Richard C. Stapleton

Multiplicative Background Risk

Although there has been much attention in recent years on the effects of additive background risks, the same is not true for its multiplicative counterpart. We consider random wealth of the multiplicative form xy, where x and y are statistically independent random variables. We assume that x is endogenous to the economic agent but that y is an exogenous and nontradable background risk that represents a type of market incompleteness. Our main focus is on how the presence of the multiplicative background risk y affects risk-taking behavior for decisions on the choice of x. We extend the results of Gollier and Pratt (1996) to characterize conditions on preferences that lead to more cautious behavior.

When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel

This paper examines the convexity bias introduced by pricing interest rate swaps off the Eurocurrency futures curve and the markets adjustment of this bias in prices over time. The convexity bias arises because of the difference between a futures contract and a forward contract on interest rates, since the payoff to the latter is non-linear in interest rates. Using daily data from 1987-1996, the differences between market swap rates and the swap rates implied from Eurocurrency futures prices are studied for the four major interest rate swap markets -

A Simple Technique for the Valuation and Hedging of American Options

, £, DM and ¥. The evidence suggests that swaps were being priced off the futures curve (i.e. by ignoring the convexity adjustment) during the earlier years of the study, after which the market swap rates drifted below the rates implied by futures prices. The empirical analysis shows that this spread between the market and futures-implied swap rates cannot be explained by default risk differences, liquidity differences or information asymmetries between the swap and the futures markets. Using alternative term structure models (one-factor Vasicek, Cox-Ingersoll and Ross, Hull and White, Black and Karasinski, and the two-factor Heath, Jarrow and Morton), the theoretical value of the convexity bias is found to be related to the empirically observed swap-futures differential. We interpret these results as evidence of mispricing of swap contracts during the earlier years of the study, with a gradual elimination of that mispricing by incorporation of a convexity adjustment in swap pricing over time.

Risk taking with additive and multiplicative background risks

The value and hedge ratio of an American-style option are shown to be closely approximated by a simple quadratic formula. The technique requires the estimation of the values and hedge ratios of just two options: a European option and a twice-exercisable option. These can be computed instantaneously, and hence the American values and hedge ratios can be rapidly computed for a large book options with little computational effort.

Leases, debt and taxable capacity

We examine the effects of background risks on optimal portfolio choice. Examples of background risks include uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities. While some of these risks are additive and have been amply studied, others are multiplicative in nature and have received far less attention. The simultaneous effect of both additive and multiplicative risks has hitherto not received attention and can explain some paradoxical choice behavior. We rationalize such behavior and show how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor.

The analysis and valuation of interest rate options

Finance theory suggests that finance leases and corporate debt are substitutes, and that taxable capacity has a negative influence on leasing. There have been few tests of these predictions however. Previous work by Ang and Peterson, using US data, tested the prediction that finance leases and debt are inversely related, but ignored the prediction that the degree of leasing is negatively influenced by taxable capacity. Also, the results of the study were contradictory to the prediction of the theory, indicating that finance leases and debt complement each other empirically rather than acting as substitutes. In the present study, the two predictions stated above are tested, using data from a sample of UK quoted companies for the period 1990-92. The results indicate that, for a sub-sample of companies that use finance leases, the degree of leasing and debt financing are negatively related, as predicted by the theory. The results also support the suggestion that shortage of taxable capacity is an important explanation for leasing, and that inadequate access to the debt capital markets is another. We also find little evidence of an industry effect on the use of finance leases.

The Valuation of American Options on Bonds

Abstract This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the Black-Scholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general, and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps.

Capital Market Equilibrium in a Mixed Economy, Optimal Public Sector Investment Decision Rules, and the Social Rate of Discount

The valuation of American-style bond options involves two important aspects that need to be modeled carefully. First, stochastic interest rates influence the volatility of the price of the bond, the underlying asset, in a complex fashion as the bond approaches maturity, and hence, the incremental value of the early exercise (American) feature. Second, the early exercise decision for such options is affected by the term structure of interest rates on future dates, since the live value of the claim on each future date depends on the discount rates on that date. These two aspects are modeling in this paper. The paper analyzes the value of American options on bonds using a generalization of the Geske-Johnson (1984) technique. The method uses as inputs the valuation of European options, and options with multiple exercise dates. It is proved that a risk-neutral valuation relationship along the lines of the Black-Scholes (1973) model holds for options exercisable on multiple dates, even under stochastic interest rates, when the price of the underlying asset is lognormally distributed. The proposed computational method uses the maximized value of these options, where the maximization is over all possible exercise dates. The value of the American option is then computed by Richardson extrapolation. The volatility of the underlying default-free bond is modeled using a two-factor model, with a short-term and a long-term interest rate factor. The paper reports the results of simulations of American option values and show how they vary with the key parameter inputs, such as the maturity of the bond, its volatility, and the option strike price.

European tax systems and the neutrality of corporate financing policy

I. Introduction, 399.—II. Asset prices in a mixed economy, 401—III. Optimal levels of investment in a mixed economy, 403.—IV. Conclusion, 408.

The pricing of Bermudan-style options on correlated assets

Abstract The different tax systems of European illustrate the variety of ways in which the double taxation of dividends can be reduced. This paper analyses the effect of corporate financing policy under the imputation, dual rate, mixed and classical tax systems, and derives conditions for neutrality of the systems with respect to financing policy-neutrality in the sense that no type of financial policy has favourable tax treatment. The effect of the capital gains tax and heterogenous personal tax rates across individuals are analysed by using a model of stock value. Neutrality depend on the parameters of the tax system and a weighted average of personal tax rates.