Accelerated Scenario-Based Portfolio Risk and Optimization with Derivatives

Date

2026-8-22

Author

Tokmak, Bahri

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

74
views

0
downloads

Cite This

Scenario-based risk measurement and portfolio optimization for derivative-containing portfolios require heterogeneous instruments to be revalued under many simulated market states. This becomes computationally demanding for stochastic-volatility, path dependent, and early-exercise products. Moreover, percentage-return formulations become undefined or unstable for instruments with zero or negligible current value, even when their future scenario P&L remains economically significant. This thesis develops an integrated framework for accelerated scenario-based portfolio risk measurement and optimization with derivatives. Portfolio decisions are represented in position units, while risk and reward are calculated from scenario-wise unit P&L. This unit-space formulation remains well posed for zero-valued instruments and supports direct Conditional Value-at-Risk (CVaR) minimization together with Sharpe, Information, Sortino, Omega, and Stable Tail-Adjusted Return Ratio (STARR) optimization. Computational cost is reduced through an array-based repricing architecture that replaces repeated scenario-specific market-object construction with valuation-ready arrays, reusable market inputs, cached numerical objects, and product-specific pricing kernels. Vectorized CPU execution and selective GPU acceleration are combined with batched calibration, fractional-programming methods, and parallel sparse optimization for scenario-expanded tail-risk problems. The numerical study validates the stochastic, pricing, and calibration components before evaluating a heterogeneous nine-instrument portfolio. Convergence analysis identifies 50,000 scenarios as a practical balance between tail-risk stability and computational cost. At this scenario count, the measured end-to-end runtime for scenario generation, calibration, repricing, and STARR optimization decreases from approximately 55.29 minutes to 22.68 seconds when numerical methods are used for Asian and American option valuation. At the 99% confidence level, direct CVaR optimization reduces both VaR and Expected Shortfall by approximately 79%, while preserving the fixed-budget and expected-P&L requirements. The Information-ratio and STARR solutions also assign positive positions to a future with zero current value, demonstrating the practical value of the unit-space formulation. Overall, the thesis shows that financially consistent unit-space modeling and selective computational acceleration can be combined within a single auditable framework while preserving the numerical structure of the underlying pricing, risk, and optimization problems.

Subject Keywords

Forward-looking portfolio optimization, Zero-valued instruments, CVaR, Fractional programming, GPU acceleration

URI

https://hdl.handle.net/11511/120716

Collections

Graduate School of Applied Mathematics, Thesis