Related papers: Option Pricing for Symmetric L\'evy Returns with A…
We consider a class of assets whose risk-neutral pricing dynamics are described by an exponential L\'evy-type process subject to default. The class of processes we consider features locally-dependent drift, diffusion and default-intensity…
We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation…
An option market maker incurs funding costs when carrying and hedging inventory. To hedge a net long delta inventory, for example, she pays a fee to borrow stock from the securities lending market. Because of haircuts, she posts additional…
Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie…
In this paper, we consider the problem of equal risk pricing and hedging in which the fair price of an option is the price that exposes both sides of the contract to the same level of risk. Focusing for the first time on the context where…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
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…
We study the performance of anonymous posted-price selling mechanisms for a standard Bayesian auction setting, where $n$ bidders have i.i.d. valuations for a single item. We show that for the natural class of Monotone Hazard Rate (MHR)…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
We study the problem of reconstruction of special special time dependent local volatility from market prices of options with different strikes at two expiration times. For a general diffusion process we apply the linearization technique and…
In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of…
The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian…
We propose the deep parametric PDE method to solve high-dimensional parametric partial differential equations. A single neural network approximates the solution of a whole family of PDEs after being trained without the need of sample…
We develop a general method for derivative pricing. This approach has its roots in Shannon's Information Theory. The notion of $\lambda$-analyticity of L\'{e}vy models is introduced on the basis of which new representations of the pricing…
The objective of the paper is to price weather contracts using temperature as the underlying process when the later follows a mean-reverting dynamics driven by a time-changed Brownian motion coupled to a Gamma Levy subordinator and…
The Black-Scholes model anticipates rather well the observed prices for options in the case of a strike price that is not too far from the current price of the underlying asset. Some useful extensions can be obtained by an adequate…