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York University (35,409)
Lecture

# Lecture 3

4 Pages
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School
Department
Course
Professor
Nabil Tahani
Semester
Winter

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 = πΉ -28 27 1.5 = 450/300 = 193.10 - πΉ 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 (πΉπ- πΉ0) = 300 X ( 193.10-200) = -2070 CHAPTER 5 β Risk neutral pricingβ 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 π0= 40 T = 0.25 ( 3 months) r = 5% CC ππππππ‘ πΉ = 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 π5%,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 wouldnβ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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