tabel Opsi saham IBM

8 Opsi American vs. European Options American - the option can be exercised at any time before expiration or maturity European - the option can only be exercised on the expiration or maturity date

9 Opsi Jenis Opsi Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options

10 Opsi Payoffs and Profits at Expiration - Calls Notation Stock Price = S T Exercise Price = X Payoff to Call Holder (S T - X) if S T >X 0 if S T < X Profit to Call Holder Payoff - Purchase Price

11 Opsi - Calls Payoffs and Profits at Expiration - Calls Payoff to Call Writer - (S T - X) if S T >X 0 if S T < X Profit to Call Writer Payoff + Premium

12 Opsi Grafik Payoff dan Profit to Call Option saat Expiration

13 Opsi Grafik Payoff dan Profit to Call Writers saat Expiration

14 Opsi - Puts Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0 if S > X T (X - S ) if S < X T T Profit to Put Holder Payoff - Premium

15 Opsi Payoffs and Profits at Expiration Puts Continued Payoffs to Put Writer 0 if S T > X -(X - S T ) if S T < X Profits to Put Writer Payoff + Premium

16 Opsi Strategi Opsi Straddle (Same Exercise Price) Long Call and Long Put Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration. Vertical or money spread: Same maturity Different exercise price Horizontal or time spread: Different maturity dates

17 Opsi Table 20.3 Value of a Straddle Position at Option Expiration

18 Opsi If the prices are not equal arbitrage will be possible Put Call Parity X C S P 0 r (1 ) T f

19 Opsi Contoh Put Call Parity - Disequilibrium Stock Price = 110 Call Price = 17 Put Price = 5 Risk Free = 5% Maturity = 1 yr X = X105 C S0 P (1 r ) T f 117 > 115 Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative

20 Opsi Tabel Strategi Arbitrasi

21 Opsi Sekuritas yang mirip Opsi Callable Bonds Convertible Securities Warrants Collateralized Loans

22 Opsi Exotic Options Asian Options Barrier Options Lookback Options Currency Translated Options Digital Options

23 Outline Bagian 2: Valuasi Opsi

24 Valuasi Opsi Nilai intrinsic (Intrinsic value) - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put: exercise price - stock price Nilai waktu - the difference between the option price and the intrinsic value

25 Valuasi Opsi Grafik Call Option Value sebelum Expiration

26 Valuasi Opsi Tabel Faktor Determinan Nilai Call Option

27 Valuasi Opsi Restriksi pada nilai opsi : Call Value cannot be negative Value cannot exceed the stock value Value of the call must be greater than the value of levered equity C > S 0 - ( X + D ) / ( 1 + r f ) T C > S 0 - PV ( X ) - PV ( D )

28 Valuasi Opsi Grafik Range of Possible Call Option Values

29 Valuasi Opsi Grafik Call Option Value as a Function of the Current Stock Price

30 Valuasi Opsi Contoh: Binomial Option Pricing C 90 0 Stock Price Call Option Value X = 110

31 Valuasi Opsi Binomial Option Pricing: Alternative Portfolio Buy 1 share of stock at $100 Borrow $81.82 (10% Rate) Net outlay $18.18 Payoff Value of Stock Repay loan Net Payoff Payoff Structure is exactly 3 times the Call

32 Valuasi Opsi Binomial Option Pricing: C 0 0 3C = $18.18 C = $6.06

33 Valuasi Opsi Expanding to Consider Three Intervals: Assume that we can break the year into three intervals For each interval the stock could increase by 5% or decrease by 3% Assume the stock is initially selling at 100

34 Valuasi Opsi Expanding to Consider Three Intervals Continued S + + S S + S S S - S + - S - - S S - - -

35 Valuasi Opsi Possible Outcomes with Three Intervals Event Probability Final Stock Price 3 up 1/8 100 (1.05) 3 = up 1 down 3/8 100 (1.05) 2 (.97) = up 2 down 3/8 100 (1.05) (.97) 2 = down 1/8 100 (.97) 3 = 91.27

36 Valuasi Opsi Valuasi dengan model Black-Scholes C o = S o N(d 1 ) - Xe -rt N(d 2 ) d 1 = [ln(s o /X) + (r + 2 /2)T] / ( T 1/2 ) d 2 = d 1 + ( T 1/2 ) where C o = Current call option value S o = Current stock price N(d) = probability that a random draw from a normal distribution will be less than d

37 Valuasi Opsi Black-Scholes Option Valuation X = Exercise price e = , the base of the natural log r = Risk-free interest rate (annualizes continuously compounded with the same maturity as the option) T = time to maturity of the option in years ln = Natural log function Standard deviation of annualized cont. compounded rate of return on the stock

38 Valuasi Opsi Grafik Kurva Distribusi Normal

39 Valuasi Opsi Contoh Call Option: S o = 100 X = 95 r =.10 T =.25 (quarter) =.50 d 1 = [ln(100/95) + (.10+( 5 2 /2))] / ( /2 ) =.43 d 2 =.43 + (( /2 ) =.18

40 Valuasi Opsi Probabilities dari Distribusi Normal N (.43) =.6664 Table 21.2 d N(d) Interpolation

41 Valuasi Opsi Probabilities from Normal Distribution Continued N (.18) =.5714 Table 21.2 d N(d)

42 Valuasi Opsi Tabel Cumulative Normal Distribution

43 Valuasi Opsi Nilai Opsi Call C o = S o N(d 1 ) - Xe -rt N(d 2 ) C o = 100 X e -.10 X.25 X.5714 C o = Implied Volatility Using Black-Scholes and the actual price of the option, solve for volatility. Is the implied volatility consistent with the stock?

44 Valuasi Opsi Contoh Spreadsheet utk menghitung nilai opsi Black-Scholes

45 Valuasi Opsi Menggunakan Goal Seek utk mendapatkan Implied Volatility

46 Valuasi Opsi Grafik Implied Volatility of the S&P 500 (VIX Index)

47 Valuasi Opsi Black-Scholes Model dengan Dividend The call option formula applies to stocks that pay dividends One approach is to replace the stock price with a dividend adjusted stock price Replace S 0 with S 0 - PV (Dividends)

48 Valuasi Opsi Put Value Using Black-Scholes P = Xe -rt [1-N(d 2 )] - S 0 [1-N(d 1 )] Using the sample call data S = 100 r =.10 X = 95 g =.5 T =.25 95e -10x.25 ( )-100( ) = 6.35

49 Valuasi Opsi Put Option Valuation: Using Put-Call Parity P = C + PV (X) - S o = C + Xe -rt - S o Using the example data C = X = 95 S = 100 r =.10 T =.25 P = e -.10 X P = 6.35

50 Valuasi Opsi Using the Black-Scholes Formula Hedging: Hedge ratio or delta The number of stocks required to hedge against the price risk of holding one option Option Elasticity Call = N (d 1 ) Put = N (d 1 ) - 1 Percentage change in the option s value given a 1% change in the value of the underlying stock

51 Valuasi Opsi Portfolio Insurance Buying Puts - results in downside protection with unlimited upside potential Limitations Tracking errors if indexes are used for the puts Maturity of puts may be too short Hedge ratios or deltas change as stock values change

52 Valuasi Opsi Hedging On Mispriced Options Option value is positively related to volatility: If an investor believes that the volatility that is implied in an option s price is too low, a profitable trade is possible Profit must be hedged against a decline in the value of the stock Performance depends on option price relative to the implied volatility

53 Valuasi Opsi Hedging dan Delta The appropriate hedge will depend on the delta Recall the delta is the change in the value of the option relative to the change in the value of the stock Delta = Change in the value of the option Change of the value of the stock

54 Outline Bagian 3: Pasar Futures

55 3. Pasar Futures Futures dan Forwards Forward - an agreement calling for a future delivery of an asset at an agreed-upon price Futures - similar to forward but feature formalized and standardized characteristics Key difference in futures Secondary trading - liquidity Marked to market Standardized contract units Clearinghouse warrants performance

56 3. Pasar Futures Key Terms untuk Futures Contracts Futures price - agreed-upon price at maturity Long position - agree to purchase Short position - agree to sell Profits on positions at maturity Long = spot minus original futures price Short = original futures price minus spot

57 3. Pasar Futures Tabel Futures Listing

58 3. Pasar Futures Grafik Profits to Buyers and Sellers of Futures and Option Contracts

59 3. Pasar Futures Tabel Contoh Kontrak Future

60 3. Pasar Futures Clearinghouse - acts as a party to all buyers and sellers Obligated to deliver or supply delivery Closing out positions Reversing the trade Take or make delivery Most trades are reversed and do not involve actual delivery Open Interest Trading Mechanics

61 3. Pasar Futures Skema Panel A, Trading without a Clearinghouse. Panel B, Trading with a Clearinghouse

62 3. Pasar Futures Margin and Trading Arrangements Initial Margin - funds deposited to provide capital to absorb losses Marking to Market - each day the profits or losses from the new futures price are reflected in the account Maintenance or variation margin - an established value below which a trader s margin may not fall

63 3. Pasar Futures Margin and Trading Arrangements Continued Margin call - when the maintenance margin is reached, broker will ask for additional margin funds Convergence of Price - as maturity approaches the spot and futures price converge Delivery - Actual commodity of a certain grade with a delivery location or for some contracts cash settlement Cash Settlement some contracts are settled in cash rather than delivery of the underlying assets

64 3. Pasar Futures Strategi Perdagangan Speculation - short - believe price will fall long - believe price will rise Hedging - long hedge - protecting against a rise in price short hedge - protecting against a fall in price

65 3. Pasar Futures Basis dan Basis Risk Basis - the difference between the futures price and the spot price over time the basis will likely change and will eventually converge Basis Risk - the variability in the basis that will affect profits and/or hedging performance

66 3. Pasar Futures 3. Pasar Futures Grafik Hedging Revenues Using Futures (Futures Price = $97.15)

67 3. Pasar Futures Harga Futures Spot-futures parity theorem - two ways to acquire an asset for some date in the future Purchase it now and store it Take a long position in futures These two strategies must have the same market determined costs

68 3. Pasar Futures Spot-Futures Parity Theorem With a perfect hedge the futures payoff is certain -- there is no risk A perfect hedge should return the riskless rate of return This relationship can be used to develop futures pricing relationship

69 3. Pasar Futures Contoh Hedge : Investor owns an S&P 500 fund that has a current value equal to the index of $1,500 Assume dividends of $25 will be paid on the index at the end of the year Assume futures contract that calls for delivery in one year is available for $1,550 Assume the investor hedges by selling or shorting one contract

70 3. Pasar Futures Contoh Hedge Value of S T 1,510 1,550 1,610 Payoff on Short (1,550 - S T ) Dividend Income Total 1,575 1,575 1,575

71 3. Pasar Futures Rate of Return for the Hedge ( F 0 D) S S 0 (1,550 25) 1,500 1, %

72 3. Pasar Futures General Spot-Futures Parity F ( F D S 0 ) 0 S 0 r f Rearranging terms 0 S0(1 rf ) D S0(1 rf d) d D S 0

73 3. Pasar Futures Kemungkinan melakukan Arbitrasi If spot-futures parity is not observed, then arbitrage is possible If the futures price is too high, short the futures and acquire the stock by borrowing the money at the risk free rate If the futures price is too low, go long futures, short the stock and invest the proceeds at the risk free rate

74 Spread Pricing: Parity for Spreads ) ( 2 1 (1 ) ( ) (1 ) ( ) ( ) ( )(1 ) T f T f T T f r d F S T r d F S T r d F F T T 3. Pasar Futures

75 3. Pasar Futures Teori Harga Futures Expectations Normal Backwardation Contango Modern Portfolio Theory

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