37 research outputs found
Forecasting trends with asset prices
In this paper, we consider a stochastic asset price model where the trend is
an unobservable Ornstein Uhlenbeck process. We first review some classical
results from Kalman filtering. Expectedly, the choice of the parameters is
crucial to put it into practice. For this purpose, we obtain the likelihood in
closed form, and provide two on-line computations of this function. Then, we
investigate the asymptotic behaviour of statistical estimators. Finally, we
quantify the effect of a bad calibration with the continuous time mis-specified
Kalman filter. Numerical examples illustrate the difficulty of trend
forecasting in financial time series.Comment: 26 pages, 11 figure
Markovian approximation of the rough Bergomi model for Monte Carlo option pricing
The recently developed rough Bergomi (rBergomi) model is a rough fractional
stochastic volatility (RFSV) model which can generate more realistic term
structure of at-the-money volatility skews compared with other RFSV models.
However, its non-Markovianity brings mathematical and computational challenges
for model calibration and simulation. To overcome these difficulties, we show
that the rBergomi model can be approximated by the Bergomi model, which has the
Markovian property. Our main theoretical result is to establish and describe
the affine structure of the rBergomi model. We demonstrate the efficiency and
accuracy of our method by implementing a Markovian approximation algorithm
based on a hybrid scheme.Comment: 20 pages, 3 figure