Alessandro Saccal

The Transactional Asset Pricing Approach (TAPA) is able to handle asset valuations on a portfolio level of size constrained markets against the backdrop of low liquidity hindering the estimation of the variance of returns. Prompted by a numerical simulation of the TAPA algorithm, we develop stability conditions associated with the valuation convergence for any maximal positive time period and positive number of assets. We present stability conditions at the local level, both in continuous and discrete algorithmic time, and we develop them by means of log-linearisation about the steady state of its equations’ variables. We conclude on the analytical existence of stability conditions at the local level up to four assets and any positive time period. We adduce analytical applications within such a region and present a solution for a benchmark calibration of the steady state parameters given two time periods and a single asset.

This study presents a self-contained derivation and solution of the Black and Scholes partial differential equation (PDE), replacing the standard Wiener process with a smoothed Wiener process, which is a differentiable stochastic process constructed via normal kernel smoothing. By presenting a self-contained, Itô-free derivation, this study bridges the gap between heuristic financial reasoning and rigorous mathematics, bringing forth fresh insights into one of the most influential models in quantitative finance. The smoothed Wiener process does not merely simplify the technical machinery but further reaffirms the robustness of the Black and Scholes framework under alternative mathematical formulations. This approach is particularly valuable for instructors, apprentices, and practitioners who may seek a deeper understanding of derivative pricing without relying on the full machinery of stochastic calculus. The derivation underscores the universality of the Black and Scholes PDE, irrespective of the specific stochastic process adopted, under the condition that the essential properties of stochasticity, volatility, and of no arbitrage may be preserved.

In the paper, using the three-statement financial modelling methodology as applied to a representative development project, we aim to analyse, ex ante, the industry-level impact of transition to mandatory escrow schemes in residential and mixed-use construction in Tashkent city (due to be implemented in Uzbekistan from 2026). Modelling single-milestone escrow plans against the current steep-discount advance-based system of off-plans as a baseline, the model accounts for salient institutional features of the Tashkent city development market, including land auctioning, full-cycle Value-added tax (VAT) accounting, and Tax loss carryforward provisions. It also incorporates a framework for demand-driven residual valuations for the development land element. Our findings indicate practically unchanged cashflow profitability of developers on the market in question. Around 30% p.a. in nominal Free-cashflow-to-equity based IRRs expressed in the national currency, provided that the transition to the greater use of leverage in funding unfolds as expected. The disappearance of steep off-plan discounts while the transition to escrows unfolds will be countervailed by the reliance on costly loans from escrow banks. Absent the greater use of leverage, the IRR (FCFE) profitability of the developers is expected to decline by some 5%. For the apartment buyers, this is effectively equivalent to increasing property transaction prices on the primary market in line with their headline asking amounts. Thus-generated economic surplus will be partially captured by the developers and partially passed through to escrow banks, increasing their gross profits by up to $50M, p.a. due to their new role in financing Tashkent city residential developments that are still largely equity-driven. Apart from this effect, we find only a moderate financial leverage influence on developers’ profitability due to the high-interest-rate environment prevailing in Uzbekistan. We also find a demand-driven pressure on land auction prices suggested by increasingly back-loaded alterations in project cashflow profiles. This study also purports to make a material contribution to the evolving body of literature on financial modelling of apartment and mixed-use property developments by offering a flexible three-statement modelling framework with innovative endogenised equity management features.