计算金融
This work develops an agent-based model for the study of how the leverage through the use of repurchase agreements can function as a mechanism for the propagation and amplification of financial shocks in a financial system. Based on the…
In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level…
We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with…
Selecting the best policy to keep the balance between what a company holds in cash and what is placed in alternative investments is by no means straightforward. We here introduce PyCaMa, a Python module for multiobjective cash management…
Using Monte Carlo simulation to calculate the Value at Risk (VaR) as a possible risk measure requires adequate techniques. One of these techniques is the application of a compound distribution for the aggregates in a portfolio. In this…
We prove that the default times (or any of their minima) in the dynamic Gaussian copula model of Cr{\'e}pey, Jeanblanc, and Wu (2013) are invariance times in the sense of Cr{\'e}pey and Song (2017), with related invariance probability…
This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In…
We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise…
On a probability space $(\Omega,\mathcal{A},\mathbb{Q})$ we consider two filtrations $\mathbb{F}\subset \mathbb{G}$ and a $\mathbb{G}$ stopping time $\theta$ such that the $\mathbb{G}$ predictable processes coincide with $\mathbb{F}$…
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic.…
Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for…
The Gerber-Shiu function provides a way of measuring the risk of an insurance company. It is given by the expected value of a function that depends on the ruin time, the deficit at ruin, and the surplus prior to ruin. Its computation…
Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…
The COS method proposed in Fang and Oosterlee (2008), although highly efficient, may lack robustness for a number of cases. In this paper, we present a Stable pricing of call options based on Fourier cosine series expansion. The Stability…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…
We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model…
We postulates, and then show experimentally, that liquidity deficit is the driving force of the markets. In the first part of the paper a kinematic of liquidity deficit is developed. The calculus-like approach, which is based on…
The realized stochastic volatility (RSV) model that utilizes the realized volatility as additional information has been proposed to infer volatility of financial time series. We consider the Bayesian inference of the RSV model by the Hybrid…
We calculate the realized volatility in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard…
A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference…