This paper examines the ability of regime-switching models to capture the dynamics of foreign exchange rates. First we test the ability of the models to fit foreign exchange rate data in-sample and forecast variance out-of-sample. A regime-switching model with independent shifts in mean and variance exhibits a closer fit and more accurate variance forecasts than a range of other models. Next we use exchange-traded currency options to determine whether market prices reflect regime-switching information. We find that observed option prices are significantly different from their theoretical levels determined by a regime-switching option valuation model and that a simulated trading strategy based on regime-switching option valuation generates higher profits than standard single-regime alternatives. Overall, the results indicate that observed option prices do not fully reflect regime-switching information. Last revised: May 8, 1998 1 REGIME-SWITCHING IN FOREIGN EXCHANGE RATES: EVIDENCE ...

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: This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S&P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premium of stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or "leverage effect" does help to explain the skewness of the volatility "smile", allowing for stochastic interest rates has minimal impact on o...

A number of recent papers find that the volatility implied by index option prices significantly overstates future stock market volatility. We investigate whether this bias is purely due to measurement error and model misspecification, or whether the bias is also apparent in option market prices. We accomplish this by examining the profits for trading strategies designed to exploit the apparent bias. Ignoring transaction costs, the strategies consistently earn significant positive profits which indicates the bias is indeed a function of option prices. The degree of bias, however, does not signal market inefficiency because the profits disappear once we impose bid/ask transaction costs. Our analysis also reveals that the bias is too large to be explained by skewness preference, but that it may be the result of market imperfections (e.g., transaction costs) and/or a premium demanded for volatility risk. We also find that the bias apparent through the trading strategies emerged only after ...

Which loss function should be used when estimating and evaluating option pricing models? Many different functions have been suggested, but no standard has emerged. We do not promote a particular function, but instead emphasize that consistency in the choice of loss functions is crucial. First, for any given model, the loss function used in parameter estimation and model evaluation should be identical, otherwise suboptimal parameter estimates will be obtained. Second, when comparing models, the estimation loss function should be identical across models, otherwise unfair comparisons will be made. We illustrate the importance of these issues in an application of the so-called Practitioner Black-Scholes (PBS) model to S&P500 index options. We find reductions of over 50 percent in the root mean squared error of the PBS model when the estimation and evaluation loss functions are aligned. We also find that the PBS model outperforms a benchmark structural model when the estimation loss functions are identical across models, but otherwise not. The new PBS model with aligned loss functions thus represents a much tougher benchmark against which future structural models can be compared.

This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. The models are calibrated to intraday FTSE 100 option prices. We apply two sets of performance criteria, namely out-of-sample valuation errors and Value-at-Risk oriented measures. When we analyze the fit to observed prices, GARCH clearly dominates both stochastic volatility and the benchmark BlackScholes model.

We present a family of hedging strategies for a European derivative security in a stochastic volatility environment. The strategies are robust to specification of the volatility process and do not need a parametric description of it or estimation of the volatility risk premium. They allow the hedger to control the probability of hedging success according to risk aversion. The formula exploits the separation between the time scale of asset price fluctuation (ticks) and the longer time scale over which volatility fluctuates, that is, the observed "persistence" of volatility. We run simulations that demonstrate the effectiveness of the strategies over the classical Black-Scholes strategy. 1 Introduction In this article we present a family of hedging strategies for a European derivative security that super-replicate the claim with a controllable success probability, in a stochastic volatility environment. The strategy has the following features: ffl It is an approximate (asymptotic) solu...

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk. As an example

This article studies the equilibrium valuation of foreign exchange contingent claims.

We construct a simple representative agent model to provide a theoretical framework for the logstable option pricing model. We also implement a new parametric method for estimating the risk neutral measure (RNM) using a generalized two-factor log-stable option pricing model. Under the generalized two-factor log-stable uncertainty assumption, the RNM for the log of price is a convolution of two exponentially tilted stable distributions. Since the RNM for generalized two-factor log-stable uncertainty is expressed in terms of its Fourier Transform, we introduce a simple extension of the Fast Fourier Transform inversion procedure in order to reduce computational errors in option pricing. The generalized two-factor log-stable RNM has a very flexible parametric form for approximating other probability distributions. Thus, this model provides a sufficiently accurate tool for estimating the RNM from the observed option prices even if the log-stable assumption might not be satisfied. We estimate the RNM for the S&P 500 index options and find that the generalized two-factor log-stable model gives better performance than the Black-Scholes model, the finite moment log-stable model (Carr and Wu, 2003), and the orthogonal log-stable model (McCulloch, 2003) in fitting the observed option prices.