corp_ch21_09 - CLASS NOTES WEEK VIII BM Ch.21 Understanding...

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IRPGEN424 Corporate Finance Alex Kane 1 CLASS NOTES WEEK VIII BM Ch.21 Understanding options
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IRPGEN424 Corporate Finance Alex Kane 2 What are contingent claims (derivatives)? A derivative is a contract whose payoff is completely determined from future values of observable economic variable(s) -- called the underlying(s) Example: An employment contract may include a fixed wage plus COLA. The value of this contract is derived from the (observable) future (yet unknown) level of the CPI derivatives makes a huge class of assets. The value of a derivative is derived from the dynamics of the underlying(s). With COLA, the stochastic process of inflation (CPI) generates the market value of this feature
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IRPGEN424 Corporate Finance Alex Kane 3 Real value of wages CPI Wages (real) CPI(0) COLA would keep real wages at original level with CPI(0) -- the horizontal axis Real wage at CPI(0)
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IRPGEN424 Corporate Finance Alex Kane 4 The elementary particle of CF Definition: Arrow certificate pays $1 in one state of the world and zero otherwise PV(CF) = sum of all Arrows embedded in it PV($1) risk-free T-bill = sum of all Arrows, one for each state of the world The price of an Arrow depends on (1) the probability of the state of the world on which it’s written, and (2) the discount rate used Which Arrows get the highest value (lowest discount rate)? Arrows written on “bad” states -- insurance against widespread maladies, e.g., bad economy
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IRPGEN424 Corporate Finance Alex Kane 5 CF to owner of Arrow states of the world shown as value of an underlying, e.g., SP 500 index, GDP CF to LONG Arrow State when Arrow pays $1 $1 Arrow is a derivative. Any CF is a collection of Arrows
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IRPGEN424 Corporate Finance Alex Kane 6 Long and short positions in a stock S(T) CF (T) Long position Short position Notice : each CF is a collection of Arrows. Short position has unlimited risk The principle with short positions is simple: CF (short) = –CF(long) 0
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IRPGEN424 Corporate Finance Alex Kane 7 Why values of derivatives are important With a sufficiently large collection of derivatives written on an underlying you can replicate any CF whose risk is determined by this underlying Put differently, any CF can be replicated with options Result: if you know how to price options, you can price ANY CF, that is, any economic contract or project !!
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IRPGEN424 Corporate Finance Alex Kane 8 Forwards, Calls and Puts These are standardized derivatives that trade on organized exchanges
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