A Logical Approach to Actuarial Mathematics_10 docx

214 Part 3  Thinking about options Frequently, however, on a rally the skew can remain in place, and the implieds of all strikes are unchanged. Effectively, the implied volatility decreases because the focal point of the skew moves to the new at-the- money strike. The solid line of Figure 20.9 illustrates this: XYZ rallies from 100 to 105, and the new ATM implied, now at the 105 strike, is less than that of the former 100 strike. This situation often occurs with skews in stock indexes as they rally to former levels. The options market is unfazed by the upside retracement. This also occurs in commodities that have negative put skews as the commodities retrace from a rally; there the graph is the mirror image of Figure 20.9. Another possibility is that on a break, the skew can remain in place. Effectively, the implied volatility increases because the focal point of the skew moves to the new at-the-money strike. The dotted line of Figure 20.9 illustrates this: XYZ breaks from 105 to 100, and the new ATM implied, now at the 100 strike, is greater than that of the former 105 strike. This latter situation often occurs with skews in stock indexes as they break. The options market is fearful that this is the big one. When it really is the big one, then the entire skew will shift vertically upward, and the put wing will become more positive. 100 105 XYZ 36 38 34 22 32 30 28 26 24 20 Figure 20.9 Horizontal skew shift, negative call skew, positive put skew 20  Volatility skews 215 A note on market sentiment In all cases where a straight long or short option is chosen for a directional strategy, skew risk can be minimised by trading the long or short call or put spread. Volatility skews are indicators of market senti- ment. Positive skews indicate fear, while negative skews indicate complacence. Sentiment, as we know, can often be wrong, but it cannot be ignored. Volatility skews are indicators of market sentiment part 4 Basic non-essentials Introduction Most of us won’t spend our options careers trading arbitrage, but when the opportunity arises, as it does from time to time, it’s an almost risk-free way to make money. So if you learn about the arb, then you’re prepared to take advantage of it when you see it. Read Part 4 at least once. Think about it from time to time. When you’re scanning the markets, ask yourself, ‘Is there an arbitrage here? Can I lock in a profit with this trade until expiration?’ If you keep this in mind, then some day you’ll find yourself making a lot of money in a very short time. If you’re prepared. 21 Futures, synthetics and put–call parity It is possible to combine options and underlying positions in ways that simulate straight call or put positions. An underlying itself may be simu- lated with a combination of options. As an example of the former, a long at-the-money call plus a short underlying position has the same risk/ return profile as a long at-the-money put, and is therefore known as a syn- thetic put. Synthetic positions are used primarily by professional market-makers to simplify the view of their options inventory in order to manage risk better. They are of little practical use to traders who take options positions based on market outlooks, but they can be studied in order to understand how options markets work. In order to understand synthetics, it is best if you understand why they exist. Like all options positions, they are based on a relation to an under- lying contract, which may be a cash investment or a futures contract. If we briefly take this subject step by step, then we will avoid future disorientation. What a futures contract is A futures contract is simply an agreement to trade a commodity, stock, bond or currency at a specified price at a specified future date. Because no cash is exchanged for the time being, the future buyer is said to have a long position, and the future seller is said to have a short position. As a result, the holder of the long position profits as the market moves up and takes a loss as the market moves down. The holder of the short position has the opposite profit/loss. 222 Part 4  Basic non-essentials If short selling were not possible, investors would only be able to buy from those who wanted to sell physical holdings; liquidity would suffer and market volatility would increase. Most exchanges require a security deposit in order to open a futures contract, and this deposit is known as initial margin. The value of the contract as traded on the exchange invariably fluctuates, and so results in a profit to one party and a loss to the other. The party who has a loss is then required to deposit the amount of the loss, and this additional deposit is known as variation margin. Margin may be in the form of cash, or it may be in the form of liquid securities such as treasury bills or gilts, for which the depositor still collects interest. Meanwhile the party who has the profit is credited with variation margin, and he receives interest on the balance. Futures contracts have traditionally been used in commodities markets in order to hedge supply shortages and surpluses. They are now used in stocks, stock indexes, bonds and currencies. Many excellent books describe how these forms of futures contracts operate. An example of a futures contract Consider the following example of a closing price of the S&P 500 index with the settlement price of the December futures contract and the settle- ment prices of the at-the-money call and put on the futures contract. S&P index: 1133.68 December future: 1140.70 December 1140 call: 34.40 December 1140 put: 33.70 Here, the S&P futures contract multiplier is $250. An investor who trades one of the above December contracts is hedging 1140.70 × $250 = $285,175 worth of stocks that track the index. The options contract multi- plier is $25. We know that the December future, here with approximately six weeks until expiration, trades at a premium to the cash. This is because taking a long position in the futures contract instead of buying all the stocks in the index requires a margin deposit only. The holder of the futures position therefore has the use of his cash for the next six weeks. The value of the futures contract is increased by the cost of carrying on the stocks. 21  Futures, synthetics and put–call parity 223 On the other hand, the holder of the long futures position forgoes the dividends payable for the next six weeks, and therefore the value of the December future is decreased by that amount. The formula for the value of the futures contract is approximated as follows: Futures contract = cash value of index + interest or cost of carry on index until expiration – dividends payable until expiration In practice, the formula is more complicated because annualised rates of carry and dividend yields are used. Here, we are simply concerned with why the above future trades above or below the cash. Until recently short-term interest rates paid more than dividend yields, and so stock index futures traded at a premium to their underlying indexes. The situation is now reversed, and it is similar to the 1950s, where dividend yields paid more than short-term interest rates in order to compensate for the risk of owning stock. This was a holdover from the crash of 1929, when many stock-holders’ investments were wiped out. The reason now, however, is that after the recent bank- ing crisis, the central banks are trying to maintain liquidity by keeping interest rates low. Occasionally, shortly before expiration, there may be a large amount of dividends payable in a stock or stock index. Then the dividend outweighs the interest amount and the future trades at a discount to the index. Once the dividend or dividends are paid, then the future trades above the cash. In any event, the futures contract and the cash index converge at expira- tion because then there is no remaining differential between cost of carry and payable dividends. The futures contract simply expires to the current cash value of the index. There, the holder of the long futures contract pays the cash value of all the stocks in the index. The holder of the short futures contract receives the cash value of all the stocks in the index. The ultimate amount exchanged is deter- mined by the value of the index at expiration times the contract multiplier. In the case of a physical commodity such as corn or crude oil, the futures contract is deliverable to the quantity of the commodity specified in the contract at the settlement price. The futures contract and the cash index converge at expiration because then there is no remaining differential between cost of carry and payable dividends [...]... If you’ve read this book with open eyes, you’ve already arrived at the same conclusion, at least intuitively The mysterious and complex world of put–call parity is now exposed as a trifle You, the intelligent reader, have more important things to think about, such as choosing your socks in the morning 231 232 Part 4  Basic non-essentials A call and a put at the same strike have the same amount of time... small discrepencies in the put–call parity values If the put–call parity formula were applied to options on the OEX or other American-style index options, large discrepencies would result due to early exercise premium Significant discrepancies also result with American-style options on individual stocks, i.e most stock options Put–call parity can be a helpful way of pricing options, but its limitations... practical risks large options portfolios are those of pin risk and early assignment A long box is the purchase of a synthetic underlying at a lower strike and the sale of a synthetic underlying at a higher strike A short box is the opposite position Because the box is both long and short the underlying, its profit/loss does not change regardless of market movement Again, the only practical risks are... 1140 call 22  Conversions reversals, boxes and options arbitrage By keeping the conversions in line, the arbitrageurs, or arbs, help to maintain efficient pricing in the market As a result, we benefit by getting a fair price for our options Reverse conversion, or reversal A reversal is a short underlying plus a long call and a short put at the same strike If XYZ is at 100, you could buy one 100 call,... 1140 call SPZ Short 1140 put Figure 22.2 SPZ 1140 reversal Short futures 235 236 Part 4  Basic non-essentials Conversion and reversals on individual stocks and on other stock indexes The conversion and reversal markets on stocks operate in basically the same manner Remember that with stocks there are no futures contracts, but that the options combine to form synthetic futures contracts The situation... reversals, boxes and options arbitrage Conversions, reversals, and boxes are used almost exclusively by marketmakers and risk managers to neutralise the risk of large options portfolios At one time, they were traded in order to profit from small price discrepancies in synthetic positions, but now most mature options markets have eliminated this opportunity A short synthetic underlying position can be... is similar to the S&P 500 cash–futures–options relationship given in Chapter 20: S&P 500 cash index at 1133.68 December future at 1140.70 December 1140 call at 34.40 December 1140 put at 33.70 If the futures contract were eliminated, and the options were exercisable instead to cash, then the relationship would be the same as between stocks and stock options The OEX options are traded in this manner,... offset each other because below 1140 you have the right to sell what you own at the price at which it was purchased less the cost of the put Above 1140 you are simply long the futures contract Being net long a futures contract above 1140 is the same as owning a December 1140 call The cost of your synthetic call breaks down as follows The futures contract costs 1140.70, and the right to sell it at 1140...224 Part 4  Basic non-essentials Synthetic futures contract As we already know, a long XYZ 100 call, by virtue of its right to buy, equals a long XYZ position when XYZ is above 100 at expiration We also know that a short XYZ 100 put, by virtue of its obligation to buy, equals a long XYZ position when XYZ is below 100 at expiration The sum of these two options positions, therefore, equals a synthetic... future at the same price There is no profit or loss to this position, nor will it change for the life of the options contract At expiration the short synthetic pairs off against the long future, and the result is no position There is minimal risk Figure 22.1 shows is a graph of the conversion Occasionally, there is a small amount of profit to be made by trading the components of a conversion separately . disorientation. What a futures contract is A futures contract is simply an agreement to trade a commodity, stock, bond or currency at a specified price at a specified future date. Because no cash is exchanged. said to have a long position, and the future seller is said to have a short position. As a result, the holder of the long position profits as the market moves up and takes a loss as the market. contract as traded on the exchange invariably fluctuates, and so results in a profit to one party and a loss to the other. The party who has a loss is then required to deposit the amount of