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Great research efforts have been devoted to exploiting deep neural networks in stock prediction. While long-range dependencies and chaotic property are still two major issues that lower the performance of state-of-the-art deep learning…
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving…
The problem of European-style option pricing in time-changed L\'{e}vy models in the presence of compound Poisson jumps is considered. These jumps relate to sudden large drops in stock prices induced by political or economical hits. As the…
The crisis that affected financial markets in the last years leaded market practitioners to revise well known basic concepts like the ones of discount factors and forward rates. A single yield curve is not sufficient any longer to describe…
We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which…
The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by…
The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities decay as exp(-lambda|x|) or…
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…
Overnight rates, such as the SOFR (Secured Overnight Financing Rate) in the US, are central to the current reform of interest rate benchmarks. A striking feature of overnight rates is the presence of jumps and spikes occurring at…
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral…
In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of…
We consider a diffusive model for optimally distributing dividends, while allowing for Knightian model ambiguity concerning the drift of the surplus process. We show that the value function is the unique solution of a non-linear…
Models which postulate lognormal dynamics for interest rates which are compounded according to market conventions, such as forward LIBOR or forward swap rates, can be constructed initially in a discrete tenor framework. Interpolating…
The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American…
We present the first formal treatment of \emph{yield tokenization}, a mechanism that decomposes yield-bearing assets into principal and yield components to facilitate risk transfer and price discovery in decentralized finance (DeFi). We…
This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed…
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to…
We investigate the utility in employing asymptotic results related to a clustering criterion to the problem of testing for the presence of jumps in financial models. We consider the Jump Diffusion model for option pricing and demonstrate…
A growing body of literature suggests that heavy tailed distributions represent an adequate model for the observations of log returns of stocks. Motivated by these findings, here we develop a discrete time framework for pricing of European…