Related papers: Pricing derivatives in Hermite markets
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for…
The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…
Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under…
We present a new combinatorial market maker that operates arbitrage-free combinatorial prediction markets specified by integer programs. Although the problem of arbitrage-free pricing, while maintaining a bound on the subsidy provided by…
We introduce a general class of stochastic processes driven by a multifractional Brownian motion (mBm) and study the estimation problems of their pointwise H\"older exponents (PHE) based on a new localized generalized quadratic variation…
We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index $H\geq \frac12$. We show the convergence of these schemes at first and second order. The processes obtained in the limit…
We consider a fractional version of the Heston volatility model which is inspired by [16]. Within this model we treat portfolio optimization problems for power utility functions. Using a suitable representation of the fractional part,…
We propose a hybrid estimation procedure to estimate global fixed parameters and subject-specific random effects in a mixed fractional Black-Scholes model based on discrete-time observations. Specifically, we consider $N$ independent…
We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
This paper investigates the hedging performance of pegged foreign exchange market in a regime switching (RS) model introduced in a recent paper by Drapeau, Wang and Wang (2019). We compare two prices, an exact solution and first order…
In the past decades, advanced probabilistic methods have had significant impact on the field of finance, both in academia and in the financial industry. Conversely, financial questions have stimulated new research directions in probability.…
In this paper we complete and extend our previous work on stochastic control applied to high frequency market-making with inventory constraints and directional bets. Our new model admits several state variables (e.g. market spread,…
In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use…
Considering that both the entropy-based market information and the Hurst exponent are useful tools for determining whether the efficient market hypothesis holds for a given asset, we study the link between the two approaches. We thus…
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 classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the…
We present a semi-static hedging algorithm for callable interest rate derivatives under an affine, multi-factor term-structure model. With a traditional dynamic hedge, the replication portfolio needs to be updated continuously through time…
We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\langle X \rangle$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest…
In this paper, we consider the drawdown and drawup of the fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in financial market. We derive the…