https://quantfilab.github.io/pmarupanthorn/tags/capital-allocation/Capital AllocationHugo Blox Builder (https://hugoblox.com)en-usFri, 28 Aug 2026 00:00:00 +0000https://quantfilab.github.io/pmarupanthorn/media/icon_hu68170e94a17a2a43d6dcb45cf0e8e589_3079_512x512_fill_lanczos_center_3.pnghttps://quantfilab.github.io/pmarupanthorn/tags/capital-allocation/https://quantfilab.github.io/pmarupanthorn/publication/op2026/Fri, 28 Aug 2026 00:00:00 +0000https://quantfilab.github.io/pmarupanthorn/publication/op2026/<div class="research-bilingual" data-research-bilingual> <section id="research-content-OP2026-en" class="research-language-panel" lang="en"> <figure class="research-concept-map research-concept-map--image"> <img src="https://quantfilab.github.io/pmarupanthorn/pmarupanthorn/publication/op2026/concept-map-en.png" alt="Conceptual map: European option underwriting as a capital-normalized liability portfolio" loading="eager"> </figure> <h2>The problem</h2> <p>Writing unhedged European options creates a liability-management problem rather than an ordinary investment problem. The writer must decide where downside put claims and upside call claims attach, and how a finite underwriting-capital sleeve should be allocated across them. Cash-secured puts have a genuine terminal claim bound, but an uncovered call remains unbounded even when a finite capital proxy is used to size the position.</p> <p><strong>Who benefits:</strong></p> <ul> <li>Option writers and derivatives portfolio managers</li> <li>Broker, exchange, and market-maker risk teams</li> <li>Quantitative analysts designing strike and capital-allocation policies</li> <li>Capital, margin, and solvency analysts</li> <li>Researchers studying crypto derivatives and nonlinear portfolio risk</li> </ul> <h2>Method</h2> <p>The paper develops a static terminal framework for European cash-settled written puts and calls with a common maturity. It separates observed formation premiums from expected physical claims, divides each claim by a declared capital unit, and maximizes expected underwriting surplus minus a quadratic penalty based on the raw second moment of aggregate normalized claims. Under a multivariate lognormal terminal law, the study derives closed-form put, call, and cross-claim moments, conditional KKT capital allocations, local strike conditions, dependence effects, and a liability-side frontier. The empirical implementation applies staged contract screening and capped allocation to archived Deribit crypto-option formations, using only point-in-time information, 365 preceding aligned returns, fixed 90% put and 110% call benchmarks, paired HAC intervals, and circular block bootstrap diagnostics.</p> <h2>Results</h2> <p>In 209 matched BTC/ETH put formations, the staged 70%-cap policy raises mean gross surplus from 0.294% to 0.945%, a paired difference of 0.651 percentage points with a 95% HAC interval of [0.382, 0.920], but it has higher dispersion and does not establish downside-risk dominance. In the same 209 two-sided formations, mean surplus is 3.112% versus 0.601%, a 2.511-point difference [1.499, 3.522]; the worst-5% mean improves, while the volatility difference remains imprecise. Across 23 retained USDC multi-asset formations, mean surplus is 5.685% versus 1.684%, a 4.001-point difference [2.885, 5.116] with 20 wins, but volatility rises from 1.376% to 3.864%. A realized fixed BTC uncovered-call claim exceeds its finite capital proxy and produces a -99.917% formation surplus. The evidence therefore supports a solvency-aware diagnostic framework, not calibrated tail probabilities, executable net profitability, or broker-margin survival.</p> </section> </div>