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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 »

Strategies to reduce option cost

A US investor has purchased Sterling Treasury bills and wishes to hedge against the falling value of Sterling. Buying the out-of-the-money put (strike price $1.8500) will protect against a fall below that figure. The sale of the out-of-the-money call at $1.8900 will mean that the investor will benefit from any rise in Sterling to $1.8900 but not above that figure. The cost of buying the put is off-set by the revenue from writing the call, resulting in this instance in a zero cost strategy.

The reader will note that if Sterling rises above $1.8900, the written call position will make a loss. This is off-set by the rising value in dollar terms of the underlying Sterling investment. Conversely, if Sterling falls below $1.8850, the puts make a profit which off-sets the currency losses on the investment in the Sterling Treasury bills. Read more »

Using currency options to manage risk

This section explains two of the many uses of options that rely upon the ability of the option buyer to abandon the option at no extra cost. The first is the purchase of options to insure against a fall in the value of a currency. The second is the hedging of the currency risk in a foreign currency tender.

Purchasing options as a form of insurance

If a US investment manager has strong expectations of a rise in the value of Sterling but wishes to insure against being totally wrong, slightly out-of-the money puts will provide the required insurance. 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 »

Empirical evidence of the term structure continue…

Term structure based option-pricing models

Term structure models of pricing contingent claims have followed one of two approaches. One approach followed by Cox, Ingersoll and Ross (1985) actually model the expected returns from movements in the term structure in order to price the contingent claims. In effect, the term structure becomes endogenous to the pricing of the contingent claim.

The second approach followed by Ho and Lee (1986), Heath, Jarrow and Morton (1989), Black, Derman and Toy (1990) and Hull and White (1990) utilizes the volatilities of the various sectors of the term structure to derive a probability distribution of an arbitrage-free binomial, trinomial or multinomial lattice of the term structure. From this lattice, contingent claims are priced. These models all have one thing in common: they allow for the whole-term structure to be stochastic instead of the price of a single underlying instrument or a single interest rate. The whole-term structure is represented at each node of the binomial, trinomial or even multinomiaf lattice. 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 »

Reasons for the swap markets’ existence

Currency swaps, which were developed before interest rate swaps, were derivations of the 1970s practice of establishing parallel loans between two parties whereby, for example, company A would lend its domestic currency to company B, in return for a loan of company B’s domestic currency. These parallel loans were often used to manage exchange risk or to circumvent exchange control regulations.

This system of mutual lending had two serious drawbacks. First, there was no automatic off-set of the cash flows between parties. Thus, if company A defaulted on its loan from B, company B would still have to honour its commitment to A. Secondly, although the two loans effectively cancelled each other out, they were still shown on the balance sheets of each company. Read more »

Enjoy my New Discovery of Commodity swaps

Another new area of the swaps market is that of commodity swaps. The mechanics of these swaps are similar to interest rate swaps, in that the swap establishes a fixed commodity price and a floating commodity index, with which the fixed price can be compared. There is a notional principal physical quantity of the commodity which establishes the value of the periodic cash flows. To illustrate these mechanics and give some insight into the use of commodity swaps as risk management instruments, consider the following scenario regarding a manufacturer that is a substantial consumer of copper. Read more »

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