Related papers: Pricing Bermudan options under local L\'evy models…
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…
We investigate the (functional) convex order of for various continuous martingale processes, either with respect to their diffusions coefficients for L\'evy-driven SDEs or their integrands for stochastic integrals. Main results are bordered…
A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general…
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…
We consider the problem of computing the Value Adjustment of European contingent claims when default of either party is considered, possibly including also funding and collateralization requirements. As shown in Brigo et al. (\cite{BLPS},…
In this work, we study the value of an Asian option in the case of exponential Levy markets. More specifically, we are interested in the NIG (normal inverse Gaussian) the VG (variance gamma) models. The exponential Levy models produce…
The present article provides a novel theoretical way to evaluate tradeability in markets of ordinary exponential L\'evy type. We consider non-tradeability as a particular type of market illiquidity and investigate its impact on the price of…
The aim of this work is to provide fast and accurate approximation schemes for the Monte-Carlo pricing of derivatives in the L\'evy LIBOR model of Eberlein and \"Ozkan (2005). Standard methods can be applied to solve the stochastic…
We propose a quasi maximum likelihood estimation method for Bergomi-type stochastic volatility models with parametrized kernels, focusing on the estimation of the kernel parameters from high-frequency time-series observations of option…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…
This paper proposes a market consistent valuation framework for variable annuities with guaranteed minimum accumulation benefit, death benefit and surrender benefit features. The setup is based on a hybrid model for the financial market and…
In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation…
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed…
Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an…
The rough Bergomi (rBergomi) model can accurately describe the historical and implied volatilities, and has gained much attention in the past few years. However, there are many hidden unknown parameters or even functions in the model. In…
In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as…
We consider the problem of pricing American Exchange options driven by a L\'evy process. We study the properties of American Exchange options, we represented it as the sum of the price of the corresponding European exchange option price and…