Related papers: Scaling Limits for Super--replication with Transie…

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…

A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…

We study superreplication of European contingent claims in discrete time in a large trader model with market indifference prices recently proposed by Bank and Kramkov. We introduce a suitable notion of efficient friction in this framework,…

Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently…

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…

Consider a discrete finite-dimensional, Markovian market model. In this setting, discretely sampled American options can be priced using the so-called ``non-recombining'' tree algorithm. By successively increasing the number of exercise…

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…

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static…

We give the ``quenched'' scaling limit of Bouchaud's trap model in ${d\ge 2}$. This scaling limit is the fractional-kinetics process, that is the time change of a $d$-dimensional Brownian motion by the inverse of an independent…

Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for…

We prove a scaling limit theorem for the simple random walk on critical lattice trees in $\mathbb{Z}^d$, for $d\geq 8$. The scaling limit is the Brownian motion on the Integrated Super-Brownian Excursion (BISE) which is the same one that we…

We study the problem of finding probability densities that match given European call option prices. To allow prior information about such a density to be taken into account, we generalise the algorithm presented in Neri and Schneider (2011)…

Power corrections to exclusive processes are usually calculated using models for twist-four distribution amplitudes (DA) which are based on the leading-order terms in the conformal expansion. In this work we develop a different approach…

We consider large uniform random trees where we fix for each vertex its degree and height. We prove, under natural conditions of convergence for the profile, that those trees properly renormalized converge. To this end, we study the paths…

Option contracts can be valued by using the Black-Scholes equation, a partial differential equation with initial conditions. An exact solution for European style options is known. The computation time and the error need to be minimized…

We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a…

We give a new proof of the vanishing noise limit theorem for exit times of 1-dimensional diffusions conditioned on exiting through a point separated from the starting point by a potential wall. We also prove a scaling limit for exit…

For many quantum systems of interest, the classical computational cost of simulating their time evolution scales exponentially in the system size. At the same time, quantum computers have been shown to allow for simulations of some of these…

Using the Donsker-Prokhorov invariance principle we extend the Kim-Stoyanov-Rachev-Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the…

We prove a scaling limit theorem for discrete Galton-Watson processes in varying environments. A simple sufficient condition for the weak convergence in the Skorokhod space is given in terms of probability generating functions. The limit…