We estimate affine models using the Eurodollar futures and options data. The rationale for this exercise comes from a combination of recent theoretical and empirical work, which documents a trade-off in models abilities to match the expectations hypothesis and generate conditional volatility, and suggests to break this tight connection by explicitly removing volatility from the term structure d...

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or ‘leverage’) correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these mode...

We study comovements between standardized option values and spot stock prices for the S&P 100 equity index and ten large U.S. firms over 1988 to 1995. To standardize option values, we use a weighted average of option implied volatilities (IV) to control for the option’s moneyness, interest rates, and time to maturity. We find differences in the comovement behavior across individual stocks and t...

The skew effect in market implied volatility can be reproduced by option pricing theory based on stochastic volatility models for the price of the underlying asset. Here we study the performance of the calibration of the S&P 500 implied volatility surface using the asymptotic pricing theory under fast mean-reverting stochastic volatility described in [7]. The time-variation of the fitted skew-s...

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with t...

In this paper I analyze a broad class of continuous-time jump diffusion models of asset returns. In the models, stochastic volatility can arise either from a diffusion part, or a jump part, or both. The jump component includes either compound Poisson or Lévy α-stable jumps. To be able to estimate the models with latent Lévy α−stable jumps, I construct a new Markov chain Monte Carlo algorithm. I...

This paper provides a semiparametric model to estimate processes of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we estimate the volatility process by filtering. We prove the consistency of the model in the sense that estimated processes converge to the true ones as the number ...

The fact that the implied volatility smiles for equity indices are strongly downward sloping, while the typical individual stock exhibits either a flat or even an upward sloping smile is sometimes considered puzzling. We show that this effect can easily be generated in a simple and parsimonious two-factor stochastic volatility model in the spirit of Bates (2000). From a theoretical perspective ...

This paper deals with an option pricing model which can be thought of as a hybrid stochastic and local volatility model. This model is built on the local volatility term of the well-known constant elasticity of variance (CEV) model multiplied by a stochastic volatility term driven by a fast mean-reverting Ornstein-Uhlenbeck process. An asymptotic formula for European option price is derived to ...

We study the eeect of stochastic volatility on option prices. In the fast-mean reversion model for stochastic volatility of 5], we show that there is a full asymptotic expansion for the option price, centered at the Black-Scholes price. We show, however, that this price does not converge in a strong sense to Black-Scholes as the mean-reversion rate increases. We also introduce a general (possib...