相关论文: Synthetic American Option Pricing via Jump-HMM-Dri…

In the first part of this thesis, we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic…

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 path dependency of volatility on a set of N square-root state…

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using…

In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…

In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…

In the regime switching extension of Black-Scholes-Merton model of asset price dynamics, one assumes that the volatility coefficient evolves as a hidden pure jump process. Under the assumption of Markov regime switching, we have considered…

We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…

In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First,…

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…

We apply path integration techniques to obtain option pricing with stochastic volatility using a generalized Black-Scholes equation known as the Merton and Garman equation. We numerically simulate the option prices using the technique of…

In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…

In American options, the early exercise feature allows the option to be exercised at any time prior to expiration. However, this flexibility introduces a challenge: the pricing model must value the option while simultaneously determining an…

In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlations of futures contracts with implied volatility smiles from…

Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce…

This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…

We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin convolution of functions, and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in…

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…

American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European…

In this paper similar to [P. Carr, A. Itkin, 2019] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both…