SlideShare a Scribd company logo
1 of 27
Option Pricing Sensitivity
        Greeks
    Advance Risk Models
       War on Greeks
    Jawwad Ahmed Farid
Plan
     Greeks          • Delta, Gamma, Vega, Theta


                     • Derivative Portfolio
    Hedging          • Method II, EGS Case

                     • DPD Analysis
   Credit Risk       • PD Models, Barclays Bank

Capital Adequacy     • Capital Adequacy Models
    & ICAAP          • Stress Testing, Solvency II

How to kill a bank   • Integrated Bank Simulation
  in one day         • Liquidity, Capital, Market Risk
ALM           • Asset Liability Management

 Delta Hedging      • Derivative Portfolio Greeks

Barclays Bank       • Libor Crisis, FI Limits, PD Models

  Value at Risk     • Margin Lending & FI Limits
 Liquidity Stress
                    • Extending Capital Adequacy
      Testing
    Enron Gas
                    • Running a risk book
     Services
Option Greeks

  Lesson One
Moneyness & value change

Deep Out     • Change in value?

of Money     • Volatility



At or Near   • Change in value?

 Money       • Strike, Spot



 Deep in     • Change in value?
             • Time
 Money
The Greeks

Delta   • Change in value on account of a unit change in
          the underlying


Gamma   • Change in Delta on account of a unit change in
          the underlying


Vega    • Change in value on account of change in volatility



Theta   • Change in value on account of change in time



 Rho    • Change in value on account of change in interest
          rates
Delta
Gamma
Vega
Theta
Rho
The Greeks against Spot
100.0%                                                                             2.0%

 90.0%
                                                                                   1.5%
 80.0%

 70.0%
                                                                                   1.0%
 60.0%

 50.0%                                                                             0.5%

 40.0%
                                                                                   0.0%
 30.0%

 20.0%
                                                                                   -0.5%
 10.0%

  0.0%                                                                             -1.0%
         60   65   70   75      80   85     90    95 100 105 110 115 120 125 130
                        Delta        Vega        Rho   Gamma     Theta
Delta Call



            ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1




3/19/2013                  13
Delta Put



            ∆𝑃𝑢𝑡 = 1 − 𝑁(𝑑1)




3/19/2013                      14
Gamma Call


               ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1

                      𝑁′(𝑑1)
            𝛾𝐶𝑎𝑙𝑙 =
                               𝑆𝜎 𝑇

3/19/2013                             15
Gamma Put




             ?
3/19/2013               16
Gamma Put


             ∆𝑃𝑢𝑡 = 1 − 𝑁 𝑑1

                     𝑁′(𝑑1)
            𝛾𝑃𝑢𝑡 =
                              𝑆𝜎 𝑇

3/19/2013                            17
Vega Call
             ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1

                      𝑁(𝑑1)
            𝛾𝐶𝑎𝑙𝑙 =
                              𝑆𝛿 𝑇

            𝑉𝑒𝑔𝑎 𝐶𝑎𝑙𝑙 = 𝑆𝑁′(𝑑1) 𝑇



3/19/2013                            18
Vega Put




            ?
3/19/2013              19
Applications?




3/19/2013                   20
Value of a Call



     Call = Delta * S - Borrowing




3/19/2013                           21
Greeks

      Behaving badly
At, Near Money Call Options
The Greeks against Time
70.0%                                                                                20.0%

                                                                                     18.0%
60.0%
                                                                                     16.0%
50.0%                                                                                14.0%

                                                                                     12.0%
40.0%
                                                                                     10.0%
30.0%
                                                                                     8.0%

20.0%                                                                                6.0%

                                                                                     4.0%
10.0%
                                                                                     2.0%

 0.0%                                                                                0.0%
        0.01 0.03 0.04 0.08 0.10 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.00
                        Delta     Vega     Rho     Gamma       Theta
The Greeks against Vol
1.20                                                                                0.07

                                                                                    0.06
1.00
                                                                                    0.05

                                                                                    0.04
0.80
                                                                                    0.03

0.60                                                                                0.02

                                                                                    0.01
0.40
                                                                                    -

                                                                                    -0.01
0.20
                                                                                    -0.02

  -                                                                                 -0.03
       0.01 0.03 0.04 0.08 0.10 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.00
                          Delta    Vega    Rho    Gamma     Theta
The Greeks against Spot
100.0%                                                                             2.0%

 90.0%
                                                                                   1.5%
 80.0%

 70.0%
                                                                                   1.0%
 60.0%

 50.0%                                                                             0.5%

 40.0%
                                                                                   0.0%
 30.0%

 20.0%
                                                                                   -0.5%
 10.0%

  0.0%                                                                             -1.0%
         60   65   70   75      80   85     90    95 100 105 110 115 120 125 130
                        Delta        Vega        Rho   Gamma     Theta
The Greeks against Strike
120.0%                                           2.0%

100.0%                                           1.5%

                                                 1.0%
 80.0%
                                                 0.5%
 60.0%
                                                 0.0%
 40.0%
                                                 -0.5%
 20.0%                                           -1.0%

  0.0%                                           -1.5%
          75

          85
          60
          65
          70

          80

          90
          95



         110

         120
         100
         105

         115

         125
         130
         Delta   Vega   Rho   Gamma      Theta
Vol, N(d1), N(d2), Price
1.20                                                                                                                           45.00

                                                                                                                               40.00
1.00
                                                                                                                               35.00

0.80                                                                                                                           30.00

                                                                                                                               25.00
0.60
                                                                                                                               20.00

0.40                                                                                                                           15.00

                                                                                                                               10.00
0.20
                                                                                                                               5.00

  -                                                                                                                            -
              0.07




                                                                                            0.73


                                                                                                          0.85


                                                                                                                        0.97
       0.01


                     0.13
                            0.19
                                   0.25
                                          0.31
                                                 0.37
                                                        0.43
                                                               0.49
                                                                      0.55
                                                                              0.61
                                                                                     0.67


                                                                                                   0.79


                                                                                                                 0.91
                                   Volatility           N(d1)                N(d2)            Price

More Related Content

What's hot

Call and put Options
Call and put OptionsCall and put Options
Call and put OptionsXaveria Desi
 
Bond prices & their yields
Bond prices & their yieldsBond prices & their yields
Bond prices & their yieldsTata Mutual Fund
 
Swaps (derivatives)
Swaps (derivatives)Swaps (derivatives)
Swaps (derivatives)kunaljoshi79
 
CURRENCY SWAP & INTREST RATE SWAP
CURRENCY SWAP & INTREST RATE SWAPCURRENCY SWAP & INTREST RATE SWAP
CURRENCY SWAP & INTREST RATE SWAPManish Kumar
 
Introduction to derivatives
Introduction to derivativesIntroduction to derivatives
Introduction to derivativesNeelam Asad
 
Introdaction of derivative market
Introdaction of derivative marketIntrodaction of derivative market
Introdaction of derivative marketAnkur Sarswat
 
FIM - Currency Futures PPT
FIM - Currency Futures PPTFIM - Currency Futures PPT
FIM - Currency Futures PPTBishnu Kumar
 
Derivatives- CALL AND PUT OPTIONS
Derivatives- CALL AND PUT OPTIONSDerivatives- CALL AND PUT OPTIONS
Derivatives- CALL AND PUT OPTIONSDinesh Kumar
 
Interest rate derivatives
Interest rate derivativesInterest rate derivatives
Interest rate derivativesIndia Forex
 
Foreign exchange risk and hedging
Foreign exchange risk and hedgingForeign exchange risk and hedging
Foreign exchange risk and hedgingJuby John
 
3. Trading - Types of derivatives
3. Trading - Types of derivatives3. Trading - Types of derivatives
3. Trading - Types of derivativesKoffee Financial
 
6.currency and interest rate futures
6.currency and interest rate futures6.currency and interest rate futures
6.currency and interest rate futuresSunitha Karthik
 
Forward and Futures Contract
Forward and Futures ContractForward and Futures Contract
Forward and Futures ContractRana Zeshan
 

What's hot (20)

Call and put Options
Call and put OptionsCall and put Options
Call and put Options
 
Option contract
Option contractOption contract
Option contract
 
option basics
option basicsoption basics
option basics
 
Bond prices & their yields
Bond prices & their yieldsBond prices & their yields
Bond prices & their yields
 
Swaps (derivatives)
Swaps (derivatives)Swaps (derivatives)
Swaps (derivatives)
 
CURRENCY SWAP & INTREST RATE SWAP
CURRENCY SWAP & INTREST RATE SWAPCURRENCY SWAP & INTREST RATE SWAP
CURRENCY SWAP & INTREST RATE SWAP
 
Introduction to derivatives
Introduction to derivativesIntroduction to derivatives
Introduction to derivatives
 
Options strategies
Options strategiesOptions strategies
Options strategies
 
Introdaction of derivative market
Introdaction of derivative marketIntrodaction of derivative market
Introdaction of derivative market
 
FIM - Currency Futures PPT
FIM - Currency Futures PPTFIM - Currency Futures PPT
FIM - Currency Futures PPT
 
Derivatives - Classroom Presentation
Derivatives - Classroom PresentationDerivatives - Classroom Presentation
Derivatives - Classroom Presentation
 
Derivatives- CALL AND PUT OPTIONS
Derivatives- CALL AND PUT OPTIONSDerivatives- CALL AND PUT OPTIONS
Derivatives- CALL AND PUT OPTIONS
 
Interest rate derivatives
Interest rate derivativesInterest rate derivatives
Interest rate derivatives
 
Basics of options
Basics of optionsBasics of options
Basics of options
 
Foreign exchange risk and hedging
Foreign exchange risk and hedgingForeign exchange risk and hedging
Foreign exchange risk and hedging
 
3. Trading - Types of derivatives
3. Trading - Types of derivatives3. Trading - Types of derivatives
3. Trading - Types of derivatives
 
Valuation of securities
Valuation of securitiesValuation of securities
Valuation of securities
 
PRIMARY MARKET PPT
PRIMARY MARKET PPTPRIMARY MARKET PPT
PRIMARY MARKET PPT
 
6.currency and interest rate futures
6.currency and interest rate futures6.currency and interest rate futures
6.currency and interest rate futures
 
Forward and Futures Contract
Forward and Futures ContractForward and Futures Contract
Forward and Futures Contract
 

Viewers also liked

Options Trading Strategies
Options Trading StrategiesOptions Trading Strategies
Options Trading StrategiesMayank Bhatia
 
Strategic Fx Risk Management
Strategic Fx Risk ManagementStrategic Fx Risk Management
Strategic Fx Risk ManagementJan Vermeer
 
Two and a half stories
Two and a half storiesTwo and a half stories
Two and a half storiesJawwad Farid
 
Binomial Tree - Option Pricing Theory
Binomial Tree - Option Pricing TheoryBinomial Tree - Option Pricing Theory
Binomial Tree - Option Pricing TheoryJames Dazé
 
Factors affecting call and put option prices
Factors affecting call and put option pricesFactors affecting call and put option prices
Factors affecting call and put option priceskingsly nelson
 
options and their valuation
options and their valuationoptions and their valuation
options and their valuationPANKAJ PANDEY
 
Derivatives Binomial Option Pricing Model Examples
Derivatives  Binomial  Option  Pricing  Model  ExamplesDerivatives  Binomial  Option  Pricing  Model  Examples
Derivatives Binomial Option Pricing Model Examplesuichong
 
Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري
Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري
Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري Emad Saif
 
Financial derivatives ppt
Financial derivatives pptFinancial derivatives ppt
Financial derivatives pptVaishnaviSavant
 

Viewers also liked (14)

The Greeks
The GreeksThe Greeks
The Greeks
 
Option_Greeks
Option_GreeksOption_Greeks
Option_Greeks
 
Options Trading Strategies
Options Trading StrategiesOptions Trading Strategies
Options Trading Strategies
 
Strategic Fx Risk Management
Strategic Fx Risk ManagementStrategic Fx Risk Management
Strategic Fx Risk Management
 
Two and a half stories
Two and a half storiesTwo and a half stories
Two and a half stories
 
Faces Of Alchemy
Faces Of AlchemyFaces Of Alchemy
Faces Of Alchemy
 
Binomial Tree - Option Pricing Theory
Binomial Tree - Option Pricing TheoryBinomial Tree - Option Pricing Theory
Binomial Tree - Option Pricing Theory
 
Factors affecting call and put option prices
Factors affecting call and put option pricesFactors affecting call and put option prices
Factors affecting call and put option prices
 
options and their valuation
options and their valuationoptions and their valuation
options and their valuation
 
Unit iii
Unit  iiiUnit  iii
Unit iii
 
Derivatives Binomial Option Pricing Model Examples
Derivatives  Binomial  Option  Pricing  Model  ExamplesDerivatives  Binomial  Option  Pricing  Model  Examples
Derivatives Binomial Option Pricing Model Examples
 
Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري
Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري
Business Model Canvas In Arabic - إبتكار نموذج العمل التجاري
 
Sx NEFRÍTICO
Sx NEFRÍTICOSx NEFRÍTICO
Sx NEFRÍTICO
 
Financial derivatives ppt
Financial derivatives pptFinancial derivatives ppt
Financial derivatives ppt
 

Similar to Option Pricing - Greeks

Crash CUNA Lending Council - Gen Y Survey
Crash CUNA Lending Council - Gen Y SurveyCrash CUNA Lending Council - Gen Y Survey
Crash CUNA Lending Council - Gen Y Surveytrustdotcoop
 
Behavioural Economics and Finance
Behavioural Economics and FinanceBehavioural Economics and Finance
Behavioural Economics and FinanceIan-Edward Stafrace
 
CR2 Apresentação - 3Q11
CR2   Apresentação - 3Q11CR2   Apresentação - 3Q11
CR2 Apresentação - 3Q11CR2
 
Potrošačka korpa
Potrošačka korpaPotrošačka korpa
Potrošačka korpaHIPERCOM
 
“SCORECARD” Incentive Remuneration System for Microfinance
“SCORECARD” Incentive Remuneration System for Microfinance“SCORECARD” Incentive Remuneration System for Microfinance
“SCORECARD” Incentive Remuneration System for MicrofinanceMABSIV
 
Debit card promo campaign uefa citibank 23-09-09
Debit card promo campaign uefa citibank 23-09-09Debit card promo campaign uefa citibank 23-09-09
Debit card promo campaign uefa citibank 23-09-09creativetweet
 
Analysis of Morning Shows
Analysis of Morning ShowsAnalysis of Morning Shows
Analysis of Morning Showsnoumanfazal
 
Web.com Small Business Mobile Survey
Web.com Small Business Mobile SurveyWeb.com Small Business Mobile Survey
Web.com Small Business Mobile SurveyWeb.com
 
Island biogeography excel
Island biogeography excelIsland biogeography excel
Island biogeography excelchuckiecalsado
 
LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...
LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...
LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...Vinternet
 
Martin Barden – The audience centre stage | congres podiumkunsten 2012
Martin Barden – The audience centre stage | congres podiumkunsten 2012Martin Barden – The audience centre stage | congres podiumkunsten 2012
Martin Barden – The audience centre stage | congres podiumkunsten 2012Promotie Podiumkunsten
 
3 q11 presentation
3 q11 presentation3 q11 presentation
3 q11 presentationSiteriCR2
 
Investor Pain Index and Bearish Sentiment
Investor Pain Index and Bearish SentimentInvestor Pain Index and Bearish Sentiment
Investor Pain Index and Bearish SentimentJonathan Smith
 
Humed ad mes de febrero y marzo
Humed ad mes de febrero y marzoHumed ad mes de febrero y marzo
Humed ad mes de febrero y marzoMiguel Angel
 

Similar to Option Pricing - Greeks (20)

Crash CUNA Lending Council - Gen Y Survey
Crash CUNA Lending Council - Gen Y SurveyCrash CUNA Lending Council - Gen Y Survey
Crash CUNA Lending Council - Gen Y Survey
 
Behavioural Economics and Finance
Behavioural Economics and FinanceBehavioural Economics and Finance
Behavioural Economics and Finance
 
Satisfaction Scores 2
Satisfaction Scores 2Satisfaction Scores 2
Satisfaction Scores 2
 
CR2 Apresentação - 3Q11
CR2   Apresentação - 3Q11CR2   Apresentação - 3Q11
CR2 Apresentação - 3Q11
 
Potrošačka korpa
Potrošačka korpaPotrošačka korpa
Potrošačka korpa
 
“SCORECARD” Incentive Remuneration System for Microfinance
“SCORECARD” Incentive Remuneration System for Microfinance“SCORECARD” Incentive Remuneration System for Microfinance
“SCORECARD” Incentive Remuneration System for Microfinance
 
Debit card promo campaign uefa citibank 23-09-09
Debit card promo campaign uefa citibank 23-09-09Debit card promo campaign uefa citibank 23-09-09
Debit card promo campaign uefa citibank 23-09-09
 
Analysis of Morning Shows
Analysis of Morning ShowsAnalysis of Morning Shows
Analysis of Morning Shows
 
Satisfaction Scores 3
Satisfaction Scores 3Satisfaction Scores 3
Satisfaction Scores 3
 
Tabla de frecuencia
Tabla de frecuenciaTabla de frecuencia
Tabla de frecuencia
 
Satisfaction Scores 4
Satisfaction Scores 4Satisfaction Scores 4
Satisfaction Scores 4
 
Web.com Small Business Mobile Survey
Web.com Small Business Mobile SurveyWeb.com Small Business Mobile Survey
Web.com Small Business Mobile Survey
 
Island biogeography excel
Island biogeography excelIsland biogeography excel
Island biogeography excel
 
LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...
LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...
LE VIN 2.0 '11 - Atelier 01 Intervenant 01 - "Dégustation, gastronomie, touri...
 
Martin Barden – The audience centre stage | congres podiumkunsten 2012
Martin Barden – The audience centre stage | congres podiumkunsten 2012Martin Barden – The audience centre stage | congres podiumkunsten 2012
Martin Barden – The audience centre stage | congres podiumkunsten 2012
 
3 q11 presentation
3 q11 presentation3 q11 presentation
3 q11 presentation
 
gemiusAdMonitor
gemiusAdMonitorgemiusAdMonitor
gemiusAdMonitor
 
Investor Pain Index and Bearish Sentiment
Investor Pain Index and Bearish SentimentInvestor Pain Index and Bearish Sentiment
Investor Pain Index and Bearish Sentiment
 
Humed ad mes de febrero y marzo
Humed ad mes de febrero y marzoHumed ad mes de febrero y marzo
Humed ad mes de febrero y marzo
 
Chapter3
Chapter3Chapter3
Chapter3
 

More from Jawwad Farid

Asset Liability Management - Intro
Asset Liability Management - IntroAsset Liability Management - Intro
Asset Liability Management - IntroJawwad Farid
 
Pitching ideas for startups
Pitching ideas for startupsPitching ideas for startups
Pitching ideas for startupsJawwad Farid
 
Talent, Technology, Management
Talent, Technology, ManagementTalent, Technology, Management
Talent, Technology, ManagementJawwad Farid
 
Final Bap Pitch Blog Post
Final Bap Pitch Blog PostFinal Bap Pitch Blog Post
Final Bap Pitch Blog PostJawwad Farid
 
SMB Fatimah Jinnah Girls School
SMB Fatimah Jinnah Girls SchoolSMB Fatimah Jinnah Girls School
SMB Fatimah Jinnah Girls SchoolJawwad Farid
 
Alchemy Reboot @ TIE CON Karachi
Alchemy Reboot @ TIE CON KarachiAlchemy Reboot @ TIE CON Karachi
Alchemy Reboot @ TIE CON KarachiJawwad Farid
 

More from Jawwad Farid (7)

Uncommon Finance
Uncommon Finance Uncommon Finance
Uncommon Finance
 
Asset Liability Management - Intro
Asset Liability Management - IntroAsset Liability Management - Intro
Asset Liability Management - Intro
 
Pitching ideas for startups
Pitching ideas for startupsPitching ideas for startups
Pitching ideas for startups
 
Talent, Technology, Management
Talent, Technology, ManagementTalent, Technology, Management
Talent, Technology, Management
 
Final Bap Pitch Blog Post
Final Bap Pitch Blog PostFinal Bap Pitch Blog Post
Final Bap Pitch Blog Post
 
SMB Fatimah Jinnah Girls School
SMB Fatimah Jinnah Girls SchoolSMB Fatimah Jinnah Girls School
SMB Fatimah Jinnah Girls School
 
Alchemy Reboot @ TIE CON Karachi
Alchemy Reboot @ TIE CON KarachiAlchemy Reboot @ TIE CON Karachi
Alchemy Reboot @ TIE CON Karachi
 

Recently uploaded

2024.03 Strategic Resources_Pub presentation
2024.03 Strategic Resources_Pub presentation2024.03 Strategic Resources_Pub presentation
2024.03 Strategic Resources_Pub presentationAdnet Communications
 
14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf
14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf
14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdfjamie766122
 
BIHC Briefing Greece March 2024, with Crédit Agricole CIB
BIHC Briefing Greece March 2024, with Crédit Agricole CIBBIHC Briefing Greece March 2024, with Crédit Agricole CIB
BIHC Briefing Greece March 2024, with Crédit Agricole CIBNeil Day
 
Islamic banking in Afghanistan from start until now
Islamic banking in Afghanistan from start until nowIslamic banking in Afghanistan from start until now
Islamic banking in Afghanistan from start until nowhamidzafar6
 
AUDITING FRAUDS OF AN ENGLISH COMPANY.PPTX
AUDITING FRAUDS OF AN ENGLISH COMPANY.PPTXAUDITING FRAUDS OF AN ENGLISH COMPANY.PPTX
AUDITING FRAUDS OF AN ENGLISH COMPANY.PPTXkamikazekujoh
 
Stock Market Brief Deck FOR 3142024..pdf
Stock Market Brief Deck FOR 3142024..pdfStock Market Brief Deck FOR 3142024..pdf
Stock Market Brief Deck FOR 3142024..pdfMichael Silva
 
Economic Risk Factor Update: March 2024 [SlideShare]
Economic Risk Factor Update: March 2024 [SlideShare]Economic Risk Factor Update: March 2024 [SlideShare]
Economic Risk Factor Update: March 2024 [SlideShare]Commonwealth
 
Challenging Factors of Rural Women Entrepreneurs in West Bengal
Challenging Factors of Rural Women Entrepreneurs in West  BengalChallenging Factors of Rural Women Entrepreneurs in West  Bengal
Challenging Factors of Rural Women Entrepreneurs in West BengalNabarun Chakraborty
 
2024.03 Strategic Resources_Pub (1). pdf
2024.03 Strategic Resources_Pub (1). pdf2024.03 Strategic Resources_Pub (1). pdf
2024.03 Strategic Resources_Pub (1). pdfAdnet Communications
 
Stock Market Brief Deck FOR 31124 yt.pdf
Stock Market Brief Deck FOR 31124 yt.pdfStock Market Brief Deck FOR 31124 yt.pdf
Stock Market Brief Deck FOR 31124 yt.pdfMichael Silva
 
The Role of Non-Banking Financial Companies (NBFCs).pdf
The Role of Non-Banking Financial Companies (NBFCs).pdfThe Role of Non-Banking Financial Companies (NBFCs).pdf
The Role of Non-Banking Financial Companies (NBFCs).pdfChampak Jhagmag
 
powerpoint presentation about asian regioonalism
powerpoint presentation about asian regioonalismpowerpoint presentation about asian regioonalism
powerpoint presentation about asian regioonalismrezeraaisla
 
renaltumors upasana sahu Group 50.pptxism
renaltumors upasana sahu Group 50.pptxismrenaltumors upasana sahu Group 50.pptxism
renaltumors upasana sahu Group 50.pptxismthxz2fdqxw
 
Pros and Cons of Interest-Only DSCR Loans
Pros and Cons of Interest-Only DSCR LoansPros and Cons of Interest-Only DSCR Loans
Pros and Cons of Interest-Only DSCR LoansPark Place Finance LLC
 
Planning of societal re/production in a commonist society
Planning of societal re/production in a commonist societyPlanning of societal re/production in a commonist society
Planning of societal re/production in a commonist societyStefanMz
 
First, Second, and Third Generation Islamic Economicss
First, Second, and Third Generation Islamic EconomicssFirst, Second, and Third Generation Islamic Economicss
First, Second, and Third Generation Islamic EconomicssAsad Zaman
 
Buy-Side Leaps Into Gen AI Era by Jasper Colin
Buy-Side Leaps Into Gen AI Era by Jasper ColinBuy-Side Leaps Into Gen AI Era by Jasper Colin
Buy-Side Leaps Into Gen AI Era by Jasper ColinJasper Colin
 
ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...
ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...
ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...indexPub
 
Swift_Maintaining Critical Standards(...).pptx.pdf
Swift_Maintaining Critical Standards(...).pptx.pdfSwift_Maintaining Critical Standards(...).pptx.pdf
Swift_Maintaining Critical Standards(...).pptx.pdfNeo4j
 

Recently uploaded (20)

2024.03 Strategic Resources_Pub presentation
2024.03 Strategic Resources_Pub presentation2024.03 Strategic Resources_Pub presentation
2024.03 Strategic Resources_Pub presentation
 
14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf
14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf
14.11.2024 AMOO-MOCA African Creative Economy Summit London summary.pdf
 
BIHC Briefing Greece March 2024, with Crédit Agricole CIB
BIHC Briefing Greece March 2024, with Crédit Agricole CIBBIHC Briefing Greece March 2024, with Crédit Agricole CIB
BIHC Briefing Greece March 2024, with Crédit Agricole CIB
 
Islamic banking in Afghanistan from start until now
Islamic banking in Afghanistan from start until nowIslamic banking in Afghanistan from start until now
Islamic banking in Afghanistan from start until now
 
AUDITING FRAUDS OF AN ENGLISH COMPANY.PPTX
AUDITING FRAUDS OF AN ENGLISH COMPANY.PPTXAUDITING FRAUDS OF AN ENGLISH COMPANY.PPTX
AUDITING FRAUDS OF AN ENGLISH COMPANY.PPTX
 
Stock Market Brief Deck FOR 3142024..pdf
Stock Market Brief Deck FOR 3142024..pdfStock Market Brief Deck FOR 3142024..pdf
Stock Market Brief Deck FOR 3142024..pdf
 
Economic Risk Factor Update: March 2024 [SlideShare]
Economic Risk Factor Update: March 2024 [SlideShare]Economic Risk Factor Update: March 2024 [SlideShare]
Economic Risk Factor Update: March 2024 [SlideShare]
 
Closing Remarks International Women's Day 2024
Closing Remarks International Women's Day 2024Closing Remarks International Women's Day 2024
Closing Remarks International Women's Day 2024
 
Challenging Factors of Rural Women Entrepreneurs in West Bengal
Challenging Factors of Rural Women Entrepreneurs in West  BengalChallenging Factors of Rural Women Entrepreneurs in West  Bengal
Challenging Factors of Rural Women Entrepreneurs in West Bengal
 
2024.03 Strategic Resources_Pub (1). pdf
2024.03 Strategic Resources_Pub (1). pdf2024.03 Strategic Resources_Pub (1). pdf
2024.03 Strategic Resources_Pub (1). pdf
 
Stock Market Brief Deck FOR 31124 yt.pdf
Stock Market Brief Deck FOR 31124 yt.pdfStock Market Brief Deck FOR 31124 yt.pdf
Stock Market Brief Deck FOR 31124 yt.pdf
 
The Role of Non-Banking Financial Companies (NBFCs).pdf
The Role of Non-Banking Financial Companies (NBFCs).pdfThe Role of Non-Banking Financial Companies (NBFCs).pdf
The Role of Non-Banking Financial Companies (NBFCs).pdf
 
powerpoint presentation about asian regioonalism
powerpoint presentation about asian regioonalismpowerpoint presentation about asian regioonalism
powerpoint presentation about asian regioonalism
 
renaltumors upasana sahu Group 50.pptxism
renaltumors upasana sahu Group 50.pptxismrenaltumors upasana sahu Group 50.pptxism
renaltumors upasana sahu Group 50.pptxism
 
Pros and Cons of Interest-Only DSCR Loans
Pros and Cons of Interest-Only DSCR LoansPros and Cons of Interest-Only DSCR Loans
Pros and Cons of Interest-Only DSCR Loans
 
Planning of societal re/production in a commonist society
Planning of societal re/production in a commonist societyPlanning of societal re/production in a commonist society
Planning of societal re/production in a commonist society
 
First, Second, and Third Generation Islamic Economicss
First, Second, and Third Generation Islamic EconomicssFirst, Second, and Third Generation Islamic Economicss
First, Second, and Third Generation Islamic Economicss
 
Buy-Side Leaps Into Gen AI Era by Jasper Colin
Buy-Side Leaps Into Gen AI Era by Jasper ColinBuy-Side Leaps Into Gen AI Era by Jasper Colin
Buy-Side Leaps Into Gen AI Era by Jasper Colin
 
ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...
ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...
ANALYSIS OF BANK MANDIRI S HEALTH LEVEL BASED ON RISK PROFILE, GOOD CORPORATE...
 
Swift_Maintaining Critical Standards(...).pptx.pdf
Swift_Maintaining Critical Standards(...).pptx.pdfSwift_Maintaining Critical Standards(...).pptx.pdf
Swift_Maintaining Critical Standards(...).pptx.pdf
 

Option Pricing - Greeks

  • 1. Option Pricing Sensitivity Greeks Advance Risk Models War on Greeks Jawwad Ahmed Farid
  • 2. Plan Greeks • Delta, Gamma, Vega, Theta • Derivative Portfolio Hedging • Method II, EGS Case • DPD Analysis Credit Risk • PD Models, Barclays Bank Capital Adequacy • Capital Adequacy Models & ICAAP • Stress Testing, Solvency II How to kill a bank • Integrated Bank Simulation in one day • Liquidity, Capital, Market Risk
  • 3. ALM • Asset Liability Management Delta Hedging • Derivative Portfolio Greeks Barclays Bank • Libor Crisis, FI Limits, PD Models Value at Risk • Margin Lending & FI Limits Liquidity Stress • Extending Capital Adequacy Testing Enron Gas • Running a risk book Services
  • 4. Option Greeks Lesson One
  • 5. Moneyness & value change Deep Out • Change in value? of Money • Volatility At or Near • Change in value? Money • Strike, Spot Deep in • Change in value? • Time Money
  • 6. The Greeks Delta • Change in value on account of a unit change in the underlying Gamma • Change in Delta on account of a unit change in the underlying Vega • Change in value on account of change in volatility Theta • Change in value on account of change in time Rho • Change in value on account of change in interest rates
  • 10. Theta
  • 11. Rho
  • 12. The Greeks against Spot 100.0% 2.0% 90.0% 1.5% 80.0% 70.0% 1.0% 60.0% 50.0% 0.5% 40.0% 0.0% 30.0% 20.0% -0.5% 10.0% 0.0% -1.0% 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 Delta Vega Rho Gamma Theta
  • 13. Delta Call ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1 3/19/2013 13
  • 14. Delta Put ∆𝑃𝑢𝑡 = 1 − 𝑁(𝑑1) 3/19/2013 14
  • 15. Gamma Call ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1 𝑁′(𝑑1) 𝛾𝐶𝑎𝑙𝑙 = 𝑆𝜎 𝑇 3/19/2013 15
  • 16. Gamma Put ? 3/19/2013 16
  • 17. Gamma Put ∆𝑃𝑢𝑡 = 1 − 𝑁 𝑑1 𝑁′(𝑑1) 𝛾𝑃𝑢𝑡 = 𝑆𝜎 𝑇 3/19/2013 17
  • 18. Vega Call ∆𝐶𝑎𝑙𝑙 = 𝑁 𝑑1 𝑁(𝑑1) 𝛾𝐶𝑎𝑙𝑙 = 𝑆𝛿 𝑇 𝑉𝑒𝑔𝑎 𝐶𝑎𝑙𝑙 = 𝑆𝑁′(𝑑1) 𝑇 3/19/2013 18
  • 19. Vega Put ? 3/19/2013 19
  • 21. Value of a Call Call = Delta * S - Borrowing 3/19/2013 21
  • 22. Greeks Behaving badly At, Near Money Call Options
  • 23. The Greeks against Time 70.0% 20.0% 18.0% 60.0% 16.0% 50.0% 14.0% 12.0% 40.0% 10.0% 30.0% 8.0% 20.0% 6.0% 4.0% 10.0% 2.0% 0.0% 0.0% 0.01 0.03 0.04 0.08 0.10 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.00 Delta Vega Rho Gamma Theta
  • 24. The Greeks against Vol 1.20 0.07 0.06 1.00 0.05 0.04 0.80 0.03 0.60 0.02 0.01 0.40 - -0.01 0.20 -0.02 - -0.03 0.01 0.03 0.04 0.08 0.10 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 1.00 Delta Vega Rho Gamma Theta
  • 25. The Greeks against Spot 100.0% 2.0% 90.0% 1.5% 80.0% 70.0% 1.0% 60.0% 50.0% 0.5% 40.0% 0.0% 30.0% 20.0% -0.5% 10.0% 0.0% -1.0% 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 Delta Vega Rho Gamma Theta
  • 26. The Greeks against Strike 120.0% 2.0% 100.0% 1.5% 1.0% 80.0% 0.5% 60.0% 0.0% 40.0% -0.5% 20.0% -1.0% 0.0% -1.5% 75 85 60 65 70 80 90 95 110 120 100 105 115 125 130 Delta Vega Rho Gamma Theta
  • 27. Vol, N(d1), N(d2), Price 1.20 45.00 40.00 1.00 35.00 0.80 30.00 25.00 0.60 20.00 0.40 15.00 10.00 0.20 5.00 - - 0.07 0.73 0.85 0.97 0.01 0.13 0.19 0.25 0.31 0.37 0.43 0.49 0.55 0.61 0.67 0.79 0.91 Volatility N(d1) N(d2) Price