About the Speaker - Interactive Brokers...Rajib manages the course segment on option derivatives;...
Transcript of About the Speaker - Interactive Brokers...Rajib manages the course segment on option derivatives;...
Rajib manages the course segment on option derivatives; and also works with exchanges, financial & educational institutions to design educational programs. He has conducted workshops and conferences in America, Europe and Asia. Rajib has worked with leading HFT firm Optiver in Amsterdam; working on options derivatives market making, & high frequency equity arbitrage strategies across all major European & US exchanges. Before Optiver, Rajib was a management strategy consultant with PricewaterhouseCoopers where he assisted a consortium in setting up a national commodity derivatives exchange. A national Olympiad finalist, Rajib has twice represented India at the World Puzzle Championships. He has a post-graduate management degree from Indian Institute of Management Calcutta, a bachelor’s degree in Computer Engineering from National Institute of Technology Surathkal; and has internship experiences with Bloomberg in New York (equity option derivatives research) & with Solutia’s EMEA strategy HQ in Belgium.
About the Speaker
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Rajib Ranjan Borah Co-Founder & Director - QuantInsti™
Price of option from Black Scholes formula
Delta = ∂C/∂S or ½(∂C/∂S- + ∂C/∂S+) to be more precise = N(d1)
Delta
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)()( 21 dNXedSNC rtt
−−=
t
trXS
dt
σ
σ )2
()ln(2
1
++=
dzexN
zx 2
2
21)(
−
∞−∫=
π
Call Delta vs Underlying Price
Gamma: Delta vs Underlying Price
5
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
80 85 90 95 100 105 110 115 120
Delta
of o
ptio
n
Underlying Price
Call 90 Strike
Call 100 Strike
Call 110 Strike
Put Delta vs Underlying Price
Gamma: Delta vs Underlying Price
6
-1.000
-0.900
-0.800
-0.700
-0.600
-0.500
-0.400
-0.300
-0.200
-0.100
0.00080 85 90 95 100 105 110 115 120
Delta
of o
ptio
n
Underlying Price
Put 90 Strike
Put 100 Strike
Put 110 Strike
Call Delta vs Time left to expiry
Charm: Delta vs Time
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0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0.0001 25 50 75 100 125 150 175 200
Delta
of o
ptio
n
Days to Expiry
Call 90 Strike
Call 100 Strike
Call 110 Strike
Underlying Price = 100 Volatility = 20%
Put Delta vs Time left to expiry
Charm: Delta vs Time
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-1.000
-0.900
-0.800
-0.700
-0.600
-0.500
-0.400
-0.300
-0.200
-0.100
0.0000.0001 25 50 75 100 125 150 175 200
Delta
of o
ptio
n
Days to Expiry
Put 90 Strike
Put 100 Strike
Put 110 Strike
Underlying Price = 100 Volatility = 20%
Call Delta vs Volatility
Vanna: Delta vs Volatility
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0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
0.900
1.000
0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0%
Delta
of o
ptio
n
Implied Volatility
Call 90 Strike
Call 100 Strike
Call 110 Strike
Put Delta vs Volatility
Vanna: Delta vs Volatility
10
-1.000
-0.900
-0.800
-0.700
-0.600
-0.500
-0.400
-0.300
-0.200
-0.100
0.0000.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0%
Delta
of o
ptio
n
Implied Volatility
Put 90 Strike
Put 100 Strike
Put 110 Strike
Gamma
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As we have seen, deltas change with underlying price (more so towards expiry)
Gamma is the second derivative of the change of option price with respect to change in underlying price
= ∂2C/∂S2 = ∂Δ/∂S = N’(h)/ (Sσ√t)
Speed: Gamma vs Price of Underlying
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Gamma vs Price of Underlying
0.000
0.010
0.020
0.030
0.040
0.050
0.060
80 85 90 95 100 105 110 115 120
Gam
ma
of o
ptio
n
Underlying Price
Call 90 Strike
Call 100 Strike
Call 110 Strike
Color: Gamma vs Time
13
Gamma vs Time
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.0001 25 50 75 100 125 150 175 200
Delta
of o
ptio
n
Days to Expiry
Call 90 Strike
Call 100 Strike
Call 110 Strike
Zomma: Gamma vs Volatility
14
Gamma vs Volatility
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0%
Delta
of o
ptio
n
Implied Volatility
Call 90 Strike
Call 100 Strike
Call 110 Strike
Vanna: Vega vs Underlying Price
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Vega at different strikes
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
0.200
80 85 90 95 100 105 110 115 120
Vega
of o
ptio
n
Underlying Price
Call 90 Strike
Call 100 Strike
Call 110 Strike
Veta: Vega vs Time
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Vega of an option with varying time left to expiry
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.0001 25 50 75 100 125 150 175 200
Vega
of o
ptio
n
Days to Expiry
Call 90 Strike
Call 100 Strike
Call 110 Strike
Vomma: Vega vs Volatility
17
Sensitivity to volatility is sensitive to volatility itself
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.140
0.160
0.180
0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0%
Vega
of o
ptio
n
Implied Volatility
Call 90 Strike
Call 100 Strike
Call 110 Strike
Thega: Theta v/s Time to expiration
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Theta with changing time to expiry
-160
-140
-120
-100
-80
-60
-40
-20
00 20 40 60 80 100 120
Thet
a
Days to expiry
K=100
K=110
K=90
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