57 articles · sorted by date
In asset pricing, bigger models are often treated like heavier suitcases: they seem harder to carry and easier to overpack. This paper argues the real payoff from complexity is not keeping more factors, but making room to find a sparse pattern in prices. The authors separate two ideas: capacity sparsity, meaning how large the candidate feature space is, and factor sparsity, meaning that only a few risks may actually matter. They revisit the benchmark design of Didisheim et al. (2025) and push it into higher-complexity settings. There, nonlinear feature expansions paired with basis pursuit, a sparse-selection method, produce portfolios whose out-of-sample performance beats ridgeless benchmarks beyond a critical complexity threshold. The message is sharp: the virtue of complexity in asset pricing comes from expanding the space where a sparse structure of priced risks can be discovered, not from simply retaining more factors.
When an option is about to expire, its price can behave in two distinct waves instead of one simple line. This paper studies that short-time behavior for at-the-money call options in the CGMY model, a pure-jump model with activity parameter Y between 1 and 2. The key result is a two-term expansion: the normalized ATM call price satisfies c(t,0) = d1 t^{1/Y} + d2 t + o(t) as t goes to 0. The first coefficient, d1, is the familiar stable-limit term from the domain of attraction of a symmetric Y-stable law. The second, d2, is given by an explicit integral involving the characteristic exponent and the limiting stable exponent. The authors also extract higher-order coefficients in closed form by keeping the full Lipton-Lewis formula intact and using a dynamic cutoff that separates inner, core, and tail regions. They verify the coefficients numerically against existing closed-form expressions where those are available. The result sharpens short-maturity pricing in a model where small jumps drive the leading behavior and tempering shows up later.
If a trading model looks smart in a backtest, it can still fall apart when real money hits the market. This review looks at large language models (LLMs, AI systems trained on huge amounts of text) in stock price forecasting through a hedge-fund lens. It brings together recent uses of LLMs for reading financial news and social media sentiment, analyzing financial reports and earnings-call transcripts, turning price series into tokens or symbols, and building multi-agent trading systems. The paper also flags the traps that can make results look better than they are: fragile sentiment analysis, poor dataset and horizon design, weak performance metrics, data leakage, illiquidity premia, and the basic limits of stock price predictability. The point is not just to show what LLMs can do in finance, but to stress-test whether they can survive the messiness of real trading pipelines.
If you buy corporate bonds, the usual list of “risk factors” may not explain much beyond the market itself. That is the surprise in this paper. The authors revisit recent claims that several factors can explain why corporate bond returns differ across issues. Using both portfolio-level and bond-level tests, they find that nearly all previously proposed bond risk factors add no incremental explanatory power once the corporate bond market factor is included. The only marginal exception is traded liquidity, which shows a small remaining role. The result leaves the bond CAPM — a simple market-only pricing model — looking harder to beat than earlier studies suggested, because it is not dominated in pairwise or multiple model comparison tests by either traded-factor or nontraded-factor models. In other words, common factor pricing in corporate bonds appears much tougher to establish than recent work implied.
If you need to know whether tomorrow’s market swings will be wilder than today’s, options prices may give you an edge. This paper shows that information hidden in traded options can sharpen forecasts of realized volatility, the day-to-day volatility measured from high-frequency prices. The authors feed option-derived spot volatility, a model-based estimate of the market’s current turbulence, into the Heterogeneous Autoregressive (HAR) model. They infer that spot volatility under a rough stochastic volatility model and use a deep learning surrogate to speed estimation across large options panels. Against the Heston, Bates, and SVCJ stochastic volatility models, plus the VIX index, the augmented HAR-RV-RHeston model improves daily realized-volatility forecasting accuracy. The gain does not stop at one day: the model stays ahead across horizons reaching one month. The takeaway is straightforward: traded options contain forward-looking information that can complement the history embedded in realized volatility.
When the volatility and correlation of several assets are uncertain, pricing an option turns into a control problem, not a simple formula. That is exactly the challenge the uncertain volatility model creates for multidimensional European options. The paper introduces a backward actor-critic stochastic policy gradient scheme that works step by step through time, pairing Proximal Policy Optimization with shallow neural networks for both the value function and the control policy. A key design choice is a squashed Gaussian policy built on a C-vine representation of correlation matrices, which keeps the correlation matrix positive semidefinite by construction. In numerical experiments on a range of multidimensional derivatives, the method produced accurate prices, stayed computationally efficient, and compared favorably with existing Monte Carlo and machine-learning benchmarks. The result is a practical way to tackle a high-dimensional pricing problem that quickly becomes hard for standard numerical methods.
If a token only gets its price from an automated market maker, old-school Black-Scholes pricing starts to miss the shape of the market. This paper shows that such tokens follow a constant elasticity of variance (CEV) process, which means volatility rises as price falls — a leverage effect built into the pool itself. Under that model, a 20% out-of-the-money put is underpriced by about 6% in implied volatility terms, and that shortfall shows up at every pool depth. As pools get deeper, the dollar gap shrinks, but the pattern in the wings remains. The paper also tests the idea against data from 90 Bittensor subnets, finding strongly negative price elasticity in realized return variance after controlling for pool depth and flow volatility. A separate delta-hedged backtest across 82 subnets finds nearly identical hedging errors at the money, which matches the claim that the biggest pricing differences sit away from the center of the distribution.
Pricing a complex basket option can mean wrestling with a huge grid of possible market conditions. This paper shows a way to compress that grid into a tensor-train, a compact representation built directly from black-box price evaluations. The method was tested on five-asset basket options across an eight-dimensional parameter space, including asset spot levels, strike, interest rate, and time to maturity. For European geometric basket puts, the tensor surrogate reached lower test error in less training time than standard Gaussian process regression, because it could scale to much larger effective training sets. For American arithmetic basket puts trained on least-squares Monte Carlo data, it scaled more favorably as the training set grew and returned prices in millisecond-level time per query. The authors also found that hyperparameter optimization consistently preferred a large kernel length-scale, and in that limit the Gaussian process predictor becomes multilinear interpolation for off-grid inputs. The practical message is simple: when option pricing lives in many dimensions, tensor networks can make the problem far easier to evaluate, with overall runtime often dominated by data generation rather than the surrogate itself.
When an option is almost expired, even tiny price jumps can decide what it is worth. This paper works out the near-expiry, at-the-money call price and implied volatility for a broad class of exponential Lévy models, where log returns follow a Lévy process. Under mild assumptions that place the process in the small-time domain of attraction of an α-stable law with α between 1 and 2, the authors derive first-order asymptotics as time to maturity goes to zero. They show that the crucial inputs survive a share-measure change, so the needed information can be read directly from how the Lévy measure behaves near the origin. When there is no Brownian component, they obtain new convergence rates of the form t^(1/α)ℓ(t), with ℓ a slowly varying function, and give an example with rate (t / log(1/t))^(1/α). When a Brownian component is present, the jump part becomes lower order and the leading √t behavior is driven entirely by the Gaussian part.
Pricing a contract tied to rainfall, heating demand, or insurance losses is hard when events come in bursts. A new paper tackles that problem with a self-exciting marked point process, where each jump can make the next one more likely and the accumulated jump size drives the payoff. The authors derive the pricing problem as a backward partial integro-differential equation in two spatial dimensions, then shrink it by applying an exponential transform in the accumulated mark variable. That move turns the original problem into a family of one-dimensional PIDEs in the intensity variable, solved along a Bromwich contour. For Gamma-mixture mark laws, they approximate the jump term with generalized Gauss–Laguerre quadrature and march backward in time with a monotone IMEX finite difference scheme. They also prove a term-by-term global error bound covering time and space discretization, quadrature, interpolation, and boundary effects, and they test the method against numerical experiments and Monte Carlo benchmarks. The result is a computational route for pricing derivatives on clustered, self-exciting event streams.
When a pricing model has to follow an entire interest-rate curve, the computation can balloon fast. This paper tackles that problem by turning a stochastic pricing task into a deterministic partial differential equation (PDE). It then uses finance-informed neural networks, or FINNs, to solve that PDE directly, with automatic differentiation computing the exact derivatives needed along the way. On caplets, the method matches Monte Carlo benchmarks within 0.04 to 0.07 cents per dollar of contract value. Once trained, it prices caplets in a few microseconds, and the speedup grows from 300,000 to 4.5 million times as the forward-curve discretization expands from 10 to 150 nodes. The paper also shows that key sensitivities — theta and curve deltas — come at zero marginal cost during PDE evaluation. The same framework is described as extending to caps, swaptions, and callable bonds, with only boundary condition changes.
If your portfolio mixes swaps with different maturities, the way rates move together can change the price of credit risk. That is the issue this paper tackles through credit valuation adjustment, or CVA, which prices counterparty risk using the expected positive value of a netting set over time. The author studies the two-factor Hull-White interest rate model, a simple Gaussian model often used because XVA calculations stay tractable only with that kind of structure. By comparing an approximation formula with Monte Carlo simulation, the paper examines the correlation of co-initial swap rates and asks when the model really reproduces yield-curve de-correlation. The answer is precise: the two-factor Hull-White model captures that de-correlation only when its volatilities and mean-reversion strengths satisfy certain relationships. That matters because the exposure in a netting set can depend on correlation, including cases with payer and receiver swaps and CMS spread options. In short, the paper shows that this popular model is useful for XVA only in the parameter regimes where it truly matches how the yield curve spreads apart.
If you price a callable swap, the model has to look like the market’s own volatility surface, not just the average move. That is the problem this paper addresses: interest-rate skew and smile, the curved patterns seen in swaption and caplet prices, are commonly described by SABR, while callable exotic swaps are often modeled with the Libor Market Model, or Forward Market Model in the post-Libor world. The paper argues that many existing SABR/LMM treatments are too rigid for practical use in global banks. It therefore sets out a comprehensive definition of SABR/LMM and a complete description of how to implement it, with time-dependent skew and smile. In the paper’s framing, the goal is simple but demanding: build an interest-rate model that stays comparable to the SABR volatility surface while still fitting the structure traders rely on for pricing and hedging.
If an insurer prices a variable annuity, the missing gap between two birthdays can matter as much as the market. Life tables only give survival probabilities at integer ages, so they leave the deaths in between unspecified. This paper shows how to turn that missing information into hard upper and lower bounds for lifetime-dependent quantities, instead of relying on a single fractional-age assumption or mortality model. The authors derive two sets of bounds in a joint actuarial-financial framework: one where every mortality trajectory is almost surely consistent with the one-year survival probabilities, and another where mortality can vary but still matches those probabilities in expectation. The result is a robust way to characterize the worst- and best-case values of contracts whose payoffs depend on both lifespan and financial assets. That makes the output useful for life insurance and for managing mortality risk when the life table does not tell the whole story.
If an asset can jump suddenly instead of moving smoothly, pricing its options becomes a much harder math problem. The Bates model handles that reality by combining changing volatility with discontinuous price jumps, but the resulting equation is costly to solve. This paper proposes a fourth-order compact finite-difference scheme for the transformed Bates partial integro-differential equation, using an IMEX Crank–Nicolson split for the local terms and Simpson quadrature for the jump integral. In benchmarks, the new HOC-FD method reached near-fourth-order spatial accuracy, while quadratic finite elements reached near-second-order spatial accuracy. All the time integrators showed second-order temporal convergence. The striking result is speed: HOC-FD matched the accuracy of finite elements at up to two orders of magnitude lower runtime. That makes it a practical baseline for option pricing under stochastic volatility jump-diffusion models.
If one bank’s collapse can send losses rippling through a financial network, a bond’s value stops being a simple number. It becomes a moving target shaped by who owes whom, and by which defaults are rare but devastating. This paper tackles that problem for corporate bonds exposed to systemic credit risk. The authors propose a method called Bi-Level Importance Sampling with Splitting. It separates an individual bank’s default event from the network’s tangled fixed-point equations — feedback loops where each payment depends on the rest of the system. That two-stage design directly generates samples from default events, instead of relying on standard Monte Carlo simulation, which can miss the rare failures that matter most. The paper says the method is scalable and asymptotically optimal, and it validates the approach with numerical studies on empirically observed networks. In practice, that means bond pricing can account for contagion effects that ordinary simulations struggle to capture, even when the network grows large.
When two lives are tied to the same pension-like payout, their shared survival risk matters as much as the money itself. This paper tackles that problem for joint survival annuities, contracts that keep paying while both lives survive, and for guaranteed joint survival annuity options. The authors build a linear-rational mortality model using a Wishart process, a stochastic matrix-valued process that lets the two mortality intensities move together in a flexible, dependent way while staying positive. With that setup, they derive a closed-form expression for the joint survival annuity and also obtain the distribution, including the density and cumulative distribution, of that annuity. They also develop polynomial expansions for the state variable, which give fast and accurate approximations for the guaranteed annuity option and make the model easier to implement. The result is a unified framework for pricing and managing joint mortality risk in multi-life longevity products.
A song catalog is no longer just nostalgia—it can also behave like an investment. But music royalty markets are messy: deals are rare, prices are hard to observe, and transaction costs are high. This paper tackles that problem by fitting three discounted cashflow models to 1,295 transactions on the Royalty Exchange platform, then using the best model to backtest returns after transaction costs. The headline result is striking: Life of Rights music assets had risk and return characteristics comparable to stocks in the S&P 500 when held for five years. The authors also say music assets and stocks are likely uncorrelated, which means these assets could be viewed alongside a more traditional stock and bond portfolio. In other words, the study does not just ask what a song catalog is worth today—it asks how it might have performed as an investment over time, using real transaction data rather than guesswork.
If you buy insurance that lasts for years, the way your premium is set can quietly bake in unfairness. That problem gets harder when pricing depends on how people move between health states over time, not just on a simple one-time prediction. This paper tackles that gap by recasting any multi-state transition model as a set of Poisson regression problems, which lets insurers apply existing fair-pricing methods in a new setting. The authors use a stylized long-term care insurance product and data from the University of Michigan Health and Retirement Study (HRS) to show the idea in action, with a focus on a post-processing approach. They also explain that the same framework can accommodate pre-processing and in-processing fairness methods. The result is a bridge between fairness tools built for regression models and the long-term insurance models that actually drive pricing decisions.
Pricing an option gets messy fast when the payoff depends on several future decisions or many underlying assets. This paper tackles that problem with a fully forward deep-learning method called the Compound BSDE method. A backward stochastic differential equation, or BSDE, rewrites pricing as a system that works backward from the final payoff to today. The authors extend the classical deep BSDE method, which handled one BSDE, to compound BSDEs. That lets them treat compound options and optimal stopping problems such as Bermudan option pricing in a single framework. They also establish convergence properties for the algorithm and derive an a posteriori error estimate, a way to assess the error after the computation is done. In numerical experiments, the method is reported to be accurate and computationally efficient. The paper says it is effective for high-dimensional option pricing and optimal stopping problems, which are the cases that usually become hardest for traditional numerical tools.
