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Financial Derivative Securities

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Submitted By chiltpj
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Assignment 1
Financial Derivative Securities 312

P’eau James Chilton
15505480

Joyce Khuu

Question 1

Use simultaneous equation in terms of payoffs J,K and L:

J = [2,3] PJ = $0.08 Equation 1: 2J + 3K = 1
K = [3,1] PK = $0.05 Equation 2: 3J + K = 4
L = [1,4] PL = ?

Rearrange equation 2:

K = 4 – 3J

Substitute K = 4 – 3J into equation 1:

2J + 3(4 – 3J) = 1
2J + 12 – 9J = 1
-7J = -11
J = 11/7

Substitute J = 11/7 into equation 2:

3(11/7) + K = 4
K = - 5/7

Therefore, in our replication portfolio we have 11/7 of security J and -5/7 of security K tp replicate security L.

11/7 [2,3] – 5/7 [3,1] = [1,4]

If the price of PJ = $0.08 and PK = $0.05 the price of PL is the cost of the replication portfolio.

PL = 11/7 (0.08) – 5/7 (0.05)
PL = $0.09

Question 2

T = [1,0] PT = $0.60
U = [0,1] PU = $0.70
V = [4,3] PV = $4.30

Use simultaneous equation:

Equation 1: T = 4
Equation 2: U = 3

4T + 3U = V

Therefore, 4 [1,0] + 3 [0,1] = [4,3]

The fair value of V given the replication portfolio:

4 (PT) + 3 (PU) = Pv
4 (0.60) + 3 (0.70) = Pv
Pv = $4.50

It is undervalued in the market ($4.50 > $4.30). Therefore, an arbitrage exists.

To take advantage of the arbitrage we would sell the replication portfolio for $4.50 and simultaneous buy security V at Pv = $4.30

Arbitrage is the difference: $4.20 - $4.50 = - $0.20

Since, this is money today - $0.20 with no negative liability in the future this is a type 2 arbitrage.

Portfolio | Position Value (t=0) | If State 1 (t+1) | If State 2 (t+2) | (Buy) V | 4.30 | 4 | 3 | (Sell) T | 4(0.60) = -2.4 | -4(1) = -4 | -4(0) = 0 | (Sell) U | 3(0.70) = -2.1 | -3(0) = 0 | -3(1) = -3 | Portfolio: [V – 4T + 3U] | 4.30 – 4.50 | -4 + 0 + 4 = 0 | 0 – 3 +3 = 0 | Total | -0.20 | 0 | 0 |

This payoff table shows the arbitrage as breakdown of payoffs at

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