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Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative…
We establish an explicit pricing formula for the class of L\'evy-stable models with maximal negative asymmetry (Log-L\'evy model with finite moments and stability parameter $1<\alpha\leq 2$) in the form of rapidly converging series. The…
We study general properties for the family of stochastic processes with polynomial regression property, that is that every conditional moment of the process is a polynomial. It turns out that then there exists a family of polynomial…
In this paper we introduce a class of information-based models for the pricing of fixed-income securities. We consider a set of continuous- time information processes that describe the flow of information about market factors in a monetary…
We consider the supOU stochastic volatility model which is able to exhibit long-range dependence. For this model we give conditions for the discounted stock price to be a martingale, calculate the characteristic function, give a strip where…
We study some properties of the American option price in the stochastic volatility Heston model. We first prove that, if the payoff function is convex and satisfies some regularity assumptions, then the option value function is increasing…
We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional L\'evy process. We set up a valuation model in…
This paper concerns an optimal impulse control problem associated with a refracted L\'{e}vy process, involving the reduction of reserves to a predetermined level whenever they exceed a specified threshold. The ruin time is determined by…
In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…
In the general framework of a semimartingale financial model and a utility function $U$ defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a ``small'' number of random…
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time…
In this paper incomplete-information models are developed for the pricing of securities in a stochastic interest rate setting. In particular we consider credit-risky assets that may include random recovery upon default. The market…
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 provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
We propose a novel structural estimation framework in which we train a surrogate of an economic model with deep neural networks. Our methodology alleviates the curse of dimensionality and speeds up the evaluation and parameter estimation by…
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes. The focus of our study is to give new characterizations of quasi self-duality for exponential L\'evy processes…
The density hypothesis on random times becomes now a standard in modeling of risks. One of the basic reasons to introduce the density hypothesis is the desire to have a computable credit risk model. However, recent work shows that merely an…
A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not…