A general framework for the derivation of asset price bounds: an application to stochastic volatility option models

We present a generalization of Cochrane and Saá-Requejo’s good-deal bounds which allows to include in a flexible way the implications of a given stochastic discount factor model. Furthermore, a useful application to stochastic volatility models of option pricing is provided where closed-form solutions for the bounds are obtained. A calibration exercise demonstrates that our benchmark good-deal pricing results in much tighter bounds. Finally, a discussion of methodological and economic issues is also provided.      

A valuation algorithm for indifference prices in incomplete markets

A probabilistic iterative algorithm is constructed for indifference prices of claims in a multiperiod incomplete model. At each time step, a nonlinear pricing functional is applied that isolates and prices separately the two types of risk. It is represented solely in terms of risk aversion and the pricing measure, a martingale measure that preserves the conditional distribution of unhedged risks, given the hedgeable ones, from their historical counterparts.Received: 1 September 2003, Mathematics Subject Classification: 93E20, 60G40, 60J75JEL Classification: C61, G11, G13The second author acknowledges partial support from NSF Grants DMS 0102909 and DMS 0091946.     

A continuous-time model for reinvestment risk in bond markets

When comparing standard bond market models with practice we observe that, whereas the literature places no restrictions on the time to maturity of traded bonds, this is actually the case in practice. Hence, standard models ignore the reinvestment risk present in practice when considering contacts with longer time to maturity than the longest bond traded in the market. In this paper we propose a model including this reinvestment risk. We place a restriction on the bonds traded in the market by limiting the time to maturity of traded bonds. At fixed times, new bonds are issued in the market, thus extending the time of maturity of traded bonds. The initial prices of the new bonds issued in the market depend on the information generated by the market and a stochastic variable independent thereof describing the reinvestment risk. In order to quantify and control the reinvestment risk we apply the criterion of risk-minimization.     

A profitable trading and risk management strategy despite transaction costs

We present a new profitable trading and risk management strategy with transaction cost for an adaptive equally weighted portfolio. Moreover, we implement a rule-based expert system for the daily financial decision-making process using the power of spectral analysis. We use several key components such as principal component analysis, partitioning, memory in stock markets, percentile for relative standing, the first four normalized central moments, learning algorithm, and switching among several investment positions consisting of short stock market, long stock market and money market with real risk-free rates. We find that it is possible to beat the proxy for the equity market without short selling for 168 S&P 500-listed stocks during the 1998–2008 period and 213 Russell 2000-listed stocks during the 1995–2007 period. Our Monte Carlo simulation for both the various set of stocks and the interval of time confirms our findings.     

A jump-diffusion model for the euro overnight rate

In this work we introduce a jump-diffusion process for the euro overnight rate (the European over night index average) that is able to capture the main characteristics of this rate: (i) dynamics constrained to remain in the corridor of official rates fixed by the European Central Bank; (ii) mean reversion towards the official rate on main refinancing operations; and (iii) highly discontinuous pattern (with jumps), also without variations in the official rate. After calibrating the model parameters on historical data, we implement the model to price an overnight indexed swap. Finally, a comparison between our model and the most common short-term interest rate models is presented.     

A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback

Recent market events have reinvigorated the search for realistic return models that capture greater likelihoods of extreme movements. In this paper we model the medium-term log-return dynamics in a market with both fundamental and technical traders. This is based on a trade arrival model with variable size orders and a general arrival-time distribution. With simplifications we are led in the jump-free case to a local volatility model defined by a hybrid SDE mixing both arithmetic and geometric or CIR Brownian motions, whose solution in the geometric case is given by a class of integrals of exponentials of one Brownian motion against another, in forms considered by Yor and collaborators. The reduction of the hybrid SDE to a single Brownian motion leads to an SDE of the form considered by Nagahara, which is a type of ‘Pearson diffusion’, or, equivalently, a hyperbolic OU SDE. Various dynamics and equilibria are possible depending on the balance of trades. Under mean-reverting circumstances we arrive naturally at an equilibrium fat-tailed return distribution with a Student or Pearson Type~IV form. Under less-restrictive assumptions, richer dynamics are possible, including time-dependent Johnson-SU distributions and bimodal structures. The phenomenon of variance explosion is identified that gives rise to much larger price movements that might have a priori been expected, so that ‘25σ’ events are significantly more probable. We exhibit simple example solutions of the Fokker–Planck equation that shows how such variance explosion can hide beneath a standard Gaussian facade. These are elementary members of an extended class of distributions with a rich and varied structure, capable of describing a wide range of market behaviors. Several approaches to the density function are possible, and an example of the computation of a hyperbolic VaR is given. The model also suggests generalizations of the Bougerol identity. We touch briefly on the extent to which such a model is consistent with the dynamics of a ‘flash-crash’ event, and briefly explore the statistical evidence for our model.     

A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.     

A fully consistent,minimal model for non-linear market impact

We propose a minimal theory of non-linear price impact based on the fact that the (latent) order book is locally linear, as suggested by reaction–diffusion models and general arguments. Our framework allows one to compute the average price trajectory in the presence of a meta-order that consistently generalizes previously proposed propagator models. We account for the universally observed square-root impact law, and predict non-trivial trajectories when trading is interrupted or reversed. We prove that our framework is free of price manipulation and that prices can be made diffusive (albeit with a generic short-term mean-reverting contribution). Our model suggests that prices can be decomposed into a transient ‘mechanical’ impact component and a permanent ‘informational’ component.