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ADMS 4503 (13)
Lecture

Lecture 3

4 Pages
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Department
Administrative Studies
Course Code
ADMS 4503
Professor
Nabil Tahani

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LECTURE 3
Margin example :
You lose money when price of the security falls when you are in a long position
If the price falls by $2 , and the value falls by $600, means you have 3 contract of 100 units
a. Long , 3
b. Initial margin is $4500 , and because we have 3 contracts,
Per contract initial margin is $1500
c. The payoff on feb 28 = 𝐹28- 𝐹27
1.5 = 450/300 = 193.10 - 𝐹27
So the price on 27th feb is 191.6
d. Margin balance is $4500 - $1170 = $3330 on jan 30th
e. Jan 31st , we get the first margin call of $4500 - $2730 = $1770
f. Total payoff = 3x (100) x (𝐹𝑇- 𝐹0) = 300 X ( 193.10-200) = -2070
CHAPTER 5
Risk neutral pricing”
Have a range of price with lower and upper bound, where prices falling outside of this range would give
rise to arbitrage. Assumption:
- Borrow and sell at risk free rate
- Short sale proceeds are received asap
- Notations used : S , F , T and r
Example slide 8 of Chp 5 pdf
𝑆0 = 40
T = 0.25 ( 3 months)
r = 5% CC
𝑀𝑎𝑟𝑘𝑒𝑡 𝐹0= 43 ( over priced)
Arbitrage
Today
At T
Short one forward
0
43
Long Asset
-40
Borrow
+40
-40.50
Total
0
2.5
FV of loan = 40 𝑒5%,0.25 = 40.50
The price at which there will be no arbitrage is at $40.50

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Description
LECTURE 3 Margin example : You lose money when price of the security falls when you are in a long position If the price falls by $2 , and the value falls by $600, means you have 3 contract of 100 units a. Long , 3 b. Initial margin is $4500 , and because we have 3 contracts, Per contract initial margin is $1500 c. The payoff on feb 28 = 𝐹 -28 27 1.5 = 450/300 = 193.10 - 𝐹 27 So the price on 27 feb is 191.6 th d. Margin balance is $4500 - $1170 = $3330 on jan 30 e. Jan 31 , we get the first margin call of $4500 - $2730 = $1770 f. Total payoff = 3x (100) x (𝐹𝑇- 𝐹0) = 300 X ( 193.10-200) = -2070 CHAPTER 5 “ Risk neutral pricing” Have a range of price with lower and upper bound, where prices falling outside of this range would give rise to arbitrage. Assumption: - Borrow and sell at risk free rate - Short sale proceeds are received asap - Notations used : S , F , T and r Example slide 8 of Chp 5 pdf 𝑆0= 40 T = 0.25 ( 3 months) r = 5% CC 𝑀𝑎𝑟𝑘𝑒𝑡 𝐹 = 43 ( over priced) 0 Arbitrage Today At T Short one forward 0 43 Long Asset -40 Borrow +40 -40.50 Total 0 2.5 FV of loan = 40 𝑒5%,0.25 = 40.50 The price at which there will be no arbitrage is at $40.50 THE EQUATION: To have no arbitrage : Short forward + long asset + borrow = 0 Therefore, Short forward = short asset + long t-bill ( or invest) This is called : synthetic short forward. Also, Long forward = long asset + borrow This is called : synthetic long forward Benefit : you can access market like china where stocks are restricted from being traded domestically. You can invest in options and derivatives Synthetic contracts : Now, in reality, there is only one market where the contract is priced at $43. What you can do is short the contract. But you wouldn’t find a person who would want to sell their asset to you at $40.50. this is when you create a synthetic long forward ( long to kill short ) and thus create the long asset and borrow via a synthetic long forward. Investment asset provides a known income Example s
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