Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary

This paper presents a new numerical method for pricing American call options when the volatility of the price of the underlying stock is stochastic. By exploiting a log-linear relationship of the optimal exercise boundary with respect to volatility changes, we derive an integral representation of an American call price and the early exercise premium which holds under stochastic volatility. This representation is used to develop a numerical method for pricing the American options based on an approximation of the optimal exercise boundary by Chebyshev polynomials. Numerical results show that our numerical approach can quickly and accurately price American call options both under stochastic and/or constant volatility.American call option, Stochastic volatility, Early exercise boundary, Chebyshev polynomials

Option Pricing under Discrete Shifts in Stock Returns

In this paper we introduce a pricing model for a European call option when the price of the underlying stock (asset) follows a random walk with Markov chain type of shifts in the drift and volatility parameters according to the regime that the stock market lies in, at a given period of time. We show that the model can explain the main stylized facts of the option pricing literature and substantially reduce the BS option pricing biases when it allows for time-varying transition probabilities between the regimes of the stock market.Markov regime switching, Option pricing, Volatility smile

Option Pricing with a Dividend General Equilibrium Model

This paper derives a general equilibrium option pricing model for a European call assuming that the economy is exogenously driven by a dividend process following Hamilton's (1989) Markov regime switching model. The derived formula is used to investigate if the European call option prices are consistently priced with the stock market prices. This is done by obtaining the implied risk aversion coefficient of the model, for constant relative risk aversion preferences, based on traded option prices data.Markov regime switching, Option pricing, Risk aversion, Volatility smile

Is the Currency Risk Priced in Equity Markets?

In this paper we investigate whether the currency risk is priced in international stock markets. We suggest a parsimonious version of the international capital asset pricing model with an EGARCH-M(1,1) specification of the second moments' dynamics of stock and currency returns, assuming that the latter follow a multivariate t-distribution. This specification allows for asymmetric responses of volatility to stock and currency news, including leverage effects. Our results suggest that the currency risk is priced in international stock markets, once asymmetries in volatility are taken into account. The currency premium is found to be significant on both statistic and economic grounds. We find that a dynamic portfolio strategy that hedges against currency changes provides higher returns (as a reward for currency premium) than a strategy which ignores them.International asset pricing, Currency risk, Multivariate EGARCH, Density forecast, Dynamic hedging strategies

Testing for Unit Roots in Short Dynamic Panels with Serially Correlated and Heteroscedastic Disturbance Terms

In this paper we introduce fixed-T unit root tests for panel data models with serially correlated and heteroscedastic disturbance terms. The tests are based on pooled least squares estimators for the autoregressive coefficient of the AR(1) panel model adjusted for their inconsistency. The proposed test statistics have normal limiting distributions when the cross-section dimension of the panel grows large, provided a condition involving the 4+δ-th order moments of the first differences of the data is satisfied. Monte Carlo evidence suggests that the tests have empirical size close to the nominal level and considerable power, even for MA(1) disturbance terms which exhibit strong negative autocorrelation.Panel data, Unit roots, Serial correlation, Heteroscedasticity, Central limit theorem

Detection of Structural Breaks in Linear Dynamic Panel Data Models

This paper develops a break detection procedure for the well-known AR(p) linear panel data model with exogenous or pre-determined regressors. The test allows for a structural break in the slope parameters as well as in the fixed effects. Breaks in the latter are not constrained by any type of cross-sectional homogeneity and are allowed to be correlated with all past information.Panel data, Structural break, Break detection

A Bayesian Analysis of Unit Roots and Structural Breaks in the Level and the Error Variance of Autoregressive Models

In this paper, a Bayesian approach is suggested to compare unit root models with stationary models when both the level and the error variance are subject to structural changes (known as breaks) of an unknown date. The paper utilizes analytic and Monte Carlo integration techniques for calculating the marginal likelihood of the models under consideration, in order to compute the posterior model probabilities. The performance of the method is assessed by simulation experiments. Some empirical applications of the method are conducted with the aim to investigate if it can detect structural breaks in financial series, with changes in the error variance.Bayesian inference, Model comparison, Autoregressive models, Unit roots, Structural breaks

Panel Data Unit Roots Tests: The Role of Serial Correlation and the Time Dimension

We investigate the influence of residual serial correlation and of the time dimension on statistical inference for a unit root in dynamic longitudinal data, known as panel data in econometrics. To this end, we introduce two test statistics based on method of moments estimators. The first is based on the generalised method of moments estimators, while the second is based on the instrumental variables estimator. Analytical results for the IV based test in a simplified setting show that (i) large time dimension panel unit root tests will suffer from serious size distortions in finite samples, even for samples that would normally be considered large in practice, and (ii) negative serial correlation in the error terms of the panel reduces the power of the unit root tests, possibly up to a point where the test becomes biased. However, near the unit root the test is shown to have power against a wide range of alternatives. These findings are confirmed in a more general set-up through a series of Monte Carlo experiments.Dynamic longitudinal (panel) data, Generalized method of moments, Instrumental variables, Unit roots, Moving average errors

Stochastic Volatility Driven by Large Shocks

This paper presents a new model of stochastic volatility which allows for infrequent shifts in the mean of volatility, known as structural breaks. These are endogenously driven from large innovations in stock returns arriving in the market. The model has a number of interesting properties. Among them, it can allow for shifts in volatility which are of stochastic timing and magnitude. This model can be used to distinguish permanent shifts in volatility coming from large pieces of news arriving in the market, from ordinary volatility shocks.Stochastic volatility, Structural breaks