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 »

Posted: June 22nd, 2008 under Currency Futures, Futures Options, Futures Prices, Swap Futures, investment.
Comments: 4

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 »

Posted: June 20th, 2008 under Future Trading, Futures Contracts, Futures Market, Futures Prices, Interest Rate Futures.
Comments: 5

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 »

Posted: June 20th, 2008 under Future Exchange, Futures Contracts, Futures Market, Futures Prices, Interest Rate Futures.
Comments: 6

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 »

Posted: June 17th, 2008 under Equity Futures, Future Broker, Futures Contracts, Futures Quotes, Managed Futures, Stock Market Futures, Swap Futures.
Comments: 4

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 »

Posted: June 17th, 2008 under Crude Oil Futures, Futures Options, Futures Prices, Futures Spreads, Short Futures, Silver Futures.
Comments: 5

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 »

Posted: June 15th, 2008 under Currency Futures, Future Fund, Future Management, Future Trading, Futures Index, Futures Market, Futures Prices, Futures Spreads, Futures Trader, Futures Trading System, Managed Futures, S&P Futures, Stock Futures, investment.
Comments: 3

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 »

Posted: June 15th, 2008 under Future Trading, Futures Options, Futures Quotes, Stock Market Futures, Swap Futures, investment.
Comments: 4

The investment manager may have a number of bond-like assets in the portfolio, and corporate treasurers may have issued similar liabilities which have options embedded within them by virtue of the contract terms under which the bonds were issued. Common examples of such bonds are as follows.

• Bonds with call provisions allow the issuer to call the issue at a date earlier than the redemption date, at a price different from par but specified when the bond is issued. Bonds with sinking funds attached also have an embedded option.

• Putable bonds give the holder the option to put the bond back to the issuer at a predetermined price.

• Convertible bonds give the holder the option of converting the bond into the equity of the issuer. The rate of conversion and the time is specified when the bonds are issued. Some convertible bonds have been issued that provide for conversion into other bonds.

Read more »

Posted: June 15th, 2008 under Futures Options, Swap Futures.
Comments: 5

The exact nature of market risk will depend upon the nature of the swap: it will be interest rate risk, currency risk, equity market risk or commodity risk, according to the type of swap being considered. Generally intermediaries or counterparties will be able to hedge market risk, but credit risk cannot be hedged. However, it may be reduced substantially by holding a diversified portfolio of credit risks.

Credit risk

The fact that, at least for interest rate swaps, the principals are not exchanged means that the exposure to default is limited to the difference between the present value of the fixed and the floating cash flows. Consider a pay fixed/receive floating swap, first, from the viewpoint of the pay fixed side. We noted earlier that if interest rates have fallen since the swap was initiated, the swap will have a negative value to the pay fixed side — i.e. the present value of the future fixed payments to be made is greater than the present value of the floating payments to be received. Read more »

Posted: June 7th, 2008 under Futures Market.
Comments: 5

Key Points

• When currencies are exchanged for delivery more than two business days later, the governing exchange rate is the forward rate. The forward rate is given by an inviolable interest rate parity that ensures that two riskless investments generate the same total return. Under normal circumstances, the forward rate should be an unbiased predictor of the future spot rate. However, the actual future spot rate is significantly different from the forward rate. This phenomenon is referred to as the forward rate bias.
• In order to satisfy the requirement of the same return generated by two riskless assets given by interest rate parity, the currency with the higher interest rate must depreciate relative to a currency with a lower interest rate as given by the forward rate. Evidence indicates that the currency with the higher interest rate actually appreciates instead of depreciating. This pattern is confirmed for a variety of currency pairs not including high-interest-rate currencies, for many different observation periods, and many different holding periods. It seems that the bias decreased a little during the 1990s and it disappears when the holding period becomes about ten years. However, the bias at short holding periods of about one month is of most interest to investors.

Read more »

Posted: February 14th, 2008 under Currency Futures.
Comments: 4