Related papers: Pricing Path-Dependent Derivatives under Multiscal…
In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional It\^o formula…
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices…
In this paper, we present a new method for pricing CMS derivatives. We use Mallaivin's calculus to establish a model-free connection between the price of a CMS derivative and a quadratic payoff. Then, we apply Watanabe's expansions to…
This paper concerns the numerical approximation for the invariant distribution of Markovian switching L\'evy-driven stochastic differential equations. By combining the tamed-adaptive Euler-Maruyama scheme with the Multi-level Monte Carlo…
We propose a new Monte Carlo-based estimator for digital options with assets modelled by a stochastic differential equation (SDE). The new estimator is based on repeated path splitting and relies on the correlation of approximate paths of…
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth.…
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix $\underline{\underline{E}}$ onto a non-random vector. The scaling…
We consider option pricing using a discrete-time Markov switching stochastic volatility with co-jump model, which can model volatility clustering and varying mean-reversion speeds of volatility. For pricing European options, we develop a…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
In this paper we study the pricing of exchange options under a dynamic described by stochastic correlation with random jumps. In particular, we consider a Ornstein-Uhlenbeck covariance model with Levy Background Noise Process driven by…
An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin Calculus we construct an optimal log-linear…
We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns.…
In this paper, we price European Call three different option pricing models, where the volatility is dynamically changing i.e. non constant. In stochastic volatility (SV) models for option pricing a closed form approximation technique is…
In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which…
We investigate the approximation of path functionals. In particular, we advocate the use of the Karhunen-Lo\`eve expansion, the continuous analogue of Principal Component Analysis, to extract relevant information from the image of a…
In this paper, our focus lies on the Merton's jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of…
In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to…
This paper explores advancements in quantum algorithms for derivative pricing of exotics, a computational pipeline of fundamental importance in quantitative finance. For such cases, the classical Monte Carlo integration procedure provides…