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Futures on equity indices

Alternative methods of weighting

It is generally considered that capitalization weighted indices give the most accurat indication of the collective movement in corporate asset or liability prices. However two alternative methods of weighting the constituents of equity indices are fowl,equally weighted‘ and ‘price weighted‘. In the case of equally weighted indices, a’ equal amount of money is assumed to be invested in each security in the index Changes in the index thus represent changes in the value of the portfolio. Pri weighted indices reflect the average price of the securities in the index and Chang: in the index represent the average price change of the securities in the index. The Dow—Jones and the Major Market Index of the American Stock Exchange (MMI) a. both of the price weighted form. The FT 30 is a geometric average equally weight index. Only the Major Market Index has a futures contract based upon it. Read more »

Make Options Easy on equity indices

The dramatic growth of equity index futures has been accompanied by the substantial growth of equity index options. These options come in three forms:

  1. Options on the spot index itself such as the contract traded in the London International Financial Futures and Options Exchange — like the futures, these options are settled in cash, rather than by delivery of the underlying securities. Sometimes both European and American options are traded on the same index.
  2. Options on the index futures are American options that call for delivery of an equity index futures contract at expiry.

Read more »

Average rate options

Average rate currency options are based upon the average exchange rate of the underlying currency as distinct from the exchange rate on a single date — the expiry date.

The advantage of an average rate option is that the volatility of a moving average of a variable is less than the volatility of individual observations of that same variable. With daily observations, and with the volatility levels seen in the currency markets, the volatility of the moving average is in the order of 60% of that of the raw observations. Consequently, the price of an average rate option with a given exercise price will be less than an otherwise identical standard European currency option. Read more »

Are interest rate options different to other options?

The valuation of interest rate options is currently the most contested area of option- pricing theory. The problem stems from the fact that although there is a reasonable consensus about the nature of the stochastic process of share prices, equity indices and currencies, the movements in interest rates and interest rate dependent instruments are not fully understood and full agreement on the underlying process has yet to be reached.

The stochastic process of interest rates, and therefore the prices of interest rate dependent claims, has proved to be very difficult to model for a number of reasons. Read more »

Immunizing bond portfolios using bond futures

Bonds are frequently purchased to fund future liabilities because of the relative certainty of the cash flows which are set contractually. However, the certainty as to the value of the terminal value of those future cash flows depends upon two factors:

the rate at which the future coupons can be reinvested remaining unchanged;

if the bond has a maturity longer than the desired holding period, the level of interest rates is the same at the beginning and end of the holding period. Read more »

Empirical evidence of the term structure

A detailed analysis of the empirical testing of the term structure is beyond the scope of this post; however, in summary it should be stated that the empirical tests give a substantial role to expectations. However, forward rates are not unbiased estimators of future spot rates, and the bias is consistent with a liquidity premium. There is also some evidence that the premium increases with the term to maturity, but at a decreasing rate. There is less support for the segmentation hypothesis.

The dynamics of the term structure

Clearly the term structure is dynamic, but exactly what is the nature of this dynamic process? It has long been observed that long rates are less volatile than short rates; for further discussion see Kessel (1965), Malkiel (1966) and Brooks and Livingston (1990). Current long-rate volatilities are linked to current short-rate volatilities by the concept of mean reversion — i.e. where short rates have a tendency to be pulled back towards some long-term average value following a movement up or down. Read more »

The debt instruments with embedded options continue…

Bonds with equity warrants attached

Recently it has been popular among Japanese corporations to issue eurobonds with equity warrants attached. Their popularity has stemmed partly from the strength of the Tokyo stock market, the warrants giving an equity kicker to bond investors.

These warrants are usually detached from the bonds after issue, and traded separately. Bonds with warrants attached are different from convertible bonds because the warrants are long-term options which when exercised require new cash, not existing bonds, to be exchanged for the new equity. At the time of issue, the bonds constitute a portfolio consisting of one bond and one long-term option on the equity of the issuer. After the time of issue, and when the warrants have been stripped, the bonds are valued as straight bonds. Read more »

Reasons for the swap markets’ existence continue…

However, this theory of the development of the swaps market assumes that the financial markets remain informationally inefficient and that the benefits of comparative advantage are not arbitraged away. There is no doubt that in the early days of the interest rate and currency swaps markets it was possible to locate such inefficiencies that resulted in generous benefits to both parties, but in the years since the market’s inception the benefits have to some extent been reduced by arbitrage, yet the market still grows dramatically.

Thus there must be some other reason, or reasons, for the existence of the swaps market as the comparative advantage theory assumes that some markets persistently underprice credit risk relative to other markets. Three alternative reasons for the market’s existence can be postulated. Read more »

Valuation of equity swaps

The valuation of equity swaps may, at first sight, seem more complex than the pricing of interest rate swaps because the total return to the index is not known at the outset. However, as the equity index is a carryable asset, it is possible to develop an arbitrage-free value of the equity side of the swap in a manner analogous to the pricing a long-term futures contract.

For example, if a party were to pay the equity returns, it is effectively going short the equity market. This position could be hedged by buying the underlying index with the proceeds of a floating rate loan. The interest costs of the loan will be serviced from the LIBOR receipts under the swap. Read more »

Asset swaps — synthetic instruments for asset management

Asset swaps are different, in that they are linked to the purchase of an asset and the swapping of the cash flows of that asset. They are therefore used synthetically to engineer an asset structure rather than a liability structure.

The idea behind an asset swap is to enhance returns to the investor rather than hedging or lowering costs to a borrower. The objective is to find some underpriced fixed rate bond which is then purchased by an investor that would prefer a floating rate investment. The coupons are then swapped with a bank that has fixed rate liabilities at a lower cost. The bank thereby receives a fixed payment that is higher than the cost of its existing fixed rate debt. Read more »

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