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Chapter 8

2.6 The Greeks – gamma, vega, rho, theta

 Gamma – measures the rate of change of delta as the underlying asset's price
changes

 Vega – measures the sensitivity of the option value to changes in the volatility

 Rho – measures the sensitivity of the option value to changes in the risk-free
rate of interest

 Theta – measures the rate of change in the value of the option caused by the
passage of time

2.7 Delta hedging

An investor can eliminate the risk of a shareholding by constructing a ‘delta hedge’.
This means selling call options in the proportion dictated by the delta as follows:

Number of call options to sell = Number of shares held / N(d 1).

Example 1

If the delta value is 0.5, an investor with 100 shares should therefore sell 200
call options (100 / 0.5).

Then, if the share price increased by $1,

 total movement in share value = ($1 x 100) = $100

 movement in option value = (0.5 x $1 x 200) = $100

where the share value movement represents a gain, and the option value
movement represents a loss (gain to the option holder so loss to the option
writer).

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