This article proposes a semi-martingale approximation to a fractional Lévy process that is capable of capturing long and short memory in the stochastic process together with fat tails. The authors use the semi-martingale process in option pricing and empirically compare its performance to other option pricing models, including a stochastic volatility Lévy process. They contribute to the empirical literature by being the first to report the implied Hurst index computed from observed option prices using the Lévy process model. Calibrating the implied Hurst index of S&P 500 option prices in a period that covers the 2008 financial crisis, they find that the risk-neutral measure is characterized by a short memory in turbulent markets and a long memory in calm markets.

This paper investigates the pricing and hedging of a new volatility derivative in Mainland China, called volatility-linked notes. Firstly, we describe its underlying volatility-historical volatility of SHSCI and its specific clauses, then calibrate the underlying volatility using GARCH(1,1). It finds that the mean-reverting phenomenon of SHSCI volatility exists. Secondly, we propose two pricing model using replicated method and Monte-Carlo simulation, respectively. It works out similar outcomes. Finally, a Delta-hedging scheme of the volatility-linked notes is shown, however, the estimated result is not satisfactory as the absence of more efficient hedging instruments like index future.

This study employs a non-parametric approach to investigate the volatility risk premium in the major over-the-counter currency option markets. Using a large database of daily quotes on delta neutral straddle in four major currencies ? the British Pound, the Euro, the Japanese Yen, and the Swiss Franc ? we find that volatility risk is priced in all four currencies across different option maturities and the volatility risk premium is negative. The volatility risk premium has a term structure where the premium decreases in maturity. We also find evidence that jump risk may be priced in the currency option market.

This study employs a non-parametric approach to investigate the volatility risk premium in the over-the-counter currency option market. Using a large database of daily quotes on delta neutral straddle in four major currencies ? the British Pound, the Euro, the Japanese Yen, and the Swiss Franc ? we find that volatility risk is priced in all four currencies across different option maturities and the volatility risk premium is negative. The volatility risk premium has a term structure where the premium decreases in maturity. We also find evidence that jump risk may be priced in the currency option market.

We develop a nonparametric specification test for continuous-time models using the transition density. Using a data transform and correcting for boundary bias of kernel estimators, our test is robust to serial dependence in data and provides excellent finite sample performance. Besides univariate diffusion models, our test is applicable to a wide variety of continuous-time and discretetime dynamic models, including time-inhomogeneous diffusion, GARCH, stochastic volatility, regimeswitching,jump-diffusion, and multivariate diffusion models. A class of separate inference procedures is also proposed to help gauge possible sources of model misspecification. We strongly reject a variety of univariate diffusion models for daily Eurodollar spot rates and some popular multivariate affine term structure models for monthly U.S. Treasury yields.

This paper investigates a two-factor affine model for the credit spreads on corporate bonds. The Þrst factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. The riskless interest rate is modeled using a standard two-factor affine model, thus leading to a four-factor model for corporate yields. This approach allows us to model the volatility of corporate credit spreads as stochastic, and also allows us to capture higher moments of credit spreads. We use an extended Kalman Þlter approach to estimate our model on corporate bond prices for 108 Þrms. The model is found to be successful at Þtting actual corporate bond credit spreads, resulting in a signiÞcantly lower root mean square error (RMSE) than a standard alternative model in both in-sample and out-of-sample analyses. In addition,key properties of actual credit spreads are better captured by the model.