相关论文: Analytical ramifications of derivatives valuation:…

We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by…

Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices. The formulas are given via…

The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on…

Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness,…

We consider a new family of derivatives whose payoffs become strictly positive when the price of their underlying asset falls relative to its historical maximum. We derive the solution to the discretionary stopping problems arising in the…

The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…

This paper discusses the short-maturity behavior of Asian option prices and hedging portfolios. We consider the risk-neutral valuation and the delta value of the Asian option having a H\"older continuous payoff function in a local…

The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative L\'evy process \xi with unbounded variation.…

The Black-Scholes model (sometimes known as the Black-Scholes-Merton model) gives a theoretical estimate for the price of European options. The price evolution under this model is described by the Black-Scholes formula, one of the most…

We develop a tractable framework for valuing Asian options when trading the underlying generates market impact and execution costs. Starting from a discrete-time, quote-level model, we construct a reference midpoint suitable for Asian…

Neural networks with sufficiently smooth activation functions can approximate values and derivatives of any smooth function, and they are differentiable themselves. We improve the approximation capability of neural networks by utilizing the…

This work studies the valuation of currency options in markets suffering from a financial crisis. We consider a European option where the underlying asset is a foreign currency. We assume that the value of the underlying asset is a…

We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the…

G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation…

We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…

We develop an axiomatic theory of balance functions (future value functions) in the theory of interest that is derived from financial considerations and which applies to general regulated payment streams, including continuous payment…

This study investigates enhancing option pricing by extending the Black-Scholes model to include stochastic volatility and interest rate variability within the Partial Differential Equation (PDE). The PDE is solved using the finite…

The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional…

This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being…

We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures,…