Keynes, uncertainty and interest rates

Uncertainty plays an important role in The General Theory, particularlyin the theory of interest rates. Keynes did not provide a theoryof uncertainty, but he did make some enlightening remarks aboutthe direction he thought such a theory should take. I arguethat some modern innovations in the theory of probability allowus to build a theory which captures these Keynesian insights.If this is the right theory, however, uncertainty cannot carryits weight in Keynes's arguments. This does not mean that theconclusions of these arguments are necessarily mistaken; intheir best formulation they may succeed with merely an appealto risk.     

The Lévy LIBOR model

Models driven by Lévy processes are attractive because of their greater flexibility compared to classical diffusion models. First we derive the dynamics of the LIBOR rate process in a semimartingale as well as a Lévy Heath-Jarrow-Morton setting. Then we introduce a Lévy LIBOR market model. In order to guarantee positive rates, the LIBOR rate process is constructed as an ordinary exponential. Via backward induction we get that the rates are martingales under the corresponding forward measures. An explicit formula to price caps and floors which uses bilateral Laplace transforms is derived.     

A Reconsideration of the Jumbo/Non-Jumbo Mortgage Rate Differential

Consistent with a series of recent papers, the interest-rate differential between mortgages eligible for purchase based on loan size by Fannie Mae and Freddie Mac and larger loans is estimated to be 22 basis points over the 1986–2000 period. This differential averaged 19 basis points for the 1996–2000 period. Other significant effects include: loans slightly above the conforming loan limit and originated late in a calendar year often have a lower rate that nearly fully anticipates their likely characterization as a non-jumbo loan after the conforming loan limit is indexed effective each January; loan-to-value ratios affect jumbo loan rates much more than they affect non-jumbo loan rates; loans located in non-metropolitan areas have a 3 basis point differential versus loans in metropolitan areas that is surprisingly small given the likely higher cost to service non-metropolitan loans and the higher degree of uncertainty about non-metropolitan collateral values; and estimated regional mortgage rate differentials have narrowed through time.     

Planning Your Own Debt

We model the Danish market for mortgage backed securities with a two-factor interest rate model and use a stochastic programming approach to analyse how an individual home-owner should initially compose and subsequently readjust his mortgage in an optimal way. Results show that the 'rules of thumb' used by financial institutions are reasonable, although best suited for more aggressive mortgagors, for whom the delivery option is of some value. More risk-averse investors should also re-adjust frequently, but use more diversified portfolios. Results are insensitive to whether a one- or two-factor model is used, provided the former is suitably calibrated.     

Valuing and Pricing Retail Leases with Renewal and Overage Options

We consider retail leases with landlord overages options, with tenant renewal options, with both and with neither. We illustrate how the ratio of initial expected sales to the sales threshold can be manipulated to equate the value of the landlord overage options to that of the tenant renewal option at the same initial rent. Not only are the values equal, but the cumulative distributions of potential IRRs on the two leases are nearly identical, suggesting that these leases are equally attractive to risk-averse investors and thus that the same risky discount rate can be used in valuing the leases. In contrast, the appropriate risky discount rate for the overage lease is calculated to be 75–160 basis points greater than that for the renewal lease.     

Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields

Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998), de Jong and Santa-Clara (1999), Björk and Svensson (2001) and Chiarella and Kwon (2001a). However, these models usually required the introduction of a large number of state variables which, at first sight, did not appear to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models are affine functions of the state variables, and conversely that the state variables in these models can be expressed as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain affine representations for a number of popular interest rate models.     

Money and exchange rates in the Grossman-Weiss-Rotemberg model

We analyze the impact of monetary policy on inflation, interest rates and exchange rates in a model with segmented asset markets developed by Grossman and Weiss (1983) and Rotemberg (1984, 1985). We find parameters for which real and nominal exchange rates in this model are (1) much more volatile than interest rates, inflation rates, and money growth rates, (2) highly correlated with each other, and (3) highly persistent. While this model fails to match the data in other important respects, it illustrates a potentially useful approach to modelling exchange rate behavior.     

Optimal portfolio choice in the bond market

We consider the Merton problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. Working within a Markovian Heath–Jarrow–Morton model of the interest rate term structure driven by an infinite-dimensional Wiener process, we give sufficient conditions for the existence and uniqueness of an optimal trading strategy. When there is uniqueness, we provide a characterization of the optimal portfolio as a sum of mutual funds. Furthermore, we show that a Gauss–Markov random field model proposed by Kennedy [Math. Financ. 4, 247–258(1994)] can be treated in this framework, and explicitly calculate the optimal portfolio. We show that the optimal portfolio in this case can be identified with the discontinuities of a certain function of the market parameters.     

Differences in the Cost of Trade Execution Services on Floor-Based and Electronic Futures Markets

This paper provides new evidence on the impact of electronic trading on brokerage commissions by investigating a sample period that covers the period of transition from floor to electronic trading on the Sydney Futures Exchange. After controlling for liquidity, volatility and broker identity, the introduction of electronic trading remains to be associated with lower brokerage commissions relative to floor markets. The study also provides new evidence on brokerage commissions in futures markets finding that commission fees charged on futures trades average 0.002% of transaction value. This is up to 120 times smaller than the magnitude of brokerage fees charged in stock markets, and considerably lower than the magnitude of brokerage fees assumed for futures markets in previous research. Consistent with existing studies based on stock markets, commissions charged per contract decrease with order size reflecting economies of scale in the provision of brokerage services in futures markets. Commission rates are positively related to bid-ask spreads and price volatility, which proxy for the probability of execution error costs and execution difficulty, respectively. Finally, the identity of the broker is found to be a significant determinant of commissions reflecting different pricing schedules across brokers.