Peter KRIŠTOFÍK
Ekonomická fakulta UMB
Banská Bystrica, Slovensko

The key to understanding derivatives is a deeper understanding of all that's underlying. (Morgan Stanley)
Derivatives are nothing more than a set of tools. And just as a saw can build your house, it can cut off your arm if it isn't used properly. (Walter D. Hops)
Derivatives are not the devil incarnate. But they may not be the Holy
Grail either. (Andrew M. Coleman)
Derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal. (Warren
Buffet)
Derivatives don't kill companies. People kill companies. (Anonymous)





Presunutie rizík na subjekty, ktoré sú ochotné a schopné ich prevziať /zmiernenie, rozkladanie/
Elimináciu rizík je možné dosiahnuť zaujatím presne opačných pozícií, v aktívach, ktoré sú dokonale korelované
Zisky a straty z jednotlivých obchodov sa navzájom kompenzujú, výsledkom čoho je zaistenie pozície
Účinný a efektívny mechanizmus riadenia finančných rizík (trhové…kreditné)






Dosiahnutie zisku na základe očakávaní o budúcom vývoji kurzu a zaujatím adekvátnej pozície /Bull vs.
Bear/
Zisk vs. Riziko
Gearing/Leverage
Zostavenie jednoduchých/komplexných stratégií
Vytvorenie štruktúr s rôznou rizikovou expozíciou
/volatilita.../

•
•


Dosiahnutie zisku bez podstúpenia rizika
Cenové diferencie na rôznych trhoch
 medzi derivátovými trhmi v rovnakom čase
 medzi derivátovým a spotovým trhom
(cash&carry, reverse cash&carry)
Zabezpečenie efektívneho trhu bez cenových anomálií
Existencia transakčných nákladov




Kombinácia dvoch alebo viacerých investičných produktov na vytvorenie nového produktu.
Vytvorenie nových resp. zdokonalenie existujúcich finančných nástrojov a ich použitie v existujúcich/nových oblastiach
Typickým prípadom je situácia, keď neexistuje základný produkt, ktorý uspokojuje potreby jednotlivých strán.




Reštrukturalizácia existujúcich charakteristík finančných transakcií
Komplexné riadenie finančných rizík
Produkty použité arbitrážistami:


Synthetic long position on stock (viď neskôr)
Synthetic short position on stock (viď neskôr)

Opcia predstavuje právo (ale nie povinnosť) na nákup alebo predaj určitého podkladového aktíva za vopred dohodnutú cenu k stanovenému dátumu v budúcnosti.
Za toto právo zaplatí kupujúci opcie predávajúcemu opčnú prémiu.

kupujúci
(long) predávajúci
(short) kúpna (call) právo kúpiť povinnosť predať predajná (put) právo predať povinnosť kúpiť

Zisk
+
Zisk
Exspiračná cena
Zisk
+
Premia
Zisk
Cena bázy Premia
Strata
-
Strata
Bod zlomu Strata
-
Bod zlomu
Exspiračná cena
Cena bázy
Strata long call opcia short call opcia

Profil zisku a straty put opcia
+
Zisk
Zisk
EC
Strata
-
Bod zlomu long put opcia
Zisk
+
Cena bázy premia
Strata
Strata
-
Loss
Bod zlomu
EC
Zisk premia
Cena bázy short put opcia

Tradingové stratégie
Hedgingové stratégie
Arbitrážne stratégie
Singulárne
Kombinované
Bezriziková arbitráž Cenové rozdiely medzi jednotlivými spotovými trhmi
Rozdiely medzi cenami na spotovom a termínovom trhu
Rozdiely medzi cenami jednotlivých nástrojov na termínovom trhu
Riziková arbitráž
Prioritne zamerané na dosahovanie čo najvyššieho zisku pri čo najnižšom riziku.
Prioritne zamerané na zmierňovanie rizík. Sekundárny cieľ dosahovanie zisku.
Dosahovanie zisku pri minimálnej úrovni rizika.
(využítím cenových rozdielov)

Profit
+
Premium
Loss
-
Loss
Strike
Price
Break even price
Profit
+
Profit
Stock price
Loss
Loss
-
Break even price
Strike
Price
Profit Profit
Premium
Stock price
Loss
Net option cost
Long position on call + Short position on put = Synthetic long position on stock

Profit
+
Profit
Strike price
Loss
-
Break even price
Profit
+
Stock price Premium
Premium
Loss
Loss
-
Profit
Break even
Strike price price
Profit
Stock price
Loss
Loss
Long position on put
+ Short position on call
Net option cost
= Synthetic short position on stock

Stock
Direction
Up
Neutral
Down
Low
Volatility Level
Neutral High






Covered Call Writing
Put Writing
Collar
Straddle/Strangle
Spreads


Bull Spreads
Bear Spreads

Covered Call Writing
Long Stock
3.00
2.00
1.00
0.00
-1.00
8.
50
9.
80
11
.1
0
12
.4
0
13
.7
0
15
.0
0
16
.3
0
17
.6
0
18
.9
0
20
.2
0
21
.5
0
-2.00
-3.00
-4.00

Covered Call Writing
Long Stock
3,00
2,00
1,00
0,00
-1,00 8,
50
9,
80
11
,1
0
12
,4
0
13
,7
0
15
,0
0
16
,3
0
17
,6
0
18
,9
0
20
,2
0
21
,5
0
-2,00
-3,00
-4,00



Unlimited profit potential
Potential loss equivalent to the stock price
Establish a long position as it is more likely that the stock price will rise than fall

Covered Call Writing
Long Stock
3,00
2,00
1,00
0,00
-1,00 8,
50
9,
80
11
,1
0
12
,4
0
13
,7
0
15
,0
0
16
,3
0
17
,6
0
18
,9
0
20
,2
0
21
,5
0
-2,00
-3,00
-4,00
 Do you really believe that the stock will continue to climb the next three months?

Covered Call Writing
Long Stock
3.00
2.00
1.00
0.00
-1.00
8
.5
0
9
.8
0
1
1
.1
0
1
2
.4
0
1
3
.7
0
1
5
.0
0
1
6
.3
0
1
7
.6
0
1
8
.9
0
2
0
.2
0
2
1
.5
0
-2.00
-3.00
-4.00
 If your answer is no, then why not sell this potential to someone else who believes it is possible?

How?
Long Stock
3.00
2.00
1.00
0.00
-1.00
8
.5
0
9
.8
0
1
1
.1
0
1
2
.4
0
1
3
.7
0
1
5
.0
0
1
6
.3
0
1
7
.6
0
1
8
.9
0
2
0
.2
0
2
1
.5
0
-2.00
-3.00
-4.00



Determine an upside target price for the stock to reach in the next three months
Would you be ready to sell at this price?
If yes, sell a call option with a strike price close to your target price

Covered Call Writing
 Hold or buy the underlying value and sell the call option, if you wish to:

Profit from a price increase in the underlying value

Hedge against a small drop in the underlying value

Generate additional income

Covered Call Writing
Long stock Short call option
3.00
2.00
1.00
Break-Even Point
0.00
-1.00
11
.5
0
12
.5
0
-2.00
13
.5
0
14
.5
0
15
.5
0
16
.5
0
17
.5
0
18
.5
0
Strike Price
19
.5
0
20
.5
0
-3.00

Covered Call Writing
Covered call w rite position
4.00
3.00
2.00
1.00
0.00
-1.00
11
.5
0
-2.00
-3.00
12
.5
0
Break-Even Point
$14.00
Maximum Profit
$17.50
13
.5
0
14
.5
0
15
.5
0
16
.5
0
17
.5
0
18
.5
0
19
.5
0
20
.5
0

Covered Call Writing
 Example

April 19th
 Buy 1000 shares of ABC at $14
 Debit: $14,000 (1000 shares x $14)
 Sell 10 contracts ABC June 15 calls at $0.50
 Credit: $500 (10 contracts x 100 shares x $0.50)

Covered Call Writing
 Result

Scenario 1
 The stock price is above $15

What is the profit or loss?

Covered Call Writing
 Result

Scenario 2
 The stock price stays at $14

What is the profit or loss?

Put Writing
Long Stock
3.00
2.00
1.00
0.00
-1.00
8.
50
9.
80
11
.1
0
12
.4
0
13
.7
0
15
.0
0
16
.3
0
17
.6
0
18
.9
0
20
.2
0
21
.5
0
-2.00
-3.00
-4.00

Put Writing
Long Stock
3.00
2.00
1.00
0.00
-1.00
8
.5
0
9
.8
0
1
1
.1
0
1
2
.4
0
1
3
.7
0
1
5
.0
0
1
6
.3
0
1
7
.6
0
1
8
.9
0
2
0
.2
0
2
1
.5
0
-2.00
-3.00
-4.00



Unlimited profit potential
Potential loss equivalent to the stock price
Establish a long position as you believe that it is more likely that the stock price will rise than fall

Put Writing
Long Stock
3.00
2.00
1.00
0.00
-1.00
8
.5
0
9
.8
0
1
1
.1
0
1
2
.4
0
1
3
.7
0
1
5
.0
0
1
6
.3
0
1
7
.6
0
1
8
.9
0
2
0
.2
0
2
1
.5
0
-2.00
-3.00
-4.00
 Do you believe that the stock can lose its entire value in the next three months?

Put Writing
Long Stock
3.00
2.00
1.00
0.00
-1.00
8
.5
0
9
.8
0
1
1
.1
0
1
2
.4
0
1
3
.7
0
1
5
.0
0
1
6
.3
0
1
7
.6
0
1
8
.9
0
2
0
.2
0
2
1
.5
0
-2.00
-3.00
-4.00
 If your answer is no, then why not sell that potential to someone else who believes it is possible?

How?
Long Stock
3.00
2.00
1.00
0.00
-1.00
8
.5
0
9
.8
0
1
1
.1
0
1
2
.4
0
1
3
.7
0
1
5
.0
0
1
6
.3
0
1
7
.6
0
1
8
.9
0
2
0
.2
0
2
1
.5
0
-2.00
-3.00
-4.00



Determine a downside target price for the stock to reach in the next three months
Would you be ready to buy at this price?
If yes, sell a put option with a strike price close to your target price

Put Writing
 Hold cash and sell put options, if:

You wish to profit from a price increase in the underlying value

You expect a small drop in price of the underlying value

You wish to have the opportunity to buy the underlying value at a better price

You wish to generate additional income on the cash position

Put Writing
Short put option
-1.50
-2.00
-2.50
-3.00
-3.50
1.50
1.00
0.50
0.00
-0.50
8.
50
-1.00
Margin required to cover potential losses
9.
50
10
.5
0
11
.5
0
12
.5
0
13
.5
0
Put Price
$1.00
14
.5
0
15
.5
0
16
.5
0
17
.5
0
18
.5
0
19
.5
0
Strike Price
$12.50
Break-Even
Point
$11.50

Put Writing
 Example

April 19th
 You are ready to buy 1000 ABC shares at $25
 The actual ABC stock price: $27
 Sell 10 contracts of ABC June 25 puts at $1.00
 Credit: $1000 (10 contracts x 100 shares x $1.00)
 Margin required
 $25/share ($24 personal funds + $1 premium received)

Put Writing
 Result

Scenario 1
 The share price falls under $25
 What is the profit or loss?

Put Writing
 Result

Scenario 2
 The share price stays at $27
 What is the profit or loss?

Collar
 Hold or buy the underlying value
 Buy a put option and sell a call option, if you wish to:

Hedge against a drop in the underlying price

Profit from a price increase

Establish a hedging strategy at low cost

Collar
Long stock Long put option Short call option
2
1,5
1
0,5
0
-0,5
8,
5
-1
-1,5
-2
Put Strike Price
$12.50
Stock Price
$15.00
Break-Even Point
$18.35
9,
5
10
,5
11
,5
12
,5
13
,5
14
,5
15
,5
16
,5
17
,5
18
,5
19
,5
20
,5
Break-Even Point
$11.50
Call Strike Price
$17.50

Collar
Collar
3.00
2.00
1.00
0.00
-1.00
8.
5
-2.00
-3.00
Maximum Loss
$12.50
Break-Even Point
$15.15
9.
5
10
.5
11
.5
12
.5
13
.5
14
.5
15
.5
16
.5
17
.5
18
.5
19
.5
20
.5
Maximum Profit
$17.50

Collar
Collar
3,00
2,00
1,00
0,00
-1,00
8,
5
-2,00
-3,00
Maximum Loss
$12.50
Break-Even Price
$15.15
9,
5
10
,5
11
,5
12
,5
13
,5
14
,5
15
,5
16
,5
17
,5
18
,5
19
,5
20
,5
Maximum Profit
$17.50
Maximum Profit = Strike price of the call option – Stock price + Premium received – Premium paid
Maximum Loss = Stock price – Strike price of the put option – Premium received + Premium paid
Break-Even Price = Stock price + Premium received – Premium paid

Straddle
 Simultaneously buy a call option and a put option with the same strike price and the same expiry month

Volatility play

Take advantage of leverage

Take advantage of wide swings in the price of the underlying shares

Uncertain about the price direction

Straddle
Call option Put option
-1
-2
5
4
3
2
1
0
Put Price
$1.30
Call Price
$1.25
10,00 11,25 12,50 13,75 15,00 16,25 17,50 18,75 20,00

Straddle
Call option Put option Straddle
5
4
3
0
-1
-2
-3
2
1
Put Price
$1.30
$12.45
Break-Even
Point
Straddle
$2.55
Call Price
$1.25
$17.55
10,00 11,25 12,50 13,75 15,00 16,25 17,50 18,75 20,00

Straddle
Call Option Put Option Straddle
0
-1
-2
-3
2
1
5
4
3
Price of Put
$1.30
$12.45
Break-Even
Price
Price of
Straddle
$2.55
Price of Call
$17.55
$1.25
10,00 11,25 12,50 13,75 15,00 16,25 17,50 18,75 20,00
Maximum Profit = Unlimited
Maximum Loss = Cost of premiums paid
Break-Even Price = Strike Price – Premium and strike price + Premium

Strangle
 A strangle is a close cousin of a straddle
 A strangle strategy also requires the simultaneous buy of a call option and a put option with the same expiry month but with different strike prices
(Out-of-the-money)

Strangle
Call option Put option Strangle
-3
-4
4
3
2
1
0
-1
-2
9,
00
Put Price
$0.90
Break-Even
Prices
10
,0
0
$11.35
11
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
Strangle
$1.65
Call Price
$0.75
17
,0
0
18
,0
0
19
,0
0
$18.65
20
,0
0
21
,0
0

Strangle
Call Option Put Option Strangle
4
3
2
1
-3
-4
0
-1
9,
00
-2
Price of Put
$0,90
10
,0
0
$11.35
11
,0
0
12
,0
0
13
,0
0
Break-Even
Price
14
,0
0
15
,0
0
16
,0
0
Price of
Strangle
$1.65
17
,0
0
Price of Call
$0.75
$18.65
18
,0
0
19
,0
0
20
,0
0
21
,0
0
Maximum Profit = Unlimited
Maximum Loss = Cost of premiums paid
Break-Even Price = Strike price (X1) – Premium and strike price (X2) + Premium

Covered Strangle
 Hold or buy the underlying value and simultaneously sell an out-of-the-money call option and a put option with the same expiry month, for a quantity equivalent to the shares held, if you wish to:

Profit from a price increase in the underlying value





Hedge against a small drop in the underlying value
A small drop in the underlying price is expected
Have the opportunity to buy the underlying at a better price
Generate additional income on the share position
Generate additional income on the cash position

Covered Strangle
Call option Put option
1
0
-1
-2
-3
-4
4
3
2
9,00 10,00 11,00 12,00 13,00 14,00 15,00 16,00 17,00 18,00 19,00 20,00 21,00
Put Price
$0.90
Call Price
$0.75

Covered Strangle
Call option Put option Strangle
4
3
2
1
0
-1
-2
-3
-4
Strangle
$1.65
Break-Even
Price
$11.35
$18.65
9,00 10,00 11,00 12,00 13,00 14,00 15,00 16,00 17,00 18,00 19,00 20,00 21,00
Put Option
$0.90
Call Option
$0.75

Covered Strangle
Strangle Stock
4,00
3,00
2,00
1,00
0,00
-1,00
-2,00
9,
00
-3,00
-4,00
10
,0
0
$11.35
11
,0
0
Strangle
$1.65
12
,0
0
13
,0
0
14
,0
0
Break-Even
Price
Long Stock
$15
15
,0
0
16
,0
0
17
,0
0
18
,0
0
$18.65
0
19
,0
20
,0
0
21
,0
0

Covered Strangle
Combined position
-1
-2
-3
-4
-5
-6
-7
-8
4
3
2
1
0
9,
00
10
,0
0
11
,0
0
Break-Even
Price
$13.35
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
Limited profits following the sale of the initial share position
19
,0
0
20
,0
0
21
,0
0
Steeper loss line
Twice more shares

Combined Position
-1
-2
-3
-4
-5
-6
-7
-8
4
3
2
1
0
9,
00
10
,0
0
Break-Even
Price
$13.35
11
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
Capped profits following sale of
18
,0
0 initial position
19
,0
0
20
,0
0
21
,0
0
Rapidly increasing losses
Twice more shares
Maximum Profit = Strike price of the call option – Stock price + Premiums received
Maximum Loss = Stock price – Premiums received
Break-Even Price = Stock price – Premiums received

Spreads
 Simultaneous buy and sell of options
(calls or puts)

Bull spread
 With call options
 With put options

Bear spread
 With call options
 With put options

Bull Spreads


Bull spread

Purchase of an option financed in part by the sale of another option with a higher strike price
Bull call spread


ABC = $15
Buy ABC June 15 C (X1) = $2.50




Sell ABC June 20 C (X2) = $0.50
Net cost of options = Sale (X2) – Purchase (X1)
Net cost of options = $0.50 - $2.50 = -$2.00
Net cost of options = $2.00 Debit

Bull Call Spread
Long call position Short call position
8,00
6,00
Short Call
Price (X2)
$0.50
4,00
2,00
Long Call
Price (X1)
$2.50
0,00
11
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
-4,00

Bull Call Spread
4,00
3,00
2,00
$17.00
Bull Call Spread - Profit and Loss
Break-Even Price
Maximum Profit
$3.00
1,00
0,00
11
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
-2,00
-3,00
Maximum Loss
$2.00
Maximum Profit = X2 – X1 – Net cost of options ($20 - $15 - $2 = $3)
Maximum Loss = Net cost of options ($2)
Break-Even Price = X1 + Net cost of options ($15 + $2 = $17)

Bull Spreads


Bull spread

Purchase of an option financed in part by the sale of another option with a higher strike price
Bull put spread





ABC = $20
Buy ABC June 15 P (X1) = $0.50
Sell ABC June 20 P (X2) = $2.50
Net premium received = Sale (X2) – Purchase (X1)
Net premium received = $2.50 - $0.50 = $2.00 credit

Bull Put Spread
Long put position Short put position
4,00
2,00
Short Put
Price (X2)
$2.50
0,00
-2,00
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
-4,00
-6,00
Long Put
Price (X1)
$0.50
-8,00

Bull Put Spread
-2,00
-3,00
-4,00
3,00
2,00
1,00
Bull Put Spread - Profit and Loss
Break-Even Price
$18.00
Maximum Profit
$2.00
0,00
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
Maximum Loss
$3.00
Maximum Profit = Net cost of options ($2)
Maximum Loss = X2 – X1 – Net cost of options ($20 - $15 - $2 = $3)
Break-Even Price = X2 – Net cost of options ($20 - $2 = $18)

Bear Spreads


Bear spreads

Purchase of an option financed in part by the sale of another option with a lower strike price
Bear call spread





ABC = $15
Sell ABC June 15 C (X1) = $2.50
Buy ABC June 20 C (X2) = $0.50
Net premium received = Sale (X1) – Purchase (X2)
Net premium received = $2.50 - $0.50 = $2.00 credit

Bear Call Spreads
-4,00
-6,00
-8,00
Short call position (X1) Long call position (X2)
4,00
2,00
0,00
11
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
Short Call
Price (X1)
$2.50
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
Long Call
Price (X2)
$0.50

Bear Call Spread
Bear Call Spread - Profit and Loss
3,00
2,00
1,00
Maximum Profit
$2.00
Break-Even Price
$17.00
0,00
-1,00
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
-2,00
-3,00
-4,00
Maximum Loss
$3.00
Maximum Profit = Net cost of options ($2)
Maximum Loss = X2 – X1 – Net cost of options ($20 - $15 - $2 = $3)
Break-Even Price = X2 – Net cost of options ($20 - $3 = $17)

Bear Spreads
 Bear spreads

Purchase of an option financed in part by the sale of another option with a lower strike price
 Bear put spread

ABC = $20





Sell ABC June 15 P (X1) = $0.50
Buy ABC June 20 P (X2) = $2.50
Net cost of options = Sale (X1) – Purchase (X2)
Net cost of options = $0.50 - $2.50 = -$2.00
Net cost of options = $2.00 Debit

Bear Put Spread
Short put position Long put position
8,00
6,00
4,00
Short Put
Price (X1)
$0.50
2,00
0,00
-2,00
,0
0
12
,0
0
-4,00
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
Long Put
Price (X2)
$2.50
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0

Bear Put Spread
Bear Put Spread - Profit and Loss
4,00
3,00
2,00
1,00
Maximum Profit
$3.00
Break-Even Price
$18.00
0,00
-1,00
,0
0
12
,0
0
13
,0
0
14
,0
0
15
,0
0
16
,0
0
17
,0
0
18
,0
0
19
,0
0
20
,0
0
21
,0
0
22
,0
0
23
,0
0
24
,0
0
-2,00
-3,00
Maximum Loss
$2.00
Maximum Profit = X2 – X1 – Net cost of options ($20 - $15 - $2 = $3)
Maximum Loss = Net cost of options ($2)
Break-Even Price = X2 – Net cost of options ($20 - $2 = $18)

Which Strategy?
Stock
Direction
Up
Low
Buy Calls
Bull Spreads
Calls: (B) ATM/(S) OTM
Puts: (B) ATM/(S) ITM
Volatility Level
Neutral
Buy the stock
High
Put Writing
Covered Call Writing
Bull Spreads
Calls: (B) ITM/(S) ATM
Puts: (B) OTM/(S) ATM
Neutral
Buy
Straddle/Strangle
Go on vacation
Write
Straddle/Strangle
Down
Buy Puts
Bear Spreads
Calls: (B) ATM/(S) ITM
Puts: (B) ATM/(S) OTM
Sell the stock
Call Writing
Bear Spreads
Calls: (B) OTM/(S) ATM
Puts: (B) ITM/(S) ATM
ITM = In-the-money
(B) = Buy
ATM = At-the-money
(S) = Sell
OTM = Out-of-the-money
Source : Sheldon Natenveg, Option Volatility Pricing: Advanced Trading Strategies & Techniques, McGraw-Hill Publishers