Past Mathematical and Computational Finance Seminar

17 May 2018

High-frequency realized variance approaches offer great promise for 
estimating asset prices’ covariation, but encounter difficulties 
connected to the Epps effect. This paper models the Epps effect in a 
stochastic volatility setting. It adds dependent noise to a factor 
representation of prices. The noise both offsets covariation and 
describes plausible lags in information transmission. Non-synchronous 
trading, another recognized source of the effect, is not required. A 
resulting estimator of correlations and betas performs well on LSE 
mid-quote data, lending empirical credence to the approach.

  • Mathematical and Computational Finance Seminar
3 May 2018
Beatrice Acciaio

Title: Generalized McKean-Vlasov stochastic control problems.

Abstract: I will consider McKean-Vlasov stochastic control problems 
where the cost functions and the state dynamics depend upon the joint 
distribution of the controlled state and the control process. First, I 
will provide a suitable version of the Pontryagin stochastic maximum 
principle, showing that, in the present general framework, pointwise 
minimization of the Hamiltonian with respect to the control is not a 
necessary optimality condition. Then I will take a different 
perspective, and present a variational approach to study a weak 
formulation of such control problems, thereby establishing a new 
connection between those and optimal transport problems on path space.

The talk is based on a joint project with J. Backhoff-Veraguas and R. Carmona.

  • Mathematical and Computational Finance Seminar
8 March 2018

We consider calculation of VaR/TVaR capital requirements when the underlying economic scenarios are determined by simulatable risk factors. This problem involves computationally expensive nested simulation, since evaluating expected portfolio losses of an outer scenario (aka computing a conditional expectation) requires inner-level Monte Carlo. We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. Our main workhorse is an advanced Gaussian Process (GP) regression approach which uses nonparametric spatial modeling to efficiently learn the relationship between the stochastic factors defining scenarios and corresponding portfolio value. Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. The GP framework also yields better uncertainty quantification for the resulting VaR/\TVaR estimators that reduces bias and variance compared to existing methods.  Time permitting, I will highlight further related applications of statistical emulation in risk management.
This is joint work with Jimmy Risk (Cal Poly Pomona). 

  • Mathematical and Computational Finance Seminar
1 March 2018
Cecilia Mancini

Joint work with Josè E. Figueroa-Lòpez, Washington University in St. Louis

Abstract: We consider a univariate semimartingale model for (the logarithm 
of) an asset price, containing jumps having possibly infinite activity. The 
nonparametric threshold estimator\hat{IV}_n of the integrated variance 
IV:=\int_0^T\sigma^2_sds proposed in Mancini (2009) is constructed using 
observations on a discrete time grid, and precisely it sums up the squared 
increments of the process when they are below a  threshold, a deterministic 
function of the observation step and possibly of the coefficients of X. All the
threshold functions satisfying given conditions allow asymptotically consistent 
estimates of IV, however the finite sample properties of \hat{IV}_n can depend 
on the specific choice of the threshold.
We aim here at optimally selecting the threshold by minimizing either the 
estimation mean squared error (MSE) or the conditional mean squared error 
(cMSE). The last criterion allows to reach a threshold which is optimal not in 
mean but for the specific  volatility and jumps paths at hand.

A parsimonious characterization of the optimum is established, which turns 
out to be asymptotically proportional to the Lévy's modulus of continuity of 
the underlying Brownian motion. Moreover, minimizing the cMSE enables us 
to  propose a novel implementation scheme for approximating the optimal 
threshold. Monte Carlo simulations illustrate the superior performance of the 
proposed method.

  • Mathematical and Computational Finance Seminar