Question: Consider the reading that follows which deals with the effects of straightforward delta hedging. Read the events described and then answer the questions that follow.
Dynamic Hedging US equity option market participants were of one voice last week in refuting the notion that [dynamic hedging due to] equity options trading had exacerbated the stock market correction of late October, which saw the Dow Jones Industrial Average fall 554.26 points, or some 7%. Dynamic hedging is a strategy in which investors buy and sell stocks to create a payout, which is the same as going long and short options. Thus, if the market takes a big drop, a writer of puts sells stock to cut their losses. Dynamic hedgers buy and sell stock to achieve the position they desire to equalize their exposure to volatility. The purpose of dynamic hedging, also known as delta hedging, is to remain marketneutral. The hedger's objective is to have no directional exposure to the market. For example, the hedgers will buy puts, giving them the right to sell stock. They are thus essentially short the market. To offset this short position, the hedger will purchase the underlying stock. The investor is now long the put and long the stock, and thereby market-neutral. If the market falls, the investor's put goes in-the-money, increasing the short exposure to the market. To offset this, the investor will sell the underlying... "It is my humble opinion that few investors use dynamic hedging. If somebody is selling options, i.e. selling volatility, they will have an offsetting position where they are long volatility. People don't take big one-sided bets," said a senior official at another U.S. derivatives exchange. (Thomson Reuters IFR, issue 832)
a. Suppose there are a lot of put writers. How would these traders hedge their position? Show using appropriate payoff diagrams.
b. What would these traders do when markets start falling? Show on payoff diagrams.
c. Now suppose an option's trader is short volatility as the last paragraph implies. Describe how this trader can be long volatility "somewhere else."
d. Is it possible that the overall market is a bit short volatility, yet that this amount is still very substantial for the underlying (cash) markets? There are many special terms in this reading, but at this point we would like to emphasize one important aspect of dynamic hedging that was left unmentioned in the chapter. As mentioned in the reading, in order to dynamically hedge a nonlinear asset, we need a delta. Delta is the sensitiveness of the option to underlying price changes. Now if this asset is indeed nonlinear, then the delta will depend on the volatility of underlying risks. If this volatility is itself dependent on many factors, such as the strike price, then there will be a volatility smile and delta hedging may be inaccurate. To this effect, suppose you have a long options' position on FTSE-100. How would you delta hedge this position? More important, how would this delta hedge be affected by the observations in the last paragraph of the reading?