A Hidden Markov Model (HMM) is used to model the VIX (the Cboe Volatility Index). A 4- state Gaussian mixture is fitted to the VIX price history from 1990 to 2022. Using a growing window of training data, the price of the S&P500 is predicted and two trading algorithms are presented, based on the...

A common scenario risk analysis employs a multiple factor model with assumed changes in the factors to obtain changes in non-factor variables. This analysis is sometimes designated as a “predictive stress scenario”. We choose to designate the factor model as a multifactor “CAPM” model,...

According to IFRS 9, an Entity shall assess - by performing a quantitative assessment - the relevance of the modification of the time value of money element, i.e. the modification of the interest that can be observed, e.g. in all the instruments whose underlying interest rate tenors are...

We present an embarrassingly simple method for supervised learning of SABR model's European option price function based on lookup table or rote machine learning. Performance in time domain is comparable to generally used analytic approximations utilized in financial industry. However, unlike the...

We propose a consistent and computationally efficient 2-step methodology for the estimation of multidimensional non-Gaussian asset models built using Lévy processes. The proposed framework allows for dependence between assets and different tail-behaviors and jump structures for each asset. Our...

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate...

Implied volatility skew and smile are ubiquitous phenomena in the financial derivative market especially after the Black Monday 1987 crash. Various stochastic volatility models have been proposed to capture volatility skew and smile in derivative pricing and hedging. Almost 30 years after the...

We present in a Monte Carlo simulation framework a novel approach for the evaluation of hybrid local volatility (Dupire 1994, Derman and Kani 1998) models. In particular, we consider the stochastic local volatility model - see e.g. Lipton et al. (2014), Piterbarg (2007), Tataru and Fisher...

An enhanced option pricing framework that makes use of both continuous and discontinuous time paths based on a geometric Brownian motion and Poisson-driven jump processes respectively is performed in order to better fit with real-observed stock price paths while maintaining the analytical...

The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both...