In this paper we present a simple control variate method, for options pricing under stochastic volatility models by the risk-neutral pricing formula, which is based on the order moment of the stochastic factor Yt of the stochastic volatility for choosing a non-random factor Y (t) with the same order moment. We construct the control variate using a stochastic differential equation with a determi...

Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a non-decreasing Lévy process constitute a useful and very general class of stationary, non-negative continuous-time processes which have been used, in particular, for the modelling of stochastic volatility. Brockwell, Davis and Yang (2011) considered the fitting of CARMA models to closely an...

Measuring and forecasting volatility of asset returns is very important for asset trading and risk management. There are various forms of volatility estimates, including implied volatility, realized volatility and volatility assumed under stochastic volatility models and GARCH models. Research has shown that these different methods are closely related but have different perspectives, strengths ...

We see that the price of an european call option in a stochastic volatility framework can be decomposed in the sum of four terms, which identify the main features of the market that affect to option prices: the expected future volatility, the correlation between the volatility and the noise driving the stock prices, the market price of volatility risk and the difference of the expected future v...

In this paper, we consider the problem of pricing discretely-sampled variance swaps based on a hybrid model of stochastic volatility and stochastic interest rate with regime-switching. Our modeling framework extends the Heston stochastic volatility model by including the CIR stochastic interest rate and model parameters that switch according to a continuous-time observable Markov chain process....

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study an approximation, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to...

We consider a class of dynamic portfolio optimization problems that allow for models of return predictability, transaction costs, and stochastic volatility. Determining the dynamic optimal portfolio in this general setting is almost always intractable. We propose a multiscale asymptotic expansion when the volatility process is characterized by its time scales of fluctuation. The analysis of the...