In this paper, we present an innovative hybrid model for the valuation of equity options. Our approach includes stochastic volatility according to Heston (1993) [Review of Financial Studies 6 (2), 327–343] and features a stochastic interest rate that follows a three-factor short rate model based on Hull and White (1994) [Journal of Derivatives 2 (2), 37–48]. Our model is of affine structure, allows for correlations between the stock, the short rate and the volatility processes and can be fitted perfectly to the initial term structure. We determine the zero bond price formula and derive the analytic solution for European type options in terms of characteristic functions needed for fast calibration. We highlight the flexibility of our approach, by comparing the price and implied volatility surfaces of our model with the Heston model, where we in particular focus on the correlation structure. Our approach forms a comprehensive market model with an intuitive correlation structure that connects both the equity and interest market to the market volatility.
In this paper, we devise a stochastic asset–liability management (ALM) model for a life insurance company and analyze its influence on the balance sheet within a low-interest rate environment. In particular, a flexible procedure for the generation of insurers’ compressed contract portfolios that respects the given biometric structure is presented, extending the existing literature on stochastic ALM modeling. The introduced balance sheet model is in line with the principles of double-entry bookkeeping as required in accounting. We further focus on the incorporation of new business, i.e. the addition of newly concluded contracts and thus of insured in each period. Efficient simulations are obtained by integrating new policies into existing cohorts according to contract-related criteria. We provide new results on the consistency of the balance sheet equations. In extensive simulation studies for different scenarios regarding the business form of today’s life insurers, we utilize these to analyze the long-term behavior and the stability of the components of the balance sheet for different asset–liability approaches. Finally, we investigate the robustness of two prominent investment strategies against crashes in the capital markets, which lead to extreme liquidity shocks and thus threaten the insurer’s financial health.
We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load the corresponding distribution onto the states. We implement the expectation value of the option pricing formula as a composition of the price probabilities, the payout and an indicator function, mapping their respective values to amplitudes of additional qubits. Thus, the underlying no longer has to be discretized into the same bit values for different times, resulting in smaller quantum circuits. The algorithm may be used with quantum amplitude estimation, enabling a quadratic speed-up over classical Monte Carlo methods.
ZusammenfassungUm die Möglichkeiten der Nutzung der Chancen-Risiko Klassen (CRK) für staatlich geförderte Altersvorsorgeprodukte durch die Produktinformationsstelle Altersvorsorge gGmbH (PIA) bei der Kundenberatung zu maximieren, entwickeln wir ein Verfahren zur Bestimmung der CRK verschiedener Portfolios solcher Produkte, so dass die CRK des Portfolios nicht größer ist als die Risikopräferenz des zu beratenden Kunden. Dafür betrachten wir zum einen ein Portfolio aus zwei neu zu erwerbenden Produkten und zum anderen eines aus einem bereits beim Kunden vorhandenen Produkt und einem Neuprodukt. Wir untersuchen die Eigenschaften der verschiedenen Chancen- und Risikoparameter samt zugehöriger Abbildungen und zeigen, dass ein Diversifikationseffekt bei der Klassifizierung vorliegt. Aufbauend auf den Eigenschaften erhalten wir als Ergebnis, dass als Obergrenze der CRK des Portfolios die gemittelten Endvermögen heranzuziehen sind und übersetzen dies in Empfehlungen für die Kundenberatung.
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