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The Greek Letters (Ch. 18)
Management of Market Risk
Delta
Gamma
V
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Vega
Other Greek Letters
Theta
Rho
Example (Hull 18.1)
A bank has sold (for $300,000) a European call
option on 100,000 shares of a nondividend
paying stock
S
0
= 49,
X
= 50,
r
= 5%,
= 20%,
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T =
20 weeks
The BlackScholes value of the option is $240,000
How does the bank hedge its risk?
In, at or out of the money?
What risk does the bank face?
Naked & Covered Positions (Hull 18.2)
Naked position
Take no action

how much could the bank lose?
Covered position
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Buy 100,000 shares today
 what is wrong with this strategy?
Both strategies leave the bank exposed to significant
risk.
When does the bank ‘need’ the underlying
?
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StopLoss Strategy (Hull 18.3)
Buy 100,000 shares as soon as price reaches $50
Sell 100,000 shares as soon as price falls below
$50
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This simple hedging strategy does not work well.
Why not?
1)
transaction costs
2) how do you decide whether the price will go up or
down or will continue?
3)
Buy high and sell low
More Sophisticated Hedging Strategies
Try to hedge option price risk
How?
Look for the factors that have effects on the option price
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Figure out relation between these factors and option price
Measure how sensitive of the option price is to the
changes in value of these factors
Come up a strategy to reduce the sensitivity, i.e., riskfree
(risk neutral) portfolio
Determinants of option prices
Five factors determine option prices:
Price of the underlying
S
Exercise price
X
Volatility of returns of S
σ
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time to maturity of option
T or (Tt)
risk free rate
r
What is the effect of a change of one of these
factors on the option price holding all others
constant?