Promotion Rules, Licensing Constraints,
and Strategy-Proofness in Sports Leagues

Abstract: In sports leagues, promotion and relegation rules should reward sporting performance while preserving proper incentives. This paper studies incentive problems in football competitions where promotion depends not only on results on the pitch, but also on licensing constraints. The paper is motivated by a recent episode in Russian football. In the 2024/25 season of Leon Second League A (third tier of Russian football), it became known before the last round that Mashuk, one of the clubs that could potentially qualify for a promotion play-off, would not receive the license required for promotion. Conditional on the other results, Chelyabinsk could prefer losing to drawing. This paper asks a general question: when can licensing constraints make a multi-tournament promotion system incentive incompatible, and what properties must the rules satisfy to eliminate profitable deliberate underperformance? It appears that once some clubs may become ineligible for promotion, it is not enough to track overlaps among winners across stages. The designer must also specify, in advance and in a monotonic way, how promotion rights and play-off positions are reassigned when an ineligible club occupies a promotion-relevant place.

Tale of Two Tails: What Options Reveal About Bitcoin Returns

Co-author: Aleksey Kolokolov

Abstract: We show that Bitcoin’s distinctive upside does not make its investment outlook independent of traditional financial markets. Using options and high-frequency returns, we distinguish expected jump variation from its market valuation. A higher premium on Bitcoin’s own upside is associated with stronger four-week returns. A higher equity-market downside premium is associated with lower Bitcoin returns over the following half-year, even after controlling for Bitcoin’s own downside premium. The evidence suggests that Bitcoin combines unusual upside opportunities with sensitivity to broader financial conditions: its investment appeal cannot be assessed from crypto-specific uncertainty alone

Information Extraction from Latent Rough Volatility Parameters:
A Neural SBIL Approach to the fOU-SV Model

Abstract: This paper sets out a theoretical framework for estimating the four structural parameters of a fractional Ornstein-Uhlenbeck stochastic volatility model from intraday returns in the rough regime where the Hurst index is below one half. The first two moments of daily integrated variance estimate the vol-of-vol and mean reversion jointly; the two move along a ridge on which the stationary variance of the log-variance stays constant. That ridge is the subject of this working paper. I prove that, for fixed H, the autocovariance of the log-variance depends on these two parameters only through this stationary variance and a time rescaling by the mean reversion. The working paper explains why intraday autocovariances can separate them. At intraday lags, autocovariances change as the parameters move along the ridge, while the first two daily moments stay largely fixed. The estimator, NNE_adj, is a shallow neural network trained by least squares on simulated pairs of parameters and statistics, and under regularity conditions on the pseudo-prior its population target is the posterior mean of the parameters given the statistic.

The Cost of Silence: When Strong Brands Stop Advertising.
Evidence From a Large Natural Experiment

Abstract: We study the impact of advertising cessation (“going dark”) on brand performance in FMCG markets, exploiting the large-scale and abrupt withdrawal of advertising by foreign brands in Russia following the 2022 sanctions. Using panel data from a major Russian e-commerce platform spanning 2021–2024, we analyze sales and market share dynamics across five product categories. Employing fixed-effects regressions and exponential decay models, we document economically meaningful declines in market share following advertising halts, with an average decrease of 1.37 percentage points. The effects of going dark are highly heterogeneous across categories. High-churn categories, such as diapers, experience rapid and severe declines (e.g., Pampers: −62%), whereas more habitual, “sticky” categories, such as detergents and deodorants, exhibit substantially greater resilience. We further show that domestic and Asian brands capitalize on the exit of foreign advertisers, gaining market share, and that rebranding strategies partially mitigate losses for some affected brands. We further document that some dominant brands, such as Rexona in deodorants, do not experience meaningful market share declines after going dark, suggesting that sustained advertising investment over long horizons can create durable brand equity that continues to support performance even in the absence of ongoing advertising.

Occupation Games with Stable Matching Mechanisms:
Not All Blocking Pairs Threaten Equilibrium

Co-author: Vasily Gusev

Abstract: The classical stable marriage model takes the two sides of a market as given. In some environments, however, the composition of the two sides is itself the outcome of earlier decisions. For example, workers acquire complementary qualifications. These choices determine potential partnersas well as roles in a team. This paper studies a simple two-stage model in which agents choose their roles before being matched. We call it an occupation game. Equilibrium of an occupation game depends on the rematching induced by a change of role: even a pair that blocks the current matching may be unable to realize its preferred relationship. We characterize equilibrium in terms of how rematching prevents blocking pairs from being realized, establish existence and strong-equilibrium results for specific classes of preferences, and prove that several natural existence and implementation problems are NP-complete.

Securitisation with Climate Risks

Abstract: Banks must hold a buffer of their own money against possible loan losses. This buffer is called regulatory capital, and the rules that set it largely ignore the risk of physical climate events such as hurricanes and floods. Recognising that risk would force banks to hold more capital, so they have no reason to volunteer it. We study what happens when such an event strikes a bank that has bundled many loans into a pool and sold slices of it to investors. This practice is called securitisation. The slices, called tranches, are ranked by who bears losses first. The bottom slice absorbs the first losses, and the top slice is hit only if the pool loses a great deal. The capital attached to each slice comes from a standard regulatory formula. We extend a model of default risk in a loan pool so that a climate event hits all borrowers at once,  and we feed the resulting higher losses into the existing formula, leaving the slice boundaries unchanged. We compare a simple first-order approximation, which is quick to compute, with a full simulation, and in a worked example the two disagree sharply. The approximation says that only the middle slice is affected. The simulation shows that the capital the whole pool needs is three to five times larger. The middle slice is pushed to the maximum capital charge the rules allow, and moving the slice boundaries does not restore the original charge. Capital depends far more on how severe the damage is than on how often events occur. Finally, we show how a climate damage swap could help. This is a contract that pays the bank when an index of physical damage rises, so it works like insurance against the event itself. By covering the loss, it can release part of the extra capital. In our analysis, covering many events roughly is better than covering a few precisely. A payout that is too small can be fixed with a larger contract, but a missed event cannot.

Recursive Equilibrium with Relaxed Consistency

Abstract: Recursive equilibrium equates beliefs with laws generated by optimal behavior, yet weak convergence of joint laws need not preserve the conditionals required for recursive decisions. We introduce an equilibrium concept that retains exact optimization under subjective beliefs while allowing a prescribed weak discrepancy between beliefs and generated laws. Under regularity conditions on decisions and law assembly, we prove existence for every positive tolerance and every prescribed evaluation measure. When the implemented transition is also Feller, the evaluation measure can be chosen invariant under equilibrium dynamics. A regularization operator supplies the existence witness, making conditional beliefs stable under weak changes in joint laws. In a compact economy with Krusell–Smith frictions, equilibria exist at every state representation retaining price-relevant information, including moment representations; for deterministic aggregate forecasts, forecast error and joint-law closure bound each other. The framework gives an equilibrium interpretation to represented computation without presupposing an exact recursive equilibrium.

Learning from Neighbors: Spatial Information in Offshore Oil Lease Auctions.

Abstract: Offshore oil and gas leases are finite-lived options: a leaseholder can drill now or wait for neighbors’ bids, discoveries, dry holes, and expirations to reveal local geology. When adjacent tracts have different owners, this creates an information externality. I study it using nearly 20,000 Gulf of Mexico leases auctioned in 1954–2002, matched to borehole records and production through 2024. A spatial model shows that production potential is strongly correlated across adjacent tracts (oil-presence correlation above 0.8 at 5 km); I use it to build tract-year beliefs updated with each discovery and dry hole. These beliefs predict drilling and bids. Conditional on them, a new adjacent discovery is followed by a 1.8-percentage-point rise in the annual probability of first drilling, while undrilled neighbors whose leases expire before the focal lease are associated with less immediate drilling, consistent with waiting to learn. Neighbors’ winning bids, net of public geology, predict higher winning bids and more bidders on adjacent tracts sold later. Lease auctions thus allocate learning options, not only resource claims.

Regional Banking Market Structure and Monetary Policy Transmission:
Evidence from Russia

Abstract: This paper studies whether regional banking market structure shapes thetransmission of a common monetary-policy stance in Russia. Using district-level monthly and quarterly panels over 2019M4–2022M1, I estimate two-wayfixed-effects models that interact the Bank of Russia’s key rate with a lagged proxy for district banking concentration. In the full sample, more concentrated districts exhibit stronger short-run responses of short-term corporate lending ratesand investment. However, this pattern is concentrated in the upper tail of the concentration distribution and weakens materially once the Northwestern federal district is excluded. At longer horizons, heterogeneity is weaker: for investment, distributed-lag estimates point to differences in timing rather than cumulative one-year effects, while for long-term lending rates the evidence is sensitive to lag structure. Overall, local banking structure appears to matter mainly for short-run differential sensitivity, and even that evidence is not broadly distributed across districts.