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

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 »

Posted: June 15th, 2008 under Currency Futures, Future Exchange, Futures Contracts, Managed Futures, Swap Futures.
Comments: 4

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: 6