Related papers: Option pricing models without probability: a rough…
The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the…
We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of…
Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can…
The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in…
The vast majority of works on option pricing operate on the assumption of risk neutral valuation, and consequently focus on the expected value of option returns, and do not consider risk parameters, such as variance. We show that it is…
Shorting for hedging exposes to risk when the market dynamics is uncertain. Managing uncertainty and risk exposure is key in portfolio management practice. This paper develops a robust framework for dynamic minimum-variance hedging that…
We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then…
In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a…
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,…
We discuss two numerical methods, based on a path integral approach described in a previous paper (I), for solving the stochastic equations underlying the financial markets: the Monte Carlo approach, and the Green function deterministic…
Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
We give a pragmatic/pedagogical discussion of using Euclidean path integral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White…
We combine the one-dimensional Monte Carlo simulation and the semi-analytical one-dimensional heat potential method to design an efficient technique for pricing barrier options on assets with correlated stochastic volatility. Our approach…
In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of {\it three} parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet…
An investor with constant absolute risk aversion trades a risky asset with general It\^o-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the…
In a stochastic volatility framework, we find a general pricing equation for the class of payoffs depending on the terminal value of a market asset and its final quadratic variation. This allows a pricing tool for European-style claims…
This paper covers a massive acceleration of Monte-Carlo based pricing method for financial products and financial derivatives. The method is applicable in risk management settings, where a financial product has to be priced under a number…
This paper studies how to price and hedge options under stock models given as a path-dependent SDE solution. When the path-dependent SDE coefficients have Fr\'{e}chet derivatives, an option price is differentiable with respect to time and…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…