We build on of the work of Henry-Labordµere and Lewis on the small-time behaviour of the return distribution under a general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large deviations for stochastic differential equations, and then...

By exploiting the flexibility of the Wishart process, we propose an application of this framework to the pricing of Chicago Board Options Exchange (CBOE) volatility index (VIX) options. Our methodology is analytically tractable and yet flexible enough to efficiently price CBOE VIX options. In...

We analyze American put options in a hyper-exponential jump-diffusion model. Our contribution is threefold. Firstly, by following a maturity randomization approach, we solve the partial integro-differential equation and obtain a tight lower bound for the American option price. Secondly, our...

This paper proposes the sample path generation method for the stochastic volatility version of the CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 index options...

Uncertainty finance presents alternative models for derivative valuation relevant to markets willing to consider subjective information or expert criterium in their operation. This paper proposes a methodology based on experimental data for comparing the prices and the delta and vega risks for...

In this paper we propose a maximum entropy estimator for the asymptotic distribution of the hedging error for options. Perfect replication of financial derivatives is not possible, due to market incompleteness and discrete-time hedging. We derive the asymptotic hedging error for options under a...

We document the forecasting gains achieved by incorporating measures of signed, finite and infinite jumps in forecasting the volatility of equity prices, using high-frequency data from 2000 to 2016. We consider the SPY and 20 stocks that vary by sector, volume and degree of jump activity. We use...

Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and...

Daily returns of financial assets are frequently found to exhibit positive autocorrelation at lag 1. When specifying a linear AR(l) conditional mean, one may ask how this predictability affects option prices. We investigate the dependence of option prices on autoregressive dynamics under...

Recent progresses in option pricing using ARCH processes for the underlying are summarized. The stylized facts are multiscale heteroscedasticity, fat-tailed distributions, time reversal asymmetry, and leverage. The process equations are based on a finite time increment, relative returns,...