Derivatives pricing is quantitative finance’s oldest deep-math tradition, and this hub holds the collection’s densest concentration of stochastic calculus. The research spans pricing models (jump diffusions, stochastic volatility, rough volatility), numerical methods (Monte Carlo variants, PDE solvers, ML surrogates for high-dimensional pricing), and the newer deep hedging literature that learns hedge ratios directly under transaction costs.
The quadrant system earns its keep here: much of this work is mathematically airtight but empirically untested (“Lab Rats” in our scoring), which is fine for pricing engines and dangerous for trading claims. When a paper proposes a new model, the questions that matter are calibration stability — does it fit today’s surface without absurd parameters tomorrow — and hedging performance out of sample, not merely in-sample fit to option quotes.
Related hubs: Volatility Modeling, Fixed Income & Rates, Machine Learning for Forecasting.
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard models often rely on constant drift and volatility assumpti
Introduced in the late 90s, the passport option gives its holder the right to trade in a market and receive any positive gain in the resulting traded account at maturity. Pricing the option amounts to solving a stochastic control problem that for $d>1$ risky assets remains an open problem. Even in a
The dynamic hedging theory only makes sense in the setup of one given model, whereas the practice of dynamic hedging is just the opposite, with models fleeing after the data through daily recalibration. This is quite of a quantitative finance paradox. In this paper we revisit Burnett (2021) & Burne
The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number of terms N to approximate the truncated density by a cosine
In this work we present an alternative methodology to the standard Quantum Accelerated Monte Carlo (QAMC) applied to derivatives pricing. Our pipeline benefits from the combination of a new encoding protocol, referred to as the direct encoding, and a amplitude estimation algorithm, the modified Real
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is significantly faster and more accurate than any parameterized
This research addresses accurate option pricing by employing models beyond the traditional Black-Scholes framework. While Black-Scholes provides a closed-form solution, it is limited by assumptions of constant volatility, no dividends, and continuous price movements. To overcome these limitations, w
We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems in terms of a system of backward stochastic differential eq
This paper introduces a novel methodology for the pricing and management of share buyback contracts, overcoming the limitations of traditional optimal control methods, which frequently encounter difficulties with high-dimensional state spaces and the intricacies of selecting appropriate risk penalty
The paper introduces benchmark-neutral pricing and hedging for long-term contingent claims. It employs the growth optimal portfolio of the stocks as numeraire and the new benchmark-neutral pricing measure for pricing. For a realistic parsimonious model, this pricing measure turns out to be an equiva
This paper conducts an extensive analysis of Bitcoin return series, with a primary focus on three volatility metrics: historical volatility (calculated as the sample standard deviation), forecasted volatility (derived from GARCH-type models), and implied volatility (computed from the emerging Bitcoi
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 trait characterizing this category of instruments is their non-l
A framework to learn a multi-modal distribution is proposed, denoted as the Conditional Quantum Generative Adversarial Network (C-qGAN). The neural network structure is strictly within a quantum circuit and, as a consequence, is shown to represent a more efficient state preparation procedure than cu
In this paper, we revisit the inverse Black-Scholes model, the existence of the solution is proved in more rigorous way, and the empirical study is done using different approach based on finite element method. The article leads to a measure of incertitude in the option market.
We consider two data-driven approaches to hedging, Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control, under a stepwise mean-variance objective. We compare their performance for a European call option in the presence of transaction costs under discrete trading schedules. We
This paper examines the response of major cryptocurrencies to macroeconomic news announcements (MNA). While other cryptocurrencies exhibit no reaction to major MNA, Bitcoin responds negatively to inflation surprise. Price of Bitcoin decreases by 24 bps in response to a 1 standard deviation inflation
In this study, we predict next-day movements of stock end-of-day implied volatility using random forests. Through an ablation study, we examine the usefulness of different sources of predictors and expose the value of attention and sentiment features extracted from Twitter. We study the approach on
It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical Itô calculus and Taylor expansions, we write the price for out-of-the-money (OTM) and in-the-m
This paper introduces a transformative framework for managing path-dependent financial risk by shifting from traditional distribution-centric models to a geometry-based approach. We propose the SigSwap as a new regulatory instrument that allows market participants to decompose complex risk into term
The ongoing progress in quantum technologies has fueled a sustained exploration of their potential applications across various domains. One particularly promising field is quantitative finance, where a central challenge is the pricing of financial derivatives-traditionally addressed through Monte Ca