News Strategies and Analysis for Futures and Options

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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 »

Valuing American options on futures contracts

The Black model should not be used for valuing American options on currency futures because it may be optimal to exercise the options early in the same way as it may be optimal to exercise options on the spot currency early. The binomial or the Barone-Adesi and Whaley models may be used for valuing those options.

The early exercise potential of American options on futures is different to that of options on the spot. Futures prices do not exhibit the discrete jumps that accompany spot market assets when the underlying spot asset makes discrete distributions. However, as the carry basis of the future converges to zero at delivery, the futures price converges to the spot price in an orderly manner. Read more »

Pricing futures on interbank interest rates

As with all other forms of futures contract, the fair price of short-term interest rate futures should preclude any arbitrage possibilities between the futures market and the underlying cash market. In the case of bank deposit interest rate futures, there should be no arbitrage possibilities between the forward interest rate implied by the future and the forward interest rate available on the appropriate type of bank deposit. For example, a three-month eurodollar futures contract that has 135 days to maturity should not provide any arbitrage possibility with the 135-day forward rate on a three-month eurodollar deposit. Read more »

Forward interest rates and expectations

It was shown that it is possible to lock in a forward rate of interest. However, depositors will only lock in a forward deposit if the rate that results is at least as favourable as the rate that they expect to prevail at the future point in time. If the forward rate implied by the current rates was above investors’ expectations, theinvestors would increase their borrowing for 90 days, causing upward pressure on that rate, and increase their deposits for 180 days, causing downward pressure on that rate, thereby bringing the 90-day forward rate down to current expected levels.

Conversely, if the implied forward rate were below expectations, investors would borrow for the longer term, raising that rate, and deposit for the shorter term, lowering that rate, until the implied forward rate matched expectations. Read more »

Forward rate agreements (FRAs)

As the name implies, an FRA is an agreement to buy or sell a forward rate of interest on a notional principal amount. Remembering that interbank deposit rate futures also relate to forward rates of interest, the similarity between the two instruments will be obvious. Conceptually, the seller of the FRA undertakes to provide an agreed rate of interest on a notional deposit of a specified size at a previously agreed future date. Thus the FRA locks in the rate of interest on a forward deposit, the forward rate of interest.

An FRA relating to the interest rate on a six-month deposit starting in three months time is referred to in FRA market parlance as a 3 against 9 (or a 3 vs 9) FRA. This clearly indicates that, in this example, the appropriate interest rate is the six- month forward rate three months hence. Read more »

Option to choose the delivery day: the timing option

The US Treasury bond and Treasury note, and the UK gilt futures contracts, provide for delivery on any business day within a delivery month, with the short side choosing the actual day of delivery.

If future interest rates were certain, the choice of delivery day would also be certain, and the following delivery rule would apply: if the bond yield is above the repo rate (i.e. the cost of carry is negative), delivery would be on the last day of the delivery month. If, on the other hand, the bond yield is below the repo rate (i.e. positive cost of carry), delivery will be on the earliest possible delivery date. Read more »

Embedded options and the fair price of a future

The fact that these delivery options are available only to the short seller of futures contracts means that collectively they provide that seller with a series of valuable put options over the underlying bonds or notes. It is therefore instructive to delve more deeply into the nature of these options and their influence on bond futures valuation.

The existence of these options depends upon the futures contract specifications. Examples of the options that can be identified are as follows.

  1. The short seller’s option to choose the bonds that will be delivered under the futures contract; this is the so-called ‘quality option‘.
  2. The short seller’s option to choose the day of delivery within the delivery month: one form of the so-called ‘timing options‘.

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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