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Generating realistic synthetic option prices requires implied volatility as an input, yet implied volatility is itself derived from observed option prices, creating a circular dependency that limits synthetic data for machine-learning and…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to…
Pricing of high-dimensional options is one of the most important problems in Mathematical Finance. The objective of this manuscript is to present an original self-contained treatment of the multidimensional pricing. During the past decades…
We propose a general framework for the simultaneous modeling of equity, government bonds, corporate bonds and derivatives. Uncertainty is generated by a general affine Markov process. The setting allows for stochastic volatility, jumps, the…
The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare…
In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [Hur\'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections to…
This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…
The non-exponential Schilder-type theorem in Backhoff-Veraguas, Lacker and Tangpi [Ann. Appl. Probab., 30 (2020), pp. 1321-1367] is expressed as a convergence result for path-dependent partial differential equations with appropriate notions…
Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…
We present a general Markovian framework for order book modeling. Through our approach, we aim at providing a tool enabling to get a better understanding of the price formation process and of the link between microscopic and macroscopic…
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…
We present a non-probabilistic, pathwise approach to continuous-time finance based on causal functional calculus. We introduce a definition of self-financing, free from any integration concept and show that the value of a self-financing…
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…
We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged…
We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…
This study delves into the intricate realm of risk evaluation within the domain of specific financial derivatives, notably options. Unlike other financial instruments, like bonds, options are susceptible to broader risks. A distinctive…
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock…
We consider a semimartingale market model when the underlying diffusion has a singular volatility matrix and compute the hedging portfolio for a given payoff function. Recently, the representation problem for such degenerate diffusions with…
In this chapter we first briefly review the existing approaches to hedging in rough volatility models. Next, we present a simple but general result which shows that in a one-factor rough stochastic volatility model, any option may be…