Rational Asset Prices

The mean, co-variability, and predictability of the return of different classes of financial assets challenge the rational economic model for an explanation. The unconditional mean aggregate equity premium is almost seven percent per year and remains high after adjusting downwards the sample mean premium by introducing prior beliefs about the stationarity of the price-dividend ratio and the (non) forecastability of the long-term dividend growth and price-dividend ratio. Recognition that idiosyncratic income shocks are uninsurable and concentrated in recessions contributes toward an explanation. Also borrowing constraints over the investors' life cycle that shift the stock market risk to the saving middle-aged consumers contribute toward an explanation.

Stochastic Dominance Bounds on Derivative Prices in a Multiperiod Economy with Proportional Transaction Costs

By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility.

Constrained LQR for Low-Precision Data Representation

Performing computations with a low-bit number representation results in a faster implementation that uses less silicon, and hence allows an algorithm to be implemented in smaller and cheaper processors without loss of performance. We propose a novel formulation to efficiently exploit the low (or non-standard) precision number representation of some computer architectures when computing the solution to constrained LQR problems, such as those that arise in predictive control. The main idea is to include suitably-defined decision variables in the quadratic program, in addition to the states and the inputs, to allow for smaller roundoff errors in the solver. This enables one to trade off the number of bits used for data representation against speed and/or hardware resources, so that smaller numerical errors can be achieved for the same number of bits (same silicon area). Because of data dependencies, the algorithm complexity, in terms of computation time and hardware resources, does not necessarily increase despite the larger number of decision variables. Examples show that a 10-fold reduction in hardware resources is possible compared to using double precision floating point, without loss of closed-loop performance

Optimal Bond Trading with Personal Taxes: Implications for Bond Prices and Estimated Tax Brackets and Yield Curves

The assumption that bondholders follow either a buy-and-hold or a continuous realization trading policy, rather than the optimal trading policy,is at variance with reality and, as we demonstrate, may seriously bias the estimation of the yield curve and the implied tax bracket of the marginal investor. Tax considerations which govern a bondholder's optimal trading policy include the following: realization of capital losses, short term if possible; deferment of the realization of capital gains, especially if they are short term; changing the holding period status from long term to short term by sale of the bond and repurchase, so that future capital losses may be realized short term; and raising the basis through sale of the bond and repurchase in order to deduct from ordinary income the amortized premium. Because of the interaction of these factors, no simple characterization of the optimal trading policy is possible. We can say, however, that it differs substantially from the buy-and-hold policy irrespective of whether the bondholder is a bank, a bond dealer, or an individual. We obtain these strong results even when we allow for transactions costs and explicitly consider numerous IRS regulations designed to curtail tax avoidance.

Seeing Shapes in Clouds: On the Performance-Cost trade-off for Heterogeneous Infrastructure-as-a-Service

In the near future FPGAs will be available by the hour, however this new Infrastructure as a Service (IaaS) usage mode presents both an opportunity and a challenge: The opportunity is that programmers can potentially trade resources for performance on a much larger scale, for much shorter periods of time than before. The challenge is in finding and traversing the trade-off for heterogeneous IaaS that guarantees increased resources result in the greatest possible increased performance. Such a trade-off is Pareto optimal. The Pareto optimal trade-off for clusters of heterogeneous resources can be found by solving multiple, multi-objective optimisation problems, resulting in an optimal allocation of tasks to the available platforms. Solving these optimisation programs can be done using simple heuristic approaches or formal Mixed Integer Linear Programming (MILP) techniques. When pricing 128 financial options using a Monte Carlo algorithm upon a heterogeneous cluster of Multicore CPU, GPU and FPGA platforms, the MILP approach produces a trade-off that is up to 110% faster than a heuristic approach, and over 50% cheaper. These results suggest that high quality performance-resource trade-offs of heterogeneous IaaS are best realised through a formal optimisation approach.Comment: Presented at Second International Workshop on FPGAs for Software Programmers (FSP 2015) (arXiv:1508.06320

Option Pricing: Real and Risk-Neutral Distributions

The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.Option; Pricing