The effectiveness of Lévy processes and stochastic-volatility models in pricing structured products
Seven models — Black-Scholes, Merton jump-diffusion, Variance Gamma, NIG, CGMY, Heston and Bates — are calibrated to live option chains from July 2026 on the S&P 500, Apple and SPY, eight maturities each. The same calibrated parameters then price four structured products: a capital-protected note, an ATM digital call, a barrier reverse convertible and a Phoenix autocall. European payoffs go through Carr–Madan FFT, path-dependent ones through Monte Carlo.
The question is not which model fits best — that answer is unsurprising. The question is how much money the answer moves.
On the same market data, the fair coupon on a barrier reverse convertible nearly doubles depending on which model you price it with. That difference is not academic: it is the entire margin on the trade. And the hedging-error tables say the left tail is dominated by unhedgeable jump and gap risk, not by the choice of model — so a better smile fit buys you a fairer price, not a safer book.
Correlation is a hyperbolic distance
The parameter space of a stochastic-volatility model is not flat. This paper works out the geometry explicitly: correlation maps to a distance in the hyperbolic plane through ρ = tanh(δ), the SPD(2) covariance cone factorises into a radius and a point of H², and the Fisher metric on SABR and Heston parameters has a curvature you can compute in closed form.
Every statement carries a label — exact (symbolic, residual identically zero), measured (numerical, with stated accuracy), or known (in the literature, reproduced here). Each one maps to a named CSV in the repository, so a reader can check the claim rather than trust it.
Averaging covariance matrices entry by entry — what almost every risk system does — understates risk by a quarter to a third, and the error is systematic, not noise. Interpolating a stress path in straight lines distorts it by up to a factor of two. Both are consequences of using Euclidean arithmetic on a space that is not Euclidean, and both are measured here, not asserted.
Hidden Markov model with Student's-t emissions for regimes of a bank bond portfolio return
A four-regime multivariate hidden Markov model with heavy-tailed Student's t emissions, estimated on 904 trading days of daily MOEX data across a 124-issue, seven-segment RUB bond portfolio. The point is tail calibration: whether a regime-switching model with honest tails beats the Gaussian approximation out of sample while still producing states a risk committee can read.
It is validated the way a supervisor would validate it — rolling one-day-ahead forecasts, Kupiec and Christoffersen coverage tests on VaR, the Acerbi–Székely test on Expected Shortfall, against Gaussian, historical simulation, EVT-GPD, GARCH-t and DCC-GARCH benchmarks.
The Gaussian model breached its 99% VaR two and a half times more often than it promised, and its Expected Shortfall was statistically too small — on a plain government-and-corporate bond book, in a sample with no exotic instruments in it. EVT-GPD, GARCH-t and DCC-GARCH match the far-tail coverage, but none of them tells you which state the market is in, and the sell-off regime here is distinguished from the high-volatility recovery regime only because drift is modelled per state.
What these papers do not claim
Each repository ships its own limitations section, and they are worth reading before the results. In short: the bond portfolio is equal-weighted across segments, so absolute VaR and segment contributions will move on a live book; coupon income is approximated by smoothed daily carry rather than exact payment dates; Eurobonds are excluded for want of consistent MOEX history; the macro-transition model is reduced-form, estimated on a decoded regime path rather than jointly. In the structured-products work, CGMY is implemented for European payoffs only. In the geometry paper, no result claims scientific priority — the contribution is the exact identifications, the measured limits of validity, and three refuted a-priori hypotheses.