FINM1001 Lecture Notes - Lecture 21: Forward Contract, Cash Flow

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30 May 2018
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FINM1001 Week 11 Lecture A
If we construct a portfolio (pf) and show that the instruments in the portfolio are worth 0
dollars in the future (irrespective of market prices) thus in theory, in pf today should be
worth 0 as well.
Pf:
Short call:
Initial CF (cash flow): +c
Terminal Values ST > X: -(ST - X)
Terminal Values X > ST: 0
Long put:
Initial CF (cash flow): -p
Terminal Values for ST > X: 0
Terminal Values for X > ST : X - ST
Buy Stock:
Initial CF (cash flow): -S0
Terminal Values ST > X: ST
Terminal Values for X > ST: ST
Borrow:
Initial CF (cash flow): +X(1+ff)-T
Terminal Values ST > X: -X
Terminal Values for X > ST: - X
Total:
Initial CF (cash flow): c - p - So + X(1+rf)-T
Terminal Values ST > X: 0
Terminal Values for X > ST: 0
Created a strategy that will give you a 0 pay off no matter the market price
Thus c - p - So + X(1+rf)-T = 0 thus c = p+S0 - X(1+rf)-T
Arbitrage profit obtained immediately.form the put call parity violation
Sell call:
Initial CF: +2.50 (+c)
ST > X: -10
X > ST: 0
Buy put:
Initial CF: -1.50 (-p)
ST > X: 0
X > ST: 10
Buy stock:
Initial CF: -20
ST > X: 30 (ST)
X > ST: 10
Borrow PV of X:
Initial CF: +20(1+0.08)-0.5
ST > X: -20
X > ST: -20
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Document Summary

If we construct a portfolio (pf) and show that the instruments in the portfolio are worth 0 dollars in the future (irrespective of market prices) thus in theory, in pf today should be worth 0 as well. Terminal values st > x: -(st - x) Terminal values for st > x: 0. Terminal values for x > st : x - st. Terminal values for x > st: st. Terminal values for x > st: - x. Terminal values for x > st: 0. Initial cf (cash flow): c - p - so + x(1+rf)-t. Created a strategy that will give you a 0 pay off no matter the market price. Thus c - p - so + x(1+rf)-t = 0 thus c = p+s0 - x(1+rf)-t. Arbitrage profit obtained immediately. form the put call parity violation. Buy call -> payoff (st - x) max. Sell put -> payoff (st - x) min. Thus company wants at least 750,000 aud.

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