This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE...

Calibrating option pricing models to market prices often leads to optimisation problems to which standard methods (like such based on gradients) cannot be applied. We investigate two models: Heston's stochastic volatility model, and Bates's model which also includes jumps. We discuss how to...

This paper proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. We proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the...

We propose a pairs trading model that incorporates a time-varying volatility of the Constant Elasticity of Variance type. Our approach is based on stochastic control techniques; given a fixed time horizon and a portfolio of two cointegrated assets, we define the trading strategies as the...

We build an optimal trading model for submitting market orders in volatile market. We show some analytical properties of our computational solution. We conduct simulation and empirical study to investigate the model performance. In comparison with other two alternative models, the empirical...

In this study I apply forward sensitivity analysis to the dynamical system of nonlinear asset flow differential equations (AFDE). I find that all parameters in AFDE are needed and can be estimated from market prices and net asset values data. Moreover, the market price is the most fluctuating...

Using equations that arise in quantum mechanics, this paper describes a way to more accurately and efficiently represent non-Gaussian return distributions than the standard method of invoking skewness and kurtosis. Then, it provides a new single intuitive number, defined here as the “crash...

The volatility of concern in conventional volatility-managed strategies such as volatility-targeting strategy and mean-variance optimization is the expected conditional volatility. However for investors, it is the realized volatility that is important, because there is only one realization in...

The popular conditional autoregressive Wishart (CAW) model for dynamics of realized covariance matrices provides a flexible parametrisation. However, the number of parameters grows quadratically with the number of assets, which causes enormous computational difficulties in higher dimensions....