arXiv subjects

Yue Kuen Kwok

Publications and source records attributed to Yue Kuen Kwok.

5 recordsLinked to original sources

arXiv2026

Stochastic Mortality Model with Fractional Lévy Dynamics

A substantial body of empirical evidence suggests that stochastic mortality models ignoring long range dependence tend to underestimate life expectancy, which may lead to profound implications for pension schemes and funding arrangements. This paper addresses the modelling of stochastic mortality via a mixture of a fractional Lévy process and standard Brownian motion. Our stochastic mortality model exhibits nice analytical tractability in actuarial valuations and flexibility in the choice of underlying Lévy specifications. The long range dependence feature embedded in our stochastic mortality model is well reflected in our empirical studies on the mortality shocks during World War II and COVID-19. For efficient numerical pricing of longevity derivatives, we construct an effective singular value decomposition approximation scheme to overcome the computational challenges arising from the non-Markovian nature of the fractional Lévy process. Truncation errors in singular value decomposition approximation can be reduced by an effective residual correction scheme.

q-fin.MF↗

arXiv2026

Simulation of stochastic volatility models via operator splitting schemes

The standard Euler discretization schemes for numerical option pricing under stochastic volatility models are known to exhibit high biases and potential unreliability. The alternative use of the exact (unbiased) simulation approach invariably involves numerical evaluation of integrated variance (and / or volatility) conditional on terminal variance (volatility) value. To resolve the technical challenge, most simulation schemes either employ the tedious Fourier inversion of conditional characteristic function or numerical approximation by moment matched distribution. We propose a general framework of constructing efficient and reliable simulation schemes for stochastic volatility models via the Strang operator splitting approximation. The simulation procedure completely circumvents the necessity of evaluation of conditional integrated variance (and / or) volatility. Our simulation schemes compete favorably well with most existing exact simulation schemes and the biased Euler schemes in terms of accuracy, efficiency, reliability and ease of implementation. Extensive numerical tests were conducted to illustrate the versatility and success of our operator splitting approach for most common stochastic volatility models, such as the Heston-type models, lifted Heston model, Hull-White model, and Barndorff-Nielsen and Shephard model. We also establish the proof of second-order convergence of the operator splitting schemes.

q-fin.CP↗

arXiv2026

Efficient simulation schemes for pricing options under the Ornstein--Uhlenbeck driven stochastic volatility model

We develop an efficient Monte Carlo simulation scheme for pricing options under the Ornstein-Uhlenbeck driven stochastic volatility model via the operator splitting approach. With an ingenious splitting of the governing stochastic differential equations, our operator splitting scheme admits analytic solutions in all sub-steps, so its implementation is simplified to require simulation of a few normal variates. This resolves the two typical numerical challenges in other simulation schemes, namely, sampling of conditional integrated variance and pathwise inverse integral transform of characteristic functions. There are three pioneering simulation schemes that attempt to overcome the above two numerical challenges. These include the Hilbert interpolation scheme of Zeng et al. (2023), Karhunen-Lo`eve expansion scheme of Choi (2025) and moment matching scheme based on the Inverse Gaussian distribution of Brignone and Sgarra (2026). We performed numerical tests to compare accuracy-speed performance of pricing options using our operator splitting scheme with these three pioneering schemes. We found that our scheme competes favorably well in terms of accuracy-speed tradeoff among all these schemes, in particular for pricing path dependent options with a large number of monitoring instants. The performance of our scheme can be well enhanced by martingale-preserving control variates and variance reduction via conditioning.

q-fin.CP↗

arXiv2025

Efficient and accurate simulation of the stochastic-alpha-beta-rho model

We propose an efficient, accurate and reliable simulation scheme for the stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR simulation lie in sampling (i) integrated variance conditional on terminal volatility and (ii) terminal forward price conditional on terminal volatility and integrated variance. For the first sampling procedure, we sample the conditional integrated variance using the moment-matched shifted lognormal approximation. For the second sampling procedure, we approximate the conditional terminal forward price as a constant-elasticity-of-variance (CEV) distribution. Our CEV approximation preserves the martingale condition and precludes arbitrage, which is a key advantage over Islah's approximation used in most SABR simulation schemes in the literature. We then adopt the exact sampling method of the CEV distribution based on the shifted-Poisson mixture Gamma random variable. Our enhanced procedures avoid the tedious Laplace inversion algorithm for sampling integrated variance and non-efficient inverse transform sampling of the forward price in some of the earlier simulation schemes. Numerical results demonstrate our simulation scheme to be highly efficient, accurate, and reliable.

q-fin.CP↗

arXiv2023

Simulation schemes for the Heston model with Poisson conditioning

Exact simulation schemes under the Heston stochastic volatility model (e.g., Broadie-Kaya and Glasserman-Kim) suffer from computationally expensive modified Bessel function evaluations. We propose a new exact simulation scheme without the modified Bessel function, based on the observation that the conditional integrated variance can be simplified when conditioned by the Poisson variate used for simulating the terminal variance. Our approach also enhances the low-bias and time discretization schemes, which are suitable for pricing derivatives with frequent monitoring. Extensive numerical tests reveal the good performance of the new simulation schemes in terms of accuracy, efficiency, and reliability when compared with existing methods.

q-fin.MF↗