1. Derivatives
Abdulla Al-Othman

2. About the Author
2
Name: Abdulla Nouri
Abdulla Abdulatif AlOthman
Biography:
Education: London School of Economics (B.Sc. First Class Honours, Mathematics & Economics); Masschussets Institute of Technology (M.Sc. Operations Research and Finance -Thesis with Distinction);Imperial College(Ph.D. Mathematics with Distinction)
Work Experience:Merrill Lynch (NY / Tokyo ):Proprietary Trader ;Ivy Software (Boston) :
CO-CEO;KMBS ( Kuwait) : Adjunct Professor of Economics and Finance.
Abdulla Alothman
3. Table of Contents

Day 1: The Structures

4. Basic Derivatives:Options,Forwards 5. Strategies: Yield Enhancement , Trading, Hedging 6. Exotic Derivatives: Digitals, Knockouts, Quantos 7. ComplexDerivatives: Ratchets 8. Day 2: Valuation (Technical) 9. Methodology : Trading Exercise / Market Price of Risk / Replication 10. Valuation: Model Choice=Market Price of Risk Specification 11. Models: Black and Scholes Model3
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12. Cont

Day 3: Applications

Trading Game (Simulator)
The Kuwaiti Dinar as a Derivative

The Subprime Debt Crisis

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13. Motivating Example
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14. Premium
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15. IQAMAS
IQAMAS
16. Payoff Structure
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17. Subsidized Fuel / Free Public Transportation
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19. Free* Public Transportation
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20. Free Electricity
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22. Free Water
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24. Free Health
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27. Day 1
The Basics
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28. BASIC DERIVATIVES
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29.

Call Options

30. Put Options 31. Forward Contracts 32. Strategies21
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33. Call Options
Are contracts, providing the holder, in return for a premium, with the right but not the obligation, to buy the underlyingasset, for a fixed price (strike price), at some future date T (expiration date).
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34. Payoff Diagram
c(x)=max (x-K,0)
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$
XT
K
35. PayoffTable
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36. Derivatives
Whom, us?
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37. Jasoom
Decides to replace his GT
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38. And take out a consumer loan / sign an IOU (Bond)
Yabeela Ferrari
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39. For 5 years at 6%
6%
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40. One year elapses...
Rates fall to 5% Note becomes more valuable.
i
5%
6%
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41. Jasoom pays off the loan..
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42. JasoomWith a new loan ...
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43. For 4 years at 5%...
5%
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44. Jasooms benefits (long a Call Option)
c(x)=max (P(5%,4)-P(6%,4),0)
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$
Pb(6%)
B1
PB(5%)
45. NBKs losses (short a Call Option)
c(x)=-max (P(5%,4)-P(6%,4),0)
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$
Pb(6%)
B1
PB(5%)
46. In Summary
Since all banks in Kuwait derive a large part of their revenues from consumer loans; all are, effectively, up to their eye balls in derivatives.
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47. Put Options
Are contracts providingthe holder , in return for a premium, with the right but not the obligation, to sell the underlyingasset for a fixed price K (strike price), at some future date T (expiration date).
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48. Payoff Diagram
p(x)=max (K-x,0)
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$
XT
K
49. PayoffTable
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50. Forwards
Are contracts, in which the holder has obligation to buy the underlyingasset for a fixed price K (strike price), at some future date T (expiration date).
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51. Payoff Diagram
f(x)=x-K
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$
K
XT
52. Payoff Table
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53. Trading Strategies
We often combine Call and Put options to create assets with interesting payoff structures.
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54. Long Call/Short Put
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55. Payoff (Synthetic Forward!!)
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56. Long Put/Short Put
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57. Payoff
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58. Long/Short Puts
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59. Payoff
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60. Yield Enhancement Strategies
Portfolio managers, often use options to enhance yields on their portfolios
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61. Covered Calls
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62. Covered Calls
450
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63. Hedging Strategies
Portfolio managers and firms often use options to preserve profits / hedge exposure
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64. Long Put
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65. Payoff
450
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66. Long Call / Short Put
K255
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67. Asset Purchase Price
Budgeted Purchase Price
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68. EXOTIC DERIVATIVES
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69. Digital Calls
c(x)=1 x > K
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$
1.00
XT
K
70. Digital Puts
p(x)=1 X < K
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$
1
XT
K
71. Jasoom pays his premium
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72. Asset Depreciates
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73. Jasoom is hedged!
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Wanassa!
74. Jasoom(long a digital put option)
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$
Asset State
75. Warba (short a digital put option)
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$
Asset State
76. Quanto Calls
c(x,y)=y*Max(x-K,0)
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1.35
$
1.25
Y
XT
K
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77. Quanto Puts
c(x,y)=y*Max(K-x,0)
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1.35
$
1.25
X
K
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78. Knockout Calls
The KnockOUT EFFECT
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Barrier not hit, same as regular call
Xt
$
Barrier hit, option knocked out
Strike K
Knock Out Barrier L
time
T
K
XT
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79. Knockout Puts
The KnockOUT EFFECT
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Xt
$
Barrier hit, option knocked out
L
Barrier not hit, same as regular put
K
time (t)
T
K
XT
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80. Knockout Digital Calls
The KnockOUT EFFECT
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Barrier not hit, same as regular digital call
Xt
$
Barrier hit, option knocked out
Strike K
Knock Out Barrier L
time (t)
T
K
XT
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81. Knockout Digital Puts
The KnockOUT EFFECT
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Xt
$
Barrier hit, option knocked out
L
Barrier not hit, same as regular digital put
K
time (t)
T
K
XT
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82. Ratchets (Gulf Banks Web Site)
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83. A Knockout Ratchet
Building Blocks
KnockOut F.X. Call Options
KnockOut F.X. Digital Call Options
Call Option Strike Price $1.5400
KnockOut Level $1.2400
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84. Example Cont....
EUR/USD
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sTRUCTURE (Simplified)
Payoff Diagram
Remaining payments Knocked Out
1
2
Scenario
EURt
Time t1t2t3
$1.60
$0.01$0.01$0.01
$0.01$0.01
$0.01
$0.00
$1.56
$0.00
$0.00$0.00
$0.02
$0.02
$1.54
$0.06
$0.00
$1.24
Payoff:$0.01 $0.01$0.07
Payoff:$0.01$0.03$0.00
t1t2t3
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85. A Call /Put Ratchet
Building Blocks
(Call Option + Put Option )/2
Call Option Strike Price $1.6500
Put Option StrikePrice $1.3500
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86. Example 2 Cont....
EUR/USD
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sTRUCTURE (Simplified)
Payoff Diagram
1
2
Scenario
EURt
Time t1t2t3
$1.75
$0.00$0.00$0.00
$0.04$0.04$0.04
$1.65
$0.00$0.00
$0.03$0.03
$0.05
$0.00
$1.35
$1.25
Payoff:$0.00 $0.00$0.05
Payoff:$0.04$0.07 $0.07
t1t2t3
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87. Day 2
Valuation
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88. At a time when
Cash was the only asset
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89. TheKing decided
To introduce another
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90. With Payoffs
Determined by the flip of afair coin
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91. And pricing
Left to Market Forces
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92. Asset Valuation (Group Exercise)
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93. Analysis
Risk Averse
Market
Price Range
Arbitrage Free Market
PriceRange
45o
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94. Market Price of Risk and Utility Theory ...
Utility of Wealth
Class MarketPriceof Risk = 5
Asset Payoff
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95. Market Price of Risk and Risk Adjusted Probabilities
45o
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96. Asset Pricing Formula
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97. TheDelighted King
Now decides to introduce a Call Option
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98. With Payoff
Determined by the flip of afair coin
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99. Option Valuation (Group Exercise)
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100. Replication
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101. Option Pricing Formula
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102. Modeling in Practice
Implied Risk Neutral Probability Measure
Q1
Q3
Q4
Q2
Model Choice
M3
M4
M1
M2
45o
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103. Cont...
Millions of Modelsto
Plough and to Sow
The Future s Uncertain
The Price We Dont Know!!!
Q2
Q3
M2
M3
45o
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104. MORAL TO THE STORY
WITH PROBABILITY ONE
ANY MODEL YOU CHOOSE WILL BE WRONG!!!
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105. Black and Scholes Model 1973
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106. Black and Scholes Model 1973
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In the Black and Scholes Economy, the parameters are constant and so we can solve the above equations explicitly to obtain:
107. Black and Scholes Model 1973
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The risk adjusted probability measure in this economy isgive by:
108. Black and Scholes Model 1973
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But then, mimicking the Al-Othman* analysis, mutatis mutandis, we see that:
*In the previous analysis it was implicitly assumed the r = 0 and so B =1
109. Black and Scholes Model 1973
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110. Black and Scholes Model 1973
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So Value of the Option is:
Since, in the Black and Scholes Model:
111. Black and Scholes Model 1973
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112. The Formula (Yawn, Yawn)
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Substituting 2 and 3 into 1 gives:
The Black and Scholes formula for a European Call Option!!
113. Black and Scholes ModelThe Greeks
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114. BINOMIAL MODELS
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115. The Two Period Binomial Model
NO ARBITRAGE CONDITION:
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116. The Risk Adjusted Probabilities in the
Binomial Model:
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117. Asset Valuation in the Two Period Binomial Model
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118. Step1: Set Up a Replicating Portfolio
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119. Step2: Calculate the Replicating Portfolio Weights:
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120. Step3: Use Market Data to Value the Replicating Portfolio:
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121. Summary:
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122. ARBITRAGE
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123. Ok. Lets Test Drive....
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124. Market Data + Model Parameters:
NO ARBITRAGE CONDITION:
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125. Calculating the Risk Adjusted Probabilities:
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126. Objective: Value the Below
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127. Step1: Set Up a Replicating Portfolio
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128. Step2: Calculate Portfolio Weights:
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129. Step3: Use Market Data to Price the Replicating Portfolio:
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130. Step4: Check Results:
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131. Market Data + Model Parameters:
NO ARBITRAGE CONDITION:
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132. Exercise 1 : Using the information in the previous slide , find the replicating portfolio for the Option belowand use this to determine it's fair value. Check your result against that obtained by takingthe expected payoff with respectto the riskadjusted probabilities .
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133. Exercise 2 : Using the information in the previous slide , find the replicating portfolio for the Option belowand use this to determine it's fair value. Check your result against that obtained by takingthe expected payoff with respect to the risk adjusted probabilities .
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134. Day 3
Applications
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135. Abdulla Alothman

Option Valuation Game: Arbitrage, Replication and Hedging

136. Multi Dimensional Derivatives:The Kuwaiti Dinar 137. Structured Assets: Mortgage BackedSecurities and the Global Debt Crisis124