Knowledge that Transforms

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that arechosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.

This study examines the effects on the stock market unitary risk premium and volatility associated with the listing of stock and stock index derivatives in Switzerland. Based on a univariate GARCH (1,1) specification of the stock index variance and a time-varying unitary risk premium representation, we can reject the hypothesis that stock and stock index derivatives listings do not affect the total risk premium. Contrarily to previous empirical evidence, we find that derivatives listings affect both the conditional market returns’ variance and the unitary risk premium through structural shocks. The gradual market completion hypothesis is further corroborated in that, cumulatively, the three stock and stock index options futures derivatives listings reduced the unitary risk premium while the marginal impact of each successive listing decayed.

This paper investigates the interaction between financial structure, liquidation values and product market equilibrium. Liquidation values depend on how many firms are liquidated, and therefore on the industry equilibrium of capital structures and of technology choices. We show that firms using a technology with high liquidation value issue less debt than those with low liquidation value even if these ones may be inefficiently liquidated. With respect to the equilibrium in the industry, we obtain that even if in equilibrium all firms use the same technology, firms will use widely different capital structures.

The optimal bond-stock mix is examined in light of an apparent inconsistency between the Tobin Separation Theorem and the advice of popular investment advisors which has been pointed out by Canner et al. (1997).It is shown that the apparent inconsistency is largely explicable in terms of the hedging demands of optimising long-term investors in an environment in which the investment opportunity set is subject to stochastic shocks. The analysis points to the importance of considering investors' time horizons in analyzing optimal portfolio policies.

This paper investigates tax effects in the Canadian government bond market during the period 1964—1986. Unlike previous studies, we apply both statistical and nonstatistical teststo analyze clientele effects and market equilibria. The results divide the sample into two distinct periods of time, with the end of 1976 marking the division. We find that tax effects are almost nonexistent in the Canadian government bond market before the end of 1976, but are predominant in the post-1976 period. Non-segmented market equilibria cannot be rejected before 1977, but are strongly rejected after 1976. In fact, segmented equilibria with clientele effects in both quantities and prices characterize the entire five year period from 1982 to 1986. These findings are consistent with tax reforms, government deficit financing and interest rate fluctuations in Canada during our sample period.

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations inthe presence of short- and long-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.

This paper examines the valuation of European- and American-style volatility options based on a general equilibrium stochastic volatility framework. Properties of the optimal exercise region and of the option price are provided when volatility follows a general diffusion process. Explicit valuation formulas are derived in four particular cases. Emphasis is placed on the MRLP(mean-reverting in the log) volatility model which has received considerable empirical support. In this context we examine the properties and hedging behavior of volatility options. Unlike American options, European call options on volatility are found to display concavity at high levels of volatility.

This paper focuses on pricing and hedging options on a zero-coupon bond in a Heath-Jarrow-Morton (1992) framework when the value and/or functional form of forward interest rates volatility is unknown, but is assumed to lie between two fixed values. Due to the link existing between the drift and the diffusion coefficients of the forward rates in the Heath, Jarrow and Morton framework, this is equivalent to hedging and pricing the option when the underlying interest rate model is unknown. We show that a continuous range of option prices consistent with no arbitrage exist. This range is bounded by the smallest upper-hedging strategy and the largest lower-hedging strategy prices, which are characterized as the solutions of two non-linear partial differential equations. We also discuss several pricing and hedging illustrations.

This paper analyzes how an investor who is convinced that he can “beat the market” should behave when the equilibrium price process is endogenous. The investor's optimal portfolio is shown to consist of three components: (1) a tangency portfolio, (2) a hedge portfolio against changes in the market's valuation of securities, and (3) a hedging position against changes in the divergence between the investor's and the market's beliefs. The sign and magnitude of this third component will depend on investor preferences and on the divergence in the investor's and the market's quality of information. A numerical example illustrates that the effect of heterogeneous beliefs on optimal portfolio allocations can be significant.