Partial hedging and cash requirements in discrete time

This paper develops a discrete time version of the continuous time model of Bouchard et al. [J. Control Optim., 2009, 48, 3123–3150], for the problem of finding the minimal initial data for a controlled process to guarantee reaching a controlled target with probability one. An efficient numerical algorithm, based on dynamic programming, is proposed for the quantile hedging of standard call and put options, exotic options and quantile hedging with portfolio constraints. The method is then extended to solve utility indifference pricing, good-deal bounds and expected shortfall problems.     

Dynamic complex hedging in additive markets

In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity.     

Stock performance by utility indifference pricing and the Sharpe ratio

We compare stock performance based on utility indifference pricing and the Sharpe ratio assuming that stock returns follow the class of discrete normal mixture distributions. The utility indifference price with an exponential utility function satisfies several desirable properties that a suitable value measure should satisfy. For utility indifference pricing, we employ the inner rate of risk aversion proposed by Miyahara [Evaluation of the scale risk. RIMS Kokyuroku, No. 1886, Financial Modeling and Analysis (2013/11/20-2013/11/22), 181–188, 2014], which is the degree of risk aversion that makes the utility indifference price with the exponential utility function zero in order to evaluate stock performance. Using a selection of U.S. stocks, the results show that the evaluation of stock performance based on the inner rate of risk aversion is more relevant for risk-averse investors than that based on the Sharpe ratio, which represents performance by the first two moments.     

Stochastic dividend yields and derivatives pricing in complete markets

When an underlying yields a stochastic dividend yield, derivatives with linear payoff at their maturities that are written on this underlying have the following properties: (i) they have a unique price only if markets are complete; (ii) the dynamic strategies that replicate these contingent claims contain hedging components against the state variables in the economy; (iii) the prices of these derivatives will depend upon the dynamics of the market prices of risk even when markets are complete. Within an affine framework, we explicitly price forward and futures contracts with stochastic dividends. We also show that the quantitative impact of assuming that dividends are deterministic when they are actually stochastic is significant. JEL Classification G12 · G13     

Risk and return in residential spatial markets: An empiric and theoretic model

The paper is concerned with price and rent fluctuations in predominantly owner-occupied residental real estate. It presents the owner-occupier household as a housing consumer as well as an investor. It conjectures that since risk and return are known to be positively related in financial markets, they might also be thus related in residential real estate markets. If that is so, neighborhoods that are known to yield high returns will be the ones less price and rent stable than low yielding ones.The Capital Asset Pricing Model is not helpful in explaining a possible risk/return relationship in housing markets. Its major assumption about portfolio diversification is contrary to the nature of owner-occupied residential real estate. An owner occupier household, by definition, holds one unit of the asset and acts simultaneously as an investor and consumer of housing. For the capital market investor, investment and consumption decisions are separable. Therefore, a new theoretical model of consumer choice is proposed. Tel-Aviv price and rent data during a volatile market period are used for testing the main risk/return conjecture as well as other related hypotheses stemming from the model. The findings lend support to the conjecture and shed light on possible spatial determinants of owners' risk.     

Pricing and hedging European options with discrete-time coherent risk

The aim of the paper is to provide as explicit as possible expressions for upper/lower prices and for superhedging/subhedging strategies based on discrete-time coherent risk measures. This is done on three levels of generality. For a general infinite-dimensional model, we prove the fundamental theorem of asset pricing. For a general multidimensional model, we provide expressions for prices and hedges. For a wide class of models, in particular, including GARCH, we give more concrete formulas, a sufficient condition for the uniqueness of a hedging strategy, and a numerical algorithm.