相关论文: Option Pricing without Price Dynamics: A Probabili…

We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient…

In the online (time-series) search problem, a player is presented with a sequence of prices which are revealed in an online manner. In the standard definition of the problem, for each revealed price, the player must decide irrevocably…

We reconsider the problem of option pricing using historical probability distributions. We first discuss how the risk-minimisation scheme proposed recently is an adequate starting point under the realistic assumption that price increments…

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…

In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different…

Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show…

We consider a generic market model with a single stock and with random volatility. We assume that there is a number of tradable options for that stock with different strike prices. The paper states the problem of finding a pricing rule that…

Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a…

This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modelled by a (possibly uncountable) family of price processes on the same probability space. Our…

In the information-based approach to asset pricing the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market…

Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with…

We study the Option pricing with linear investment strategy based on discrete time trading of the underlying security, which unlike the existing continuous trading models provides a feasible real market implementation. Closed form formulas…

In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite…

We study the problem of evaluating a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the function. Reading the value of a variable is done at the expense of some…

This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in powers of the volatility of variance. Then we introduce the…

We introduce signature payoffs, a family of path-dependent derivatives that are given in terms of the signature of the price path of the underlying asset. We show that these derivatives are dense in the space of continuous payoffs, a result…

Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies…

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…

We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other…

We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum…