Related papers: Stationary Heston model: Calibration and Pricing o…
This paper describes a general approach for stochastic modeling of assets returns and liability cash-flows of a typical pensions insurer. On the asset side, we model the investment returns on equities and various classes of fixed-income…
We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
Rough volatility models are very appealing because of their remarkable fit of both historical and implied volatilities. However, due to the non-Markovian and non-semimartingale nature of the volatility process, there is no simple way to…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
We propose a new static parameterization of the implied volatility surface which is constructed by using polynomials of sigmoid functions combined with some other terms. This parameterization is flexible enough to fit market implied…
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 and innovative approach to ensure consistency between options…
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…
The Heston model is a popular stock price model with stochastic volatility that has found numerous applications in practice. In the present paper, we study the Riemannian distance function associated with the Heston model and obtain…
In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To…
This paper addresses the challenges of pricing exotic options and structured products, which traditional models often fail to handle due to their inability to capture real-world market phenomena like fat-tailed distributions and volatility…
We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourself to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and…
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and…
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local…
We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European…
A volatility surface is an important tool for pricing and hedging derivatives. The surface shows the volatility that is implied by the market price of an option on an asset as a function of the option's strike price and maturity. Often,…
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the…