Variable annuities play an important role in protecting one's future income. The pricing of such annuities remain a big challenge to the annuities' issuers due to the presence of embedded options. Many variable annuity pricing methodologies employ constant volatility assumption for the movement of the underlying asset, which is not the case in real market. In this study, we propose a new pricing model that can account for stochastic volatility, by incorporating the Heston model into our pricing framework. Heston model is one of the commonly used methods to model volatility. Using this new pricing framework, we evaluate the mortality and expenses (M&E) fee charged by the issuers for a group of male and female aged 50-69. The M&E fee evaluated based on the constant volatility pricing model will be compared to the results obtained using our framework.
Mathematics Subject Classification: 91G80
The Hurwitz-Lerch Zeta (HLZ) family includes many well-known distributions such as the logarithmic distribution, Zipf-Mandelbrot distribution and so on. In this study, the stochastic orderings of the random variables in the HLZ family are established based on the likelihood ratio. These orderings provide a useful tool for comparing the 'magnitudes' of these random variables. The tail probability of the HLZ distribution is shown to have an interesting relation with a generalisation of the logarithmic distribution (GLD) proposed in [1]. To demonstrate the flexibility of the HLZ distribution in empirical modelling, a robust probability generating function (pgf) based estimation method using Hellinger-type divergence is implemented in data-fitting and the results are compared with various other GLD's. An augmented pgf is constructed to overcome the difficulties of this estimation method when some data are grouped. ABSTRAK Keluarga Hurwitz-Lerch Zeta (HLZ) mengandungi beberapa taburan yang ternama seperti taburan logaritma, taburan Zipf-Mandelbrot dan lain-lain. Dalam kajian ini, susunan stokastik pembolehubah-pembolehubah rawak dalam keluarga HLZ telah ditubuhkan berdasar nisbah kebolehjadian. Susunan tersebut boleh digunakan dalam perbandingan 'magnitud' antara pembolehubah-pembolehubah rawak tersebut. Hubungan antara kebarangkalian ekor bagi taburan HLZ dan taburan logaritma teritlak yang dicadangkan dalam [1] terus ditunjukkan. Demi menggambarkan kelenturan taburan HLZ, satu kaedah penganggaran teguh yang menggunakan divergen jenis Hellinger berasaskan fungsi penjana kebarangkalian (fpk) telah dilaksanakan dalam analisis data dan keputusannya dibanding dengan pelbagai generalisasi taburan logaritma yang lain. Fpk tertambah telah dibinakan untuk menyelesaikan masalah pelaksanaan kaedah ini apabila terdapat data yang terkumpul.
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