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Guaranteed annuity options (GAOs) allow policyholders to convert accumulated funds into life annuities at maturity at a guaranteed minimum rate. Thus, insurers are exposed to both investment and longevity risks. Accurate valuation of these long-term, survival-contingent contracts is essential for solvency assessment and risk management. Many existing approaches assume independence between interest rate and mortality risks. This paper develops a computationally efficient pricing framework for GAOs that jointly models interest and mortality rates as correlated stochastic processes with regime-switching dynamics governed by a finite-state continuous-time Markov chain. Model parameters are estimated using U.S. interest rates and cohort mortality data via quasi-maximum likelihood estimation. A semi-analytic valuation formula is derived based on the joint distribution of the underlying processes. Numerical results show that incorporating correlation and regime-switching materially increases GAO prices relative to conventional one-state models. The proposed semi-analytic approach delivers substantial computational advantages over standard Monte Carlo simulations. Sensitivity analysis further identifies the parameters most relevant for long-horizon pricing and solvency considerations. This highlights the practical relevance of the framework for managing longevity-linked guarantees under economic and demographic uncertainty.

Accurately valuing large portfolios of Variable Annuities (VAs) poses a significant challenge due to the high computational burden of Monte Carlo simulations and the limitations of spatial interpolation methods that rely on manually defined distance metrics. We introduce a residual portfolio valuation network (ResPoNet), a novel residual neural network architecture enhanced with weighted loss functions, designed to improve valuation accuracy and scalability. ResPoNet systematically accounts for mortality risk and path-dependent liabilities using residual layers, while the custom loss function ensures better convergence and interpretability. Numerical results on synthetic portfolios of 100,000 contracts show that ResPoNet achieves significantly lower valuation errors than baseline neural and spatial methods, with faster convergence and improved generalization. Sensitivity analysis reveals key drivers of performance, including guarantee complexity and contract maturity, demonstrating the robustness and practical applicability of ResPoNet in large-scale VA valuation.

This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17. It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses. We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation. We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions. The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.

Stochastic processes are employed in this paper to capture the evolution of daily mean temperatures, with the goal of pricing temperature-based weather options. A stochastic harmonic oscillator model is proposed for the temperature dynamics and results of numerical simulations and parameter estimation are presented. The temperature model is used to price a one-month call option and a sensitivity analysis is undertaken to examine how call option prices are affected when the model parameters are varied.

This paper addresses the problem of designing an efficient platform for pairs-trading implementation in real time. Capturing the stylised features of a spread process, i.e., the evolution of the differential between the returns from a pair of stocks, exhibiting a heavy-tailed mean-reverting process is also dealt with. Likewise, the optimal recovery of time-varying parameters in a return-spread model is tackled. It is important to solve such issues in an integrated manner to carry out the execution of trading strategies in a dynamic market environment. The Kalman and hidden Markov model (HMM) multi-regime dynamic filtering approaches are fused together to provide a powerful method for pairs-trading actualisation. Practitioners’ considerations are taken into account in the way the new filtering method is automated. The synthesis of the HMM’s expectation–maximisation algorithm and Kalman filtering procedure gives rise to a set of self-updating optimal parameter estimates. The method put forward in this paper is a hybridisation of signal-processing algorithms. It highlights the critical role and beneficial utility of data fusion methods. Its appropriateness and novelty support the advancements of accurate predictive analytics involving big financial data sets. The algorithm’s performance is tested on historical return spread between Coca-Cola and Pepsi Inc.’s equities. Through a back-testing trade, a hypothetical trader might earn a non-zero profit under the assumption of no transaction costs and bid-ask spreads. The method’s success is illustrated by a trading simulation. The findings from this work show that there is high potential to gain when the transaction fees are low, and an investor is able to benefit from the proposed interplay of the two filtering methods.

We propose a mean-reverting interest rate model whose mean-reverting level, speed of mean-reversion and volatility are all modulated by a weak Markov chain (WMC). This model features a simple way to capture the regime-switching evolution of the parameters as well as the memory property of the data. Concentrating on the second-order WMC framework, we derive the filters of the WMC and other auxiliary processes through a change of reference probability measure. Optimal estimates of model parameters are provided by employing the EM algorithm. The h -step ahead forecasts under our proposed set-up are examined and compared with those under the usual Markovian regime-switching framework. We obtain better goodness-of-fit performance based on our numerical results generated from the implementation of WMC-based filters to a 10-year dataset of weekly short-term-maturity Canadian yield rates. Some statistical inference issues of the proposed modelling approach are also discussed.

In this paper, the identifiability and the estimability of a particular phase-type ageing model (PTAM) are investigated. We consider a PTAM that is shown to be identifiable, although it has poor estimability when the only observation is the time until absorption. We use a data-cloning method to assess model estimability, which is also analysed visually via contour plots and marginal likelihood functions. The PTAM’s estimability under different scenarios is compared, from the best scenario of a fully observable Markov process for each individual to the worst scenario wherein the only observation is the time until absorption for each individual. Some in-between scenarios are also studied and include the situations where the state could be observed every several years and the state could be measured with some error. Certain conditions are provided regarding the state of the Markov chain that improves the PTAM’s estimability.

We develop an efficient algorithm to compute the likelihood of the phase-type ageing model. The proposed algorithm uses the uniformisation method to stabilise the numerical calculation. It also utilises a vectorised formula to only calculate the necessary elements of the probability distribution. Our algorithm, with an error’s upper bound, could be adjusted easily to tackle the likelihood calculation of the Coxian models. Furthermore, we compare the speed and the accuracy of the proposed algorithm with those of the traditional method using the matrix exponential. Our algorithm is faster and more accurate than the traditional method in calculating the likelihood. Based on our experiments, we recommend using 20 sets of randomly-generated initial values for the optimisation to get a reliable estimate for which the evaluated likelihood is close to the maximum likelihood.

A Markov-modulated affine framework for dependent risk factors is proposed to value a guaranteed annuity option (GAO). Concentrating on the important effect of volatilities, both diffusion components of the interest and mortality rates are driven by a finite-state continuous time Markov chain. We derive an explicit solution to the price of a pure endowment by solving a system of linear ordinary differential equations with the aid of the forward measure. Utilising the endowment-risk-adjusted measure with pure endowment as the corresponding numéraire, we provide an efficient and accurate formula in obtaining the GAO price. Such valuation efficiency and accuracy were demonstrated through numerical experiments. We benchmark our results with those of the Monte-Carlo simulation method and show significant differences in standard errors and computing times.

We consider the valuation of credit default swaps (CDSs) under an extended version of Merton's structural model for a firm's corporate liabilities. In particular, the interest rate process of a money market account, the appreciation rate, and the volatility of the firm's value have switching dynamics governed by a finite-state Markov chain in continuous time. The states of the Markov chain are deemed to represent the states of an economy. The shift from one economic state to another may be attributed to certain factors that affect the profits or earnings of a firm; examples of such factors include changes in business conditions, corporate decisions, company operations, management strategies, macroeconomic conditions, and business cycles. In this article, the Esscher transform, which is a well-known tool in actuarial science, is employed to determine an equivalent martingale measure for the valuation problem in the incomplete market setting. Systems of coupled partial differential equations (PDEs) satisfied by the real-world and risk-neutral default probabilities are derived. The consequences for the swap rate of a CDS brought about by the regimeswitching effect of the firm's value are investigated via a numerical example for the case of a two-state Markov chain. We perform sensitivity analyses for the real-world default probability and the swap rate when different model parameters vary. We also investigate the accuracy and efficiency of the PDE approach by comparing the numerical results from the PDE approach to those from the Monte Carlo simulation.