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 explores Artificial Neural Network (ANN) as a model-free solution for a calibration algorithm of option pricing models. We construct ANNs to calibrate parameters for two well-known GARCH-type option pricing models: Duan’s GARCH and the classical tempered stable GARCH that significantly im
Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data. However, the literature misses a potent approach commonly u
We investigate whether the fee income from trades on the CFM is sufficient for the liquidity providers to hedge away the exposure to market risk. We first analyse this problem through the lens of continuous-time financial mathematics and derive an upper bound for not-arbitrage fee income that would
It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard approach to risk management and option pricing. Yet, there is no c
We develop a semi-static framework for the variance-optimal hedging of multi-asset derivatives exposed to correlation and covariance risk. The approach combines continuous-time dynamic trading in the underlying assets with a static portfolio of auxiliary contingent claims. Using a multivariate Galtc
We investigate the data-driven discovery of parametric representations for implied volatility slices. Using symbolic regression, we search for simple analytic formulas that approximate the total implied variance as a function of log-moneyness and maturity. Our approach generates candidate parametriz
We present a study of the short-maturity asymptotics for VIX and European option prices in local-stochastic volatility models with compound Poisson jumps. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. The leading-order asymptotics are obtained in closed-form. We appl
The hedge fund industry presents significant challenges for investors due to its opacity and limited disclosure requirements. This pioneering study introduces two major innovations in financial text analysis. First, we apply topic modeling to hedge fund documents-an unexplored domain for automated t
Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise gradients, but doing so requires large batch sizes and can make
In this paper we use Malliavin Calculus techniques in order to obtain expressions for the short-time behavior of the at-the-money implied volatility (ATM-IV) level and skew for a jump-diffusion stock price. The diffusion part is assumed to be the stochastic volatility Bachelier model and the jumps a
Empirical studies with publicly available life tables identify long-range dependence (LRD) in national mortality data. Although the longevity market is supposed to benchmark against the national force of mortality, insurers are more concerned about the forces of mortality associated with their own p
In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and piecewise affine, which covers most of the relevant payoff functio
FLEX options are customized exchange-traded contracts allowing participants to choose nonstandard strikes, expirations, exercise styles, and settlement terms while retaining central clearing. We investigate whether single-name FLEX activity leaves measurable footprints in regular listed-option marke
Narrow Uniswap v3 liquidity ranges resemble short dated options, and Panoptic’s streaming premium echoes the short maturity concentration of Black-Scholes theta near the strike. This motivates a natural question: can implied volatility be extracted from Uniswap v3 and Panoptic using only on chain ob
Variance swaps are a convenient instrument for trading vega and convexity, and a listed contract now trades on Cboe. We ask when a trader should put such a position on and when she should take it off, and for a perpetual, continuously settled contract we answer both in closed form: each threshold is
We consider an investor who wants to hedge a path-dependent option with maturity $T$ using a static hedging portfolio using cash, the underlying, and vanilla put/call options on the same underlying with maturity $ t_1$, where $0 < t_1 < T$. We propose a model-free approach to construct such a portfo
This paper explores the concept of random-time subordination in modelling stock-price dynamics, and We first present results on the Laplace distribution as a Gaussian variance-mixture, in particular a more efficient volatility estimation procedure through the absolute moments. We generalise the Lapl
Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales exponentially with the parameters of interest, the latter often req
In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to address the large variance happening when the first simulation ti
The paper presents a Bayesian framework for the calibration of financial models using neural stochastic differential equations (neural SDEs), for which we also formulate a global universal approximation theorem based on Barron-type estimates. The method is based on the specification of a prior distr