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

From the last chapter, you know that the 50 percent or 0.5 is the option'sdelta. We also know that delta is the hedge ratio. In order to fully hedgean at-the-money calj^put) option written, an option writer needs to purchase(s^ll) a certain number of shares as determined by delta multiplied by thenumber of shares under the contract.But what if the price of Stock A drops to $90, or increases to $110?When the stock price of A drops from $100 to $90, the put option is inthe-moneyand the probability of the option being exercised is higher than50 percent. Assume that the delta is now 0.7. The option writer has tohedge 70 percent of his position by selling 70 shares of Stock A. Since hehas already sold 50, he has to sell 20 more.90 100When the stock price of A increases from $ 100 to $ 110, the put option isout-of-the-money and the probability of the option being exercised is less than50 percent, say at 30 percent, or the delta is now 0.3. At this time, the optionwriter has to buy back 20 shares of Stock A in order to remain delta neutral.(He should sell 30 shares but he has already sold 50.)100 110Trading Options is Trading Volatility