Managing an Option Portfolio and how Automated Trading makes it easier

Managing an Option Portfolio
Rajib Ranjan Borah
3-August-2013
- and how automated trading makes it easier

2
Topics
Fundamentals
Strategies
Managing
positions
Sophistication
through
automation
© Copyright 2010-2014 QuantInsti Quantitative Learning Private Limited

3
• Understanding basics of options
Topics
Fundamentals and derivatives
Strategies
Managing
positions
Sophistication
through
automation

4
• A Few Simple Option Trading
Strategies
Topics
Fundamentals
Strategies
Managing
positions
Sophistication
through
automation

5
• Initiating and Managing Option
Positions
• Handling risks – different risk
management parameters
Topics
Fundamentals
Strategies
Managing
positions
Sophistication
through
automation

6
Topics
• Advanced Trading Strategies
• Complex Position Management
using Automation
Fundamentals
Strategies
Managing
positions
Sophistication
through
automation

7
Fundamentals Strategies Position Management Automation & Sophistication
• Definitions:
• Derivative is a financial instrument whose price is derived from the price of
some other financial instrument.
• Option is a special type of derivative instrument - the buyer of the option
has the option (i.e. right but not the obligation) to buy/sell a specified
amount of underlying asset at a specified price on or before a specified
date
• Other types of common derivatives:
Future: the owner of such a derivative is obligated to buy/sell a specified
amount of underlying asset at a specified price on a specified date
Forward: Same as futures, but traded OTC instead of in the exchange

8
• Two types of options
• Call Options: Buyer has the option (but not the obligation) to buy the underlying
• Put Options: Buyer has the option (but not the obligation) to sell the underlying
• Defining Characteristics of Option Instruments
• Strike: Price of the underlying at which the option can be exercised
• Expiry Date: The date at which the option can be exercised
• Premium: Upfront payment made by the buyer of the option (to the seller)
• Option Styles
• European: can be exercised only on expiry date
• American: can be exercised anytime prior to expiry date
• Exotic – Bermudan, Asian, Binary, Barrier, etc

9
Option Types elaborated
CALL OPTION PUT OPTION
B
U
Y
E
R
S
E
L
L
E
R
The right
(but not the obligation)
to buy
The right
(but not the obligation)
to sell
The potential obligation
to buy
The potential obligation
to sell

10
Payoff from holding a call option instrument
Consider a Call Option on XYZ stock with strike = 30, expiry date = 30th
August 201X
At Expiry the payoff of the call option for the buyer is as shown below:
Strike at 30
Will only exercise the
call option if underlying
at expiry is more than
the strike
14
12
10
8
6
4
2
0
20 22 24 26 28 30 32 34 36 38 40 42
Underlying price at expiry
For e.g., if the
underlying price is at
36, the buyer of the
option can buy the
underlying at 30.
Hence, a payoff of 6.

11
Payoff from holding a put option instrument
Consider a Put Option on XYZ stock with strike = 30, expiry date = 30th August
201X.
At Expiry the payoff of the put option for the buyer is as shown below:
12
10
8
6
4
2
0
Will only exercise the
call option if underlying
at expiry is less than
the strike
Strike at 30
For e.g., if the
underlying price is at
23, the buyer of the
option can sell the
underlying at 30.
Hence, a payoff of 7.
20 22 24 26 28 30 32 34 36 38 40 42

12
Payoff - Buy Call Option
4
2
0
-2
-4
-6
-8
-10
Payoff - Sell Call Option
Payoff - Buy Put Option
4
2
0
-2
-4
-6
-8
Premium
Strike
Payoff - Sell Put Option
© Copyright 2010-2014 QuantInsti 12 Quantitative Learning Private Limited
12
10
8
6
4
2
0
-2
-4
20 22 24 26 28 30 32 34 36 38 40 42
Premium
Breakeven Point
-12
20 22 24 26 28 30 32 34 36 38 40 42
10
8
6
4
2
0
-2
-4
20 22 24 26 28 30 32 34 36 38 40 42
Underlying Price at Expiry
-10
20 22 24 26 28 30 32 34 36 38 40 42

13
Terminology – Moneyness
Terminology Call Option Put Option
In the Money (ITM) Underlying Price > Strike Underlying Price < Strike
At the Money (ATM) Underlying Price = Strike Underlying Price = Strike
Out the Money (OTM)
Underlying Price < Strike Underlying Price > Strike

14
Option Premium (price) components:
• Option price = Intrinsic Value + Time Value
• Intrinsic Value: Immediate value of the option given the current relationship
between the price of underlying and the price of the option
For call options, intrinsic value = underlying – option strike
For put options, intrinsic value = option strike - underlying
• Time Value: Because the buyer of the option has the upside benefits but not
downside obligations, therefore future price movements in the underlying
can benefit (but not harm) the buyer – therefore there is an additional value
for the option instruments for the extra benefits future price movements
might bring
An option with no intrinsic value is an Out of The Money Option

15
Option Pricing Methodology
• Pricing depends on key characteristics of instrument
• Option Strike
• Option Expiry date
• Current Underlying Price
• Characteristics of price change in underlying (volatility, price jumps, etc)
• Interest Rate & Stock Borrowing Rates
• Dividends
• Option type (Call/Put)
• Option Style (American/European)

16
Option Pricing Methodology
• Common Pricing Formulations
Underlying Characteristic Pricing Methodology
Constant Volatility Black Scholes
Constant Volatility with Dividends Black Scholes Merton
Constant Volatility with Poisson Jumps Merton Jump Diffusion
Volatility as a function of Underlying price CEV
Volatility as a function of Underlying price & time to
Derman Kani
expiry
Volatility is volatile Heston
American type expiry Barone Adesi Whaley, Bjerksund Stensland
Currency Options Garman Kohlhagen

17
Simple Option Trading Strategies
• Option Trading can be used to express following types of views
• view on the price of the underlying in the future
• view on the volatility of the price movements of the underlying
• view on interest rates
• combined view on more than one of the above factors

18
Expressing views on the price(/direction of price change) of the underlying
• Naked Call/Put option
• Call Bull Spread / Put Bull Spread
• Call Bear Spread / Put Bear Spread
• Combo/Risk Reversal
• Ratio Spread
• Ladder
• Call / Put Strip
• Synthetic underlying – conversal / reversal
• Diagonal Calendar Spread

19
Expressing views on the volatility (of price changes) of the underlying
• Straddle
• Strangle
• Guts
• Butterfly
• Condor
• Iron Butterfly
• Iron Condor
• Call / Put Strip
• Calendar Spread
• Diagonal Calendar Spread

20
Expressing views on interest rates
• Jelly Rolls
• Box

21
Risk Evaluations
• First order risks:
• Delta – i.e. change in option price with change in underlying price
• Vega – i.e. change in option price with change in underlying volatility
• Theta – i.e. change in option price as time to expiry reduces
• Rho – i.e. change in option price with change in interest rates
• Second Order risks
• Gamma ( change of Delta with change in Underlying price)
• Vanna ( change of Delta with change in Volatility)
• Charm ( change of Delta with change in Time)
• Vomma ( change of Vega with change in Volatility)
• Veta ( change of Vega with change in Time)
• Change of Vega with change in Underlying price
• Vera (change of Rho with change in Volatility)

22
Risk Evaluations
• Third order risks:
• Color ( change of Gamma with change in Time)
• Speed ( change of Gamma with change in Underlying Price)
• Zomma ( change of Gamma with change in Volatility)
• Ultima ( change of Vomma with change in Volatility)
• Other risks
• Rega - Volatility curve skew
• Sega - Volatility curve wings
• Forward Volatility (Volatility between two expiry periods)
• Skewed gamma (change in Gamma with change in volatility curve skew)
• Skewed delta (change in Delta with change in volatility curve skew)

23
Risk Evaluations (examples)
• Delta with changing underlying price
• Delta with changing volatility (Vanna)
• Delta with changing time (Charm)
• Gamma with changing underlying price

24
• Gamma with changing time (Color)
• Gamma with changing volatility (Zomma)
• Option price at different volatility levels
• Vega at different underlying levels

25
• Vega with changing time (Veta)
• Vega with changing volatility (Vomma)
• Theta with changing time
• Rho at different levels of
underlying Price

26
An example of a somewhat sophisticated strategy which benefits from
automation
• Index constituted of a basket of stocks (e.g. NIFTY50 consists of 50 stocks)
• If all stocks (in the index) go up by 5%, then index also goes up by 5%
• However, if the volatility of all stocks go up by 5%, can we infer the change in
volatility of the index ?
Not a simple answer. Depends upon correlation amongst stocks
• Volatility used to price index options = function (volatility used to price stock
options, correlation level amongst stocks)
• However, the known values are (i) volatility used to price index options and (ii)
volatility used to price stock options
we can determine the implied average correlation amongst stocks
we can then trade our view on this implied average correlation amongst stocks

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Complexities in position management of aforesaid strategy
• Approximation of index basket
• maintaining position in stocks in proportion to their weightage in the index
• Position spread across index options and stock options
• Calculating total portfolio greeks by combining greeks for individual stocks &
index
• for e.g.: portfolio vega = function ( vega position in index options + vega
position in stock1 options + ... + vega position in stockn options )
• As the market moves, the position has to be rolled from one set of option strikes
to another
• Delta to be hedge periodically

28
Any questions ?
Thank You
Merci
Danke
Gracias
Arigato
Asante
Grazi
Shukriya
See you in the QI program – EPAT (Executive Program on Algorithmic Trading)
rajib.borah@quantinsti.com

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