Related papers: Probability-free models in option pricing: statist…
We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that…
This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin…
Stochastic volatility (SV) models mimic many of the stylized facts attributed to time series of asset returns, while maintaining conceptual simplicity. The commonly made assumption of conditionally normally distributed or…
We introduce a novel signature approach for pricing and hedging path-dependent options with instantaneous and permanent market impact under a mean-quadratic variation criterion. Leveraging the expressive power of signatures, we recast an…
Diffusion Probabilistic Model (DDPM) for generating one-day-ahead arbitrage-free implied volatility surfaces. To capture the path-dependent nature of volatility dynamics, we condition our model on a set of market variables, including…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
We extend the application of the Cherny-Shiryaev-Yor invariance principle to a unified Bachelier-Black-Scholes-Merton (BBSM) dynamic pricing model. This extension incorporates the influence of the history of the dynamics (i.e., the path…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and…
We present a model for direct semi-parametric estimation of the State Price Density (SPD) implied in quoted option prices. We treat the observed prices as expected values of possible pay-offs at maturity, weighted by the unknown probability…
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is…
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…
We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a…
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a…
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…
In this paper, we present a method for constructing a (static) portfolio of co-maturing European options whose price sign is determined by the skewness level of the associated implied volatility. This property holds regardless of the…
This paper presents closed-form analytical formulas for pricing volatility and variance derivatives with nonlinear payoffs under discrete-time observations. The analysis is based on a probabilistic approach assuming that the underlying…
In this paper, we study the option pricing problems for rough volatility models. As the framework is non-Markovian, the value function for a European option is not deterministic; rather, it is random and satisfies a backward stochastic…
Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show that most stochastic processes used in traditional option pricing models can be cast as special cases of time-changed L\'evy processes. In particular these are models which…
We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the…