2. What is a derivative?
A derivative instrument is a financial contract whose payoff
structure is determined by the value of underlying
commodity, security, interest rate, share price index,
exchange rate, oil price, or the like.
2
4. Options
Options grants the right, but not the obligation, to buy or
sell a futures contract at a predetermined price for a
specified period of time.
4
5. Basic types of Options
PUT OPTION
Gives buyer right to sell underlying futures contract.
CALL OPTION
Gives buyer right to buy underlying futures contract.
Note: In both cases the underlying commodity is a futures contract, not the physical commodity
5
6. Terms used
Strike Price (Exercise price)
The predetermined price of the futures contract
i.e. price at which the futures contract can be bought or sold.
Premium
The cost of the right to buy or sell a futures contract – cost of the option.
The buyer loses the premium regardless of whether the option is used or not.
6
7. Terms used
Option Writer :
Person selling the option, and is exposed to margin requirements
Underlying Futures :
It is corresponding Future Contract which can
be transacted by exercise in the transaction.
Exercise:
Action taken by the buyer of an option whose intention is to deliver
Or
take delivery of the underlying futures
Expiration Date:
Last date on which an option can be exercised or offset
7
8. Terms used
Open interest
1. The total number of options and/or futures contracts that are not closed or delivered on a
particular day.
2. The number of buy market orders before the stock market opens.
A common misconception is that open interest is the same thing as volume of options and
futures trades. This is not correct, as demonstrated in the following example:
-On January 1, A buys an option, which leaves an open interest and also creates trading volume of 1.
-On January 2, C and D create trading volume of 5 and there are also five more options left open.
-On January 3, A takes an offsetting position, open interest is reduced by 1 and trading volume is 1.
-On January 4, E simply replaces C and open interest does not change, trading volume increases by 5.
8
10. Call Option
A call option gives the holder the right, but not the obligation, to buy a
specific futures contract at a specific price
“To call from them”
10
11. Gold Example (Call)
Suppose that on June 1, a farmer is approached by a goldsmith for purchasing 1 tola of gold at
Rs.9,000/10gm. The Goldsmith is almost certain that he wants the gold but is unable to arrange
finance for six months. The farmer propose to grant a six-month option at Rs.9,000/10gm in
exchange for a Rs.90/10gm.
Purchaser = The Goldsmith (Option-Call buyer)
Grantor = The Farmer (Option-Call seller)
Exercise price = Rs.9,000 /10gm (Strike price)
Expiration date = December 1
Call Premium = Rs.90 (paid by goldsmith – call buyer)
11
12. Put Option
A put option gives the holder the right, but not the obligation, to sell a
specific futures contract at a specific price
“To put it on them”
12
13. Gold Example (Put)
Suppose that on June 1, a farmer approaches a goldsmith for selling 1 tola of gold at
Rs.9,000 /10gm . The Farmer is almost certain that he wants to sell the gold but is
unable to arrange the delivery for six months. The Goldsmith proposes to grant a
six-month option at Rs.9,000 /10gm in exchange for a Rs.90 /10gm.
Purchaser = The Goldsmith (Option-Put seller)
Grantor = The Farmer (Option-Put buyer)
Exercise price = Rs.9,000 /10gm (Strike price)
Expiration date = December 1
Put Premium = Rs.90 (paid by farmer-option buyer)
13
14. Options are popular because
Price Insurance.
•
Limited financial obligation.
•
Marketing flexibility.
•
14
15. Factors affecting Option Premium
Changes in the price of the underlying futures contract- E.g. gold futures
Strike Price – E.g. Rs.10,000 /10gm
Time until expiration
Volatility of the underlying futures contract
Dividends
Risk free interest rates.
15
17. Intrinsic Value
“Positive” difference between the strike price and the underlying commodity futures price.
FOR A CALL OPTION –
strike price below futures price
FOR A PUT OPTION –
strike price exceeds futures price
Note: Futures price means current price of underlying futures contract.
17
18. Intrinsic Value: An Example
May Corn Futures Price= Rs.329
What is the Intrinsic Value for a:
Q: Rs.310 Call Option?
A: Rs. 19
Q: Rs.340 Put Option?
A: Rs. 11
Q: Rs.340 Call Option?
A: Rs. 0
18
19. Time Value for Mar 07 and Apr 07 Options on Jan 1, 2007
Apr 07 Futures = 237
Mar 07 Futures = 209.25
Apr 07 240 Call Option
Mar 07 210 Call Option
Premium = 20.5
Premium = 8.625
Intrinsic Value = 0
Intrinsic Value = 0
Time Value = 20.5
Time Value = 8.625
Apr 07 240 Put Option
Mar 07 210 Put Option
Premium = 23.25
Premium = 9.5
Intrinsic Value = 3
Intrinsic Value = 0.75
Time Value = 20.25
Time Value = 8.75
19
20. TIME DECAY
Time value
0.50
0.25
0
180 0
90
Days to expiration
20
23. Deep-In-the-Money (DITM)
CALL/PUT OPTIONS
No Chance of Out-of-the-Money
Close-to-the-Money (CTM)
Strike price near Futures price
Deep-Out-of-the-Money (DOTM)
No Chance of In-the-Money
23
24. Options – Exercise Mode
American Style Options –
Buyer of the options can
choose to exercise, prior to the expiry date.
European Style Options –
Buyer of the options can
choose to exercise only on the date of expiry.
≥
American Premium European Premium
24
25. Interest rate – continuous compounding
A = P (1 + r ) t
r nt
A = P (1 + )
n
n
r r rt
A = {P (1 + ) }
n
n
r r rt
A = lim{P(1 + ) }
n →∞ n
n
r r rt
A = P{lim (1 + ) } where
n →∞ n P is principal, r is rate of interest (annual), n is
A = Pe rt frequency of compounding, t is time, A is amount.
25
26. Stochastic Process
•Any variable whose value changes over time in an uncertain way is said to follow a
stochastic process.
•Markov process:
• Present Value of a variable is relevant for predicting the future.
• Weak form of market efficiency
φ(0,1)
• Change of value can be given by probability distribution
•Change in variable in two years is sum of two independent normal distributions
• Mean is sum of the means
• Variance is sum of the variances
φ (0, 2 )
φ (0, T )
•Hence we have
26
27. Wiener Process
•A Wiener process with zero drift and variance rate of 1.0
δ z =∈ δt
•A generalised Wiener process can be written down as:
dx = adt + bdz
•Now for a small time interval we can say:
δx = aδt + b ∈ δt
δs = µ sδt
S T = S 0 e µt
δt → 0
dS
= µ dt + σ ∈ δt
S
27
28. Ito’s Lemma
dx = a ( x, t ) dt + b( x, t ) dz
∂G ∂G 1 ∂ 2 G 2 ∂G
dG = ( a+ + b )dt + bdz
∂x ∂t ∂x
2 ∂x 2
Value of a stock follows log normal distribution.
This result by Japanese Mathematician was used by Black – Scholes to solve
the Black Scholes Merton PDE.
28
29. Options Pricing
C = S 0 N ( d 1 ) − Ke − rt N ( d 2 )
P = Ke − rt N ( − d 2 ) − S 0 N ( − d 1 )
σ2
σ2 S0
S0
ln( ) + (r −
ln( ) + ( r + )T
)T
K 2
K 2 d2 =
d1 =
σT
σT
Black – Scholes Formulae
Where,
S = Spot Price
N(d) = probability that a deviation less than “d” will occur in a normal distribution with a mean zero &
standard deviation is 1
E = Exercise Price or Strike Price
e = 2.71828
29
30. Option Greeks
Delta :First derivative, considers sensitivity of options to price of future
contract. (Hedge Ratio)
Gamma : Considers sensitivity of options to changes in Delta (Curvature)
Theta : Considers sensitivity of options to time factor (time decay)
Vega : Considers sensitivity of options to market volatility.
Rho : Considers sensitivity of portfolio to interest rates.
30
31. Types of Options - Exotics
•Barrier options:
•Path dependent exotics
•Become active when underlying reaches a predetermined level (barrier)
•“In” options
•start worthless and become active if predetermined level is breached
•“Out” options
•Start active and become worthless if predetermined level is breached
•Lookback options
•Path dependent exotics
•Exercise price = previous high/low (over preceding period)
•Russian options
•Lookback option till perpetuity
31
32. Types of Options - Exotics
•Binary option
•Cash or nothing; asset or nothing
•Bermuda option
•Where buyer of the option has the right to exercise the option at a set (always
discretely spaced) number of times.
•10 yr swap or 9 yr 6 month swap
•Canary option
•Where buyer can exercise at quarterly dates but only after a fixed period of time
has elapsed. (eg. 1 year)
•Compound option
•Option on an option
32
33. Types of Options - Exotics
•Swing option
•A Bermudan option where on exercise you bet a put or call.
•Parisian option
•the payoff is dependent by time spent above or below the strike price.
•Asian option
•Payoff determined by average trading price over a defined period of time.
•Eg: average price over last 3 months.
33
37. Long Call
Comment
View
Unlimited, Increases as the Spot Price increase
Profit
Loss Limited to the premium paid
Breakeven Strike price + premium
Time Decay Hurts
Use Very Bullish Outflow
Volatility increase helps the position
Volatility
Margin No
37
38. Details of Call Option
10
Deal Details: SAMPL Analysis Parameters:
Stock Price 11000.00 Deal Date 28-Jan-08 Centre Price on Graph 11200.00 Days to Expiry 32
Initial Debit/Credit Deal Expiration 28-Feb-08 Graph Increment 100.000 Analysis Date 27-Jan-08
Volatility 30.00% Dividend
Underlying Type Spot Ex Date Pricing Model: Black-Scholes European
Risk Free Rate 5.75%
Action: Option No. Trade Override Days to Option Greeks:
Buy/Sell Type Opt'ns Volatility Expiry Price Expiry Value Debit/ Credit Delta Net
Option Trades: Strike
Option Trade 1 b c 1 10900.00 31 462.3096 (462) 0.58 In' money
Option Trade 2 9999
Option Trade 3 9999
Option Trade 4 9999
Option Trade 5 9999
Option Trade 6 9999
(462) (462)
Action: No.
Buy/Sell Shares Price
Stock Trades:
Stock Trade 1 11000
Stock Trade 2 11000
11000
Days to expiry: 32 Totals: (462) (462)
38
40. Long Futures
Comment
View
Increases as the Spot Price increase
Profit
Loss Increases as the Spot Price increase
Breakeven Purchase price + Brokerage
Time Decay No impact
Use Very Bullish outlook
No Impact
Volatility
Margin Yes
40
42. Bull Call Spread
Formation
Buy Call A and,
Sell Call B.
Variant
Buy Call A, Sell Put B and,
Short futures.
Example
Buy Gold Feb Call 10800 @ Rs. 250 and,
Sell Gold Feb Call 11200 @ Rs. 100.
42
43. Bull Call Spread
Comment
View
Limited, Maximum Profit = (B – A) – Net Premium
Profit
Loss Limited, Maximum Loss = Net Premium
Breakeven Strike A + Max Loss
Time Decay Mixed – Hurts for long call and helps for short Call
Bullish outlook
Use
Volatility Neutral
Margin Yes
43
44. An example of Bull Spread
10
Deal Details: SAMPL Analysis Parameters:
Stock Price 11000.00 Deal Date 28-Jan-08 Centre Price on Graph 11200.00 Days to Expiry 32
Initial Debit/Credit Deal Expiration 28-Feb-08 Graph Increment 100.000 Analysis Date 27-Jan-08
Volatility 30.00% Dividend
Underlying Type Spot Ex Date Pricing Model: Black-Scholes European
Risk Free Rate 5.75%
Action: Option No. Trade Override Days to Option Greeks:
Buy/Sell Type Opt'ns Volatility Expiry Price Expiry Value Debit/ Credit Delta Net
Option Trades: Strike
Option Trade 1 b c 1 10800.00 250 31 518.7498 (250) 0.62 In' money
Option Trade 2 s c 1 11200.00 100 31 317.7105 100 0.46 Out' money
Option Trade 3 9999
Option Trade 4 9999
Option Trade 5 9999
Option Trade 6 9999
(150) (150)
44
46. Bull Put Spread
Formation
Buy Put A of lower strike price and,
Sell Put B of higher strike price.
Variant
Buy Put A, Sell Call B and,
Long Futures.
Example
Buy Gold Feb PA 10800 @ Rs. 50 and,
Sell Gold Feb PA 11200 @ Rs. 250.
46
47. Bull Put Spread
Comment
View
Profit Limited, Maximum Profit = Net Premium
Limited, Maximum Loss = (B – A) - Net Premium
Loss
Breakeven Strike A + Max Loss
Mixed – Hurts for long Put and helps for short Put
Time Decay
Use Bullish outlook
Neutral
Volatility
Margin Yes
47
48. Bull Put Spread - Example
10
Deal Details: SAMPL Analysis Parameters:
Stock Price 11000.00 Deal Date 28-Jan-08 Centre Price on Graph 11200.00 Days to Expiry 32
Initial Debit/Credit Deal Expiration 28-Feb-08 Graph Increment 100.000 Analysis Date 27-Jan-08
Volatility 30.00% Dividend
Underlying Type Spot Ex Date Pricing Model: Black-Scholes European
Risk Free Rate 5.75%
Action: Option No. Trade Override Days to Option Greeks:
Option Trades: Buy/Sell Type Opt'ns Strike Volatility Expiry Price Expiry Value Debit/ Credit Delta Net
Option Trade 1 b p 1 10800.00 50 31 266.1359 (50) -0.38 Out' money
Option Trade 2 s p 1 11200.00 250 31 463.1479 250 -0.54 In' money
Option Trade 3 9999
Option Trade 4 9999
Option Trade 5 9999
Option Trade 6 9999
200 200
48
50. Short Put
Comment
View
Limited to the premium received
Profit
Unlimited, increase as the spot price decrease
Loss
Strike price - Premium
Breakeven
Time Decay Helps
Use Bullish outlook
Volatility Volatility decreases helps the position
Margin Yes
50
51. Short Put - Variant
Covered Call
Have underlying or Buy Futures, and
Write A Call
Maximum Profit
Futures < Strike = Premium + ( Strike – Futures)
Futures > Strike = Premium – (Futures – Strike)
Breakeven = Call Strike – Maximum Profit
51
52. Short Put- Example
10
Deal Details: SAMPL Analysis Parameters:
Stock Price 11000.00 Deal Date 28-Jan-08 Centre Price on Graph 11200.00 Days to Expiry 32
Initial Debit/Credit Deal Expiration 28-Feb-08 Graph Increment 100.000 Analysis Date 27-Jan-08
Volatility 30.00% Dividend
Underlying Type Spot Ex Date Pricing Model: Black-Scholes European
Risk Free Rate 5.75%
Action: Option No. Trade Override Days to Option Greeks:
Buy/Sell Type Opt'ns Strike Volatility Expiry Price Expiry Value Debit/ Credit Delta Net
Option Trades:
Option Trade 1 s p 1 10800.00 50 31 266.1359 50 -0.38 Out' money
Option Trade 2 9999
Option Trade 3 9999
Option Trade 4 9999
Option Trade 5 9999
Option Trade 6 9999
50 50
52
55. Long Straddle
Formation
Buy Call A and,
Buy Put A.
Both of the same strike price
Variant
Buy 2 Calls A & Short Futures or
Buy 2 Puts A & Long Futures
Example
Buy Gold Feb CA 10800 @ Rs. 50
Buy Gold Feb PA 10800 @ Rs. 70
55
56. Long Straddle - Example
10
Deal Details: SAMPL Analysis Parameters:
Stock Price 11000.00 Deal Date 28-Jan-08 Centre Price on Graph 10800.00 Days to Expiry 32
Initial Debit/Credit Deal Expiration 28-Feb-08 Graph Increment 100.000 Analysis Date 27-Jan-08
Volatility 30.00% Dividend
Underlying Type Spot Ex Date Pricing Model: Black-Scholes European
Risk Free Rate 5.75%
Action: Option No. Trade Override Days to Option Greeks:
Buy/Sell Type Opt'ns Strike Volatility Expiry Price Expiry Value Debit/ Credit Delta Net
Option Trades:
Option Trade 1 b c 1 10800.00 50 31 518.7498 (50) 0.62 In' money
Option Trade 2 b p 1 10800.00 70 31 266.1359 (70) -0.38 Out' money
Option Trade 3 9999
Option Trade 4 9999
Option Trade 5 9999
Option Trade 6 9999
(120) (120)
Action: No.
Buy/Sell Shares Price
Stock Trades:
Stock Trade 1 11000
Stock Trade 2 11000
11000
Days to expiry: 32 Totals: (120) (120)
56
58. Long Strangle
Formation
Buy out of the money Put A and,
Buy out of the money Call B.
Example
Buy Gold Feb PA 10800 @ Rs. 50
Buy Gold Feb CA 11200 @ Rs. 150
58
62. Long Strap
Formation
Buy 2 Calls A and,
Buy Put A
Variants
Buy 3 Calls A & Short Futures
Example
Buy Gold Feb PA 11000 @ Rs. 50
Buy 2 Gold Feb CA 11000 @ Rs. 50
62
69. Short Straddle
Formation
Sell Call A and,
Sell Put A.
Variant
Sell 2 Calls A & Long Futures or
Sell 2 puts A and Short Futures..
69
70. Short Straddle
View Comment
Profit Limited to the Net premium received
Loss Unlimited
Low BEP = Middle Strike - Profit
Breakeven High BEP = Middle Strike + Profit
Time Decay Helps
Expecting a tight sideways movement
Use
Volatility Volatility decrease helps the position
Yes
Margin
70
72. Short Strangle
Formation
Sell Call A and Sell Put B.
Variants
Sell Put A and Sell Call B
Sell Put A, Sell Put B and Short Futures
Sell Call A, Sell Call B and Long Futures
72
76. Long Put
View Comment
Profit Unlimited, Increases as the Spot price decreases
Loss Limited to the premium paid
Strike price - premium
Breakeven
Time Decay Hurts
Very Bearish Outlook
Use
Volatility Volatility increases helps the Position
Margin No
76
78. Short Futures
View Comment
Profit Increases as the Spot price decreases
Loss Increases as the Spot price increases
Breakeven Sell price + Brokerage
No Impact
Time Decay
Use Very Bearish Outlook
No impact
Volatility
Margin Yes
78
79. Bear Put Spread
View Comment
Profit Limited, Maximum Profit = (B - A) - Net Premium
Strike B - Maximum Loss
Loss
Breakeven Limited, Maximum Loss = Net Premium
Mixed - Hurts for Long Put and helps for Short Put
Time Decay
Use Bearish outlook
Neutral
Volatility
Margin Yes
79
80. Bear Put Spread
Formation
Buy Put B and Sell Put A.
Variant
Buy Call B, Short Futures & Sell Put A
Example
Buy Gold Feb PE 11200 @ Rs. 250 and,
Sell Gold Feb PE 10800 @ Rs. 50.
80
81. Bear Put Spread
10
Deal Details: SAMPL Analysis Parameters:
Stock Price 11000.00 Deal Date 28-Jan-08 Centre Price on Graph 11200.00 Days to Expiry 32
Initial Debit/Credit Deal Expiration 28-Feb-08 Graph Increment 100.000 Analysis Date 27-Jan-08
Volatility 30.00% Dividend
Underlying Type Spot Ex Date Pricing Model: Black-Scholes European
Risk Free Rate 5.75%
Action: Option No. Trade Override Days to Option Greeks:
Buy/Sell Type Opt'ns Volatility Expiry Price Expiry Value Debit/ Credit Delta Net
Option Trades: Strike
Option Trade 1 s p 1 10800.00 50 31 266.1359 50 -0.38 Out' money
Option Trade 2 b p 1 11200.00 250 31 463.1479 (250) -0.54 In' money
Option Trade 3 9999
Option Trade 4 9999
Option Trade 5 9999
Option Trade 6 9999
(200) (200)
81
83. Bear Call Spread
View Comment
Profit Limited, Maximum Profit = Net Premium
Limited, Maximum Loss = (B - A) - Net Premium
Loss
Breakeven Strike B - Maximum Loss
Mixed - Hurts for Long Call and helps for Short Call
Time Decay
Bearish Outlook
Use
Neutral
Volatility
Margin Yes
83
84. Bear Call Spread
Formation
Buy Call B and Sell Call A.
Variant
Buy Call B, Short Futures & Sell Put A
Example
Buy Gold Nov CA 230 @ Rs. 7.50 and,
Sell Gold Nov CA 210 @ Rs. 18.
84
85. Short Call
View Comment
Profit Limited to the premium received
Unlimited, increases as the spot price increases
Loss
Breakeven Strike price + Premium
Helps
Time Decay
Bearish Outlook
Use
Volatility decreases helps the position
Volatility
Margin Yes
85
87. OPTIONS PRICING
Put – Call Parity
Formula:
C + PV (x) = P + S
Where,
C = present value of the call
P = present value of the put
S = present value of the underlying
PV(x) = present value of the strike price discounted from the expiration date at a suitable risk free rate.
87
