Derivatives in Plain Words by Frederic Lau, with a ... - HKU Libraries

As shown in the above graph, the down-side risk for writing options ispotentially unlimited. Because writing options is a high risk operation fora bank, the management should stipulate in the policy document the optiontrading strategies such as whether traders are allowed to write nakedoptions, i.e. writing options without holding the underlying asset, or whethertraders are required to hedge (fully or partially) the positions. If writingoptions is allowed, how the management controls this risk should be clearlywritten down in the policy statement.THE DELTA OF AN OPTIONThe payoff line of the above graph for the option buyer kinks at $100 andthen slopes upward. The slope of this line can be anywhere from zero toone for call options (-1 to 0 for put options). How does the slope of thepayoff line relate to options trading? An important point to remember is:a call option (at a specific strike price) with a slope of 0.5 means that whenthe price of the underlying increases by $ I, the price of the option increasesby $0.5. The slope of the payoff line is also called the hedge ratio. Marketparticipants commonly call the hedge ratio the option's delta. IIf the option writer does not want to take the potentially unlimited down- vside risk, he can fully hedge his positions. For every at-the-money calloption written, he needs to purchase 0.5 share of the underlying stock if thedelta is 0.5. For example, you have written 10 at-the-money options, thestock price is currently at $100 and the hedge ratio or the delta is 0.5. Youneed 5 shares of stock to fully hedge the position. This is because if thestock price increases by $1.00, the value of the 10 options increases by $0.5x 10 options = $5.00. The value of the 5 shares of stock also increases by$101 x 5 - $100 x 5 = $5.00.What if the delta is 0.7?If the delta increases from 0.5 to 0.7, you need 2 more shares of stock tofully hedge your position. This is because if the stock price increases by$1.00, the value of the 10 options increases by $0.7 x 10 options = $7.00.Delta and Volatility