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 work focuses on reconstructing a continuous implied volatility (IV) surface from a small number of option quotes, a fundamental task for option pricing and risk management. We propose Additive Martingale (AddMart), a few-shot IV surface reconstruction framework that satisfies static no-arbitrag
We develop a non-perturbative framework for stochastic-volatility option pricing organised by the two-particle-irreducible (2PI) effective action and the Dyson-Schwinger gap equations of quantum field theory. In log-price, log-volatility or Lamperti coordinates, the joint law of the state variables
Global sensitivity analysis is employed to evaluate the effective dimension reduction achieved through Chebyshev interpolation and the conditional pathwise method for Greek estimation of discretely monitored barrier options and arithmetic average Asian options. We compare results from finite differe
We develop a novel deep learning approach for pricing European basket options written on assets that follow jump-diffusion dynamics. The option pricing problem is formulated as a partial integro-differential equation, which is approximated via a new implicit-explicit minimizing movement time-steppin
The rough Bergomi (rBergomi) model can accurately describe the historical and implied volatilities, and has gained much attention in the past few years. However, there are many hidden unknown parameters or even functions in the model. In this work, we investigate the potential of learning the forwar
We study deep hedging in the context of dynamics risk measures, where sequential decisions are time-consistent. Whereas the literature in such context mainly considers low-dimensional problems with simple environment dynamics, we tackle the high-dimensional problem of basket option hedging; we show
We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying delta, offset via SPY) by trading the underlying index ETF, usin
This paper explores the application of deep Q-learning to hedging at-the-money options on the S&P500 index. We develop an agent based on the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, trained to simulate hedging decisions without making explicit model assumptions on price dynam
We consider the pricing of energy spread options for spot prices following an exponential Ornstein-Uhlenbeck process driven by a sum of independent multivariate variance gamma processes, which gives rise to mean-reverting, infinite activity price dynamics. Within this class of driving processes, the
Joint calibration to SPX and VIX market data is a delicate task that requires sophisticated modeling and incurs significant computational costs. The latter is especially true when pricing of volatility derivatives hinges on nested Monte Carlo simulation. One such example is the 4-factor Markov Path-
The generation of synthetic financial data is a critical technology in the financial domain, addressing challenges posed by limited data availability. Traditionally, statistical models have been employed to generate synthetic data. However, these models fail to capture the stylized facts commonly ob
We introduce the Volterra Stein-Stein model with stochastic interest rates, where both volatility and interest rates are driven by correlated Gaussian Volterra processes. This framework unifies various well-known Markovian and non-Markovian models while preserving analytical tractability for pricing
A new modular approximate Bayesian inferential framework is proposed that enables fast calculation of probabilistic predictions of future option prices. We exploit multiple information sources, including daily spot returns, high-frequency spot data and option prices. A benefit of this modular Bayesi
Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a c
We present a unified framework for computing CVA sensitivities, hedging the CVA, and assessing CVA risk, using probabilistic machine learning meant as refined regression tools on simulated data, validatable by low-cost companion Monte Carlo procedures. Various notions of sensitivities are introduced
This paper presents a Monte-Carlo-based artificial neural network framework for pricing Bermudan options, offering several notable advantages. These advantages encompass the efficient static hedging of the target Bermudan option and the effective generation of exposure profiles for risk management.
We propose the Chiarella-Heston model, a new agent-based model for improving the effectiveness of deep hedging strategies. This model includes momentum traders, fundamental traders, and volatility traders. The volatility traders participate in the market by innovatively following a Heston-style vola
Monroe (1978) demonstrates that any local semimartingale can be represented as a time-changed Brownian Motion (BM). A natural question arises: does this representation theorem hold when the BM and the time-change are independent? We prove that a local semimartingale is not equivalent to a BM with a
In this article, we introduce an algorithm called Backward Hedging, designed for hedging European and American options while considering transaction costs. The optimal strategy is determined by minimizing an appropriate loss function, which is based on either a risk measure or the mean squared error
This paper extends the damped-sinc (DSINC) method for American options beyond the affine Heston class to general one-factor stochastic-volatility models. We show that the collapse identity, which reduces the early-exercise integral to a single spectral integral, remains valid for these models. Dampi