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The delta of an option is the change in the value of that option for a given move in the price of the underlying asset. Because an option's delta is always less than one (in absolute value), it follows that for a given change in stock price, the option value will move accordingly for a smaller amount. This seems to contradict the general perception that options are leveraged instruments. Just as delta is the appropriate hedging ratio, however, another Greek letter lambda is the more appropriate leverage ratio for options, which incorporates both the delta factor and the gearing factor.
Option Gearing: Investment Gain/Loss Multiplier
For a start, let's look at some numerical examples. Suppose an investor has USD1,000 to invest and is bullish on ABC stock, which is trading at USD100. Obviously, the investor can buy 10 ABC shares directly. Alternatively, the investor may make the same investment via at-the-money call options (strike price at USD100) on ABC shares. Assuming a one-year investment horizon, a risk free rate of r = 1%, stock volatility *= 30%, and no dividend, the price for the at-the-money European call option is USD12.37, according to the Black-Scholes pricing formula.
At maturity the option holder will gain one-for-one for any price move above the original stock price USD100. The investor could invest in 10 at-the-money options for USD12.37 * 10 = USD123.7 and gain the same exposure for stock gains as if he invested USD1,000 in 10 shares. In other words, for the same USD1,000 capital the investor can invest...