Single Asset Pricing Research Articles

Multi-asset option pricing using an information-based model

Diversification of assets by an investor offers reduced exposure to risk compared to investing in a single asset. A multi-asset option gives an investor this advantage as its payout depends on the overall performance of several underlying assets. This study uses an information-based model to derive an approximate price for European call multi-asset options. The single asset price is derived using the risk-neutral pricing approach, and the multi-asset case uses the notion of comonotonicity. A numerical illustration is looked at to validate the theoretical results and to show the accuracy of the information-based model. The results show that prices from the information-based model provide a close fit to the empirical prices using a suitable information flow rate parameter. Hence, by making use of the information available in the market, an investor can price multi-asset European call options.

Applying Independent Component Analysis and Predictive Systems for Algorithmic Trading

In this paper, a Nonlinear AutoRegressive network with eXogenous inputs and a support vector machine are proposed for algorithmic trading by predicting the future value of financial time series. These architectures are capable of modeling and predicting vector autoregressive VAR(p) time series. In order to avoid overfitting, the input is pre-processed by independent component analysis to filter out the most noise like component. In this way, the accuracy of the prediction and the trading performance is increased. The proposed algorithms have a small number of free parameters which makes fast learning and trading possible. The method is not only tested on single asset price series, but also on predicting the value of mean reverting portfolios obtained by maximizing the predictability parameter of VAR(1) processes. The tests were first performed on artificially generated data and then on real data selected from exchange traded fund time series including bid–ask spread. In both cases the proposed method could achieve positive returns.

Semi-Markov Model for Market Microstructure

We introduce a new model based on Markov renewal processes (MRP) describing the fluctuations of a tick-by-tick single asset price. We consider a point process associated to the timestamps of the price jumps, with marks associated to price increments. By modelling the marks with a suitable Markov chain, we can reproduce the strong mean-reversion of price returns, a phenomenon known as microstructure noise. Moreover, using MRP, we can model the alternating of time intervals with high and low market activity, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behaviour of our model at large-scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with available empirical data.

Semi Markov Model for Market Microstructure

We introduce a new model for describing the fluctuations of a tick-by-tick single asset price. Our model is based on Markov renewal processes. We consider a point process associated to the timestamps of the price jumps, and marks associated to price increments. By modeling the marks with a suitable Markov chain, we reproduce the strong mean-reversion of price returns known as microstructure noise. Moreover, by using Markov renewal processes, we can model the presence of spikes in intensity of market activity, i.e. the volatility clustering, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behavior of our model at large scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with empirical data on the Euribor future.

Depicting the 'Elephant': When All Asset Pricing Models are Blind

This article presents a bias/variance trade-off framework and a model portfolio approach for diversifying asset pricing model uncertainty, as well as improving asset pricing model out-of-sample pricing precision when all models are false. The model portfolio approach improves asset pricing model out-of-sample pricing performance over six linear single asset pricing models and a dynamic model selection strategy . Asymptotically, when the true model is in the model space, the model portfolio approach assigns all weight to the true model; and when the model pricing errors are uncorrelated with identical variances, the model portfolio approach will assign equal weights to the models. Our empirical evidence that all asset pricing models in our model space are possibly false, and also models’ out-of-sample pricing errors are highly correlated provides an explanation for the performance improvement of the model portfolio approach over both single asset pricing models and “1/N” weighted model averaging.

Defining Single Asset Price Momentum in terms of a Stochastic Process

This paper looks at various definitions of momentum then investigates a particular definition of momentum via a statistical model where the asset price is assumed to follow a log Ornstein–Uhlenbeck process. Momentum is a term that is widely used to describe price behaviour but is not clearly defined in terms of statistical models. The results we derive show that asset price momentum is determined by price autocorrelation and that positive momentum, as commonly understood, would require explosive behaviour in log prices.

The Spectrum Discovery of Asset Price

This essay envisions a prism-like discovery of an asset's price spectrum. The discovery procedure matches, at a point in time, investors' shared value assessments as the constituent prices of the asset price spectrum. In this perspective, traditional price discovery allowing only a single asset price at a point in time is filter-like. The institutional source of excess volatility in financial markets is traced to the filter-like traditional price discovery's pick and announcement of herd leaders. Through observable spectrum images of asset price it is shown that the prism-like spectrum discovery would facilitate undistorted coordination and adjustment of investment behaviors.

Expected Returns and Liquidity Risk: Does Entrepreneurial Income Matter?

This paper studies the effects of jointly incorporating liquidity risk and non-tradeable wealth in a single asset pricing equation. First, I propose an overlapping-generations model with random endowment shocks and liquidity risk, evaluating their joint impact on expected returns. The model presents a single-factor asset pricing equation, with a new term capturing the covariance between assets' liquidities and non-tradeable wealth. In this economy, assets with higher liquidity or returns when non-tradeable wealth is low command lower expected returns. Second, I investigate whether risks associated with liquidity are priced after including non-tradeable wealth due to entrepreneurial income. I test the model on equally weighted and value-weighted portfolios, sorted by illiquidity levels, illiquidity variation and size, using US stock data from January 1962 to December 2004. The extra terms due to entrepreneurial income reduce liquidity risk premium by almost 40%, with an impact of -0.45% per year on expected returns of value-weighted illiquidity-sorted portfolios. Overall, liquidity risk as a whole has a yearly premium equal to 1.06%. However, liquidity levels are much more important and have a premium of 6.14% per year, contributing to most of the explanatory gains of the model.

Expected Returns and Liquidity Risk: Does Entrepreneurial Income Matter?

This paper studies the effects of jointly incorporating liquidity risk and non-tradeable wealth in a single asset pricing equation. First, I propose an overlapping-generations model with random endowment shocks and liquidity risk, evaluating their joint impact on expected returns. The model presents a single-factor asset pricing equation, with a new term capturing the covariance between assets' liquidities and non-tradeable wealth. In this economy, assets with higher liquidity or returns when non-tradeable wealth is low command lower expected returns. Second, I investigate whether risks associated with liquidity are priced after including non-tradeable wealth due to entrepreneurial income. I test the model on equally weighted and value-weighted portfolios, sorted by illiquidity levels, illiquidity variation and size, using US stock data from January 1962 to December 2004. The extra terms due to entrepreneurial income reduce liquidity risk premium by almost 40%, with an impact of -0.45% per year on expected returns of value-weighted illiquidity-sorted portfolios. Overall, liquidity risk as a whole has a yearly premium equal to 1.06%. However, liquidity levels are much more important and have a premium of 6.14% per year, contributing to most of the explanatory gains of the model.

CONTINGENT CLAIMS VALUED AND HEDGED BY PRICING AND INVESTING IN A BASIS

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and for which the family of Hermite polynomials serves as an orthonormal basis. Basis pricing synthesizes claim valuation and basis investment provides static hedging opportunities. For claims written as functions of a single asset price we infer from observed option prices the implicit prices of basis elements and use these to construct the implied equivalent martingale measure density with respect to the reference measure, which in this case is the Black‐Scholes geometric Brownian motion model. Data on S & P 500 options from the Wall Street Journal are used to illustrate the calculations involved. On this illustrative data set the equivalent martingale measure deviates from the Black‐Scholes model by relatively discounting the larger price movements with a compensating premia placed on the smaller movements.