66 citations · 77 across the 21 of their papers we have counts for
24 papers
The VIX-Derived Volatility Model: A VIX-first Joint SPX-VIX Framework
Nicola F. Zaugg, Lech A. Grzelak
We propose the VIX-derived volatility (VDV) model, a VIX-first framework for joint SPXVIX modeling. In the model, we define explicit dynamics for the VIX process to price VIX futur…
Lifted Heston Model: Efficient Monte Carlo Simulation with Large Time Steps
Nicola F. Zaugg, Lech A. Grzelak
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the p…
Volatility Parametrizations with Random Coefficients: Analytic Flexibility for Implied Volatility Surfaces
Nicola F. Zaugg, Leonardo Perotti, Lech A. Grzelak
It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model…
Modeling and Replication of the Prepayment Option of Mortgages including Behavioral Uncertainty
Leonardo Perotti, Lech A. Grzelak, Cornelis W. Oosterlee
Prepayment risk embedded in fixed-rate mortgages forms a significant fraction of a financial institution's exposure, and it receives particular attention because of the magnitude o…
Basket Options with Volatility Skew: Calibrating a Local Volatility Model by Sample Rearrangement
Nicola F. Zaugg, Lech A. Grzelak
The pricing of derivatives tied to baskets of assets demands a sophisticated framework that aligns with the available market information to capture the intricate non-linear depende…
On the Hull-White model with volatility smile for Valuation Adjustments
T. van der Zwaard, L. A. Grzelak, C. W. Oosterlee
Affine Diffusion dynamics are frequently used for Valuation Adjustments (xVA) calculations due to their analytic tractability. However, these models cannot capture the market-impli…
Consistent asset modelling with random coefficients and switches between regimes
Felix L. Wolf, Griselda Deelstra, Lech A. Grzelak
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stoc…
GPU acceleration of the Seven-League Scheme for large time step simulations of stochastic differential equations
Shuaiqiang Liu, Graziana Colonna, Lech A. Grzelak +1
Monte Carlo simulation is widely used to numerically solve stochastic differential equations. Although the method is flexible and easy to implement, it may be slow to converge. Mor…
Accelerated Computations of Sensitivities for xVA
Griselda Deelstra, Lech A. Grzelak, Felix L. Wolf
Exposure simulations are fundamental to many xVA calculations and are a nested expectation problem where repeated portfolio valuations create a significant computational expense. S…
Randomization of Short-Rate Models, Analytic Pricing and Flexibility in Controlling Implied Volatilities
Lech A. Grzelak
We focus on extending existing short-rate models, enabling control of the generated implied volatility while preserving analyticity. We achieve this goal by applying the Randomized…
On Pricing of Discrete Asian and Lookback Options under the Heston Model
Leonardo Perotti, Lech A. Grzelak
We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by…
Efficient Wrong-Way Risk Modelling for Funding Valuation Adjustments
T. van der Zwaard, L. A. Grzelak, C. W. Oosterlee
Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, the standard assumption is independence between market risks and the counterpar…
On Randomization of Affine Diffusion Processes with Application to Pricing of Options on VIX and S&P 500
Lech A. Grzelak
The class of Affine (Jump) Diffusion (AD) has, due to its closed form characteristic function (ChF), gained tremendous popularity among practitioners and researchers. However, ther…
Sensitivities and Hedging of the Collateral Choice Option
Griselda Deelstra, Lech A. Grzelak, Felix L. Wolf
The collateral choice option allows a collateral-posting party the opportunity to change the type of security in which the collateral is deposited. Due to non-zero collateral basis…
Efficient Pricing and Calibration of High-Dimensional Basket Options
Lech A. Grzelak, Juliusz Jablecki, Dariusz Gatarek
This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new a…
Relevance of Wrong-Way Risk in Funding Valuation Adjustments
T. van der Zwaard, L. A. Grzelak, C. W. Oosterlee
In March 2020, the world was thrown into financial distress. This manifested itself in increased uncertainty in the financial markets. Many interest rates collapsed, and funding sp…
Fast Sampling from Time-Integrated Bridges using Deep Learning
Leonardo Perotti, Lech A. Grzelak
We propose a methodology to sample from time-integrated stochastic bridges, namely random variables defined as conditioned on and $Y(t_2…
Pricing and Hedging Prepayment Risk in a Mortgage Portfolio
Emanuele Casamassima, Lech A. Grzelak, Frank A. Mulder +1
Understanding mortgage prepayment is crucial for any financial institution providing mortgages, and it is important for hedging the risk resulting from such unexpected cash flows.…
Monte Carlo Simulation of SDEs using GANs
Jorino van Rhijn, Cornelis W. Oosterlee, Lech A. Grzelak +1
Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can…
Sparse Grid Method for Highly Efficient Computation of Exposures for xVA
Lech A. Grzelak
Every "x"-adjustment in the so-called xVA financial risk management framework relies on the computation of exposures. Considering thousands of Monte Carlo paths and tens of simulat…
Cheapest-to-Deliver Collateral: A Common Factor Approach
Felix L. Wolf, Lech A. Grzelak, Griselda Deelstra
The collateral choice option gives the collateral posting party the opportunity to switch between different collateral currencies which is well-known to impact the asset price. Qua…
The Seven-League Scheme: Deep learning for large time step Monte Carlo simulations of stochastic differential equations
Shuaiqiang Liu, Lech A. Grzelak, Cornelis W. Oosterlee
We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a…
A Computational Approach to Hedging Credit Valuation Adjustment in a Jump-Diffusion Setting
T. van der Zwaard, L. A. Grzelak, C. W. Oosterlee
This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and…
A neural network-based framework for financial model calibration
Shuaiqiang Liu, Anastasia Borovykh, Lech A. Grzelak +1
A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal…