This paper aims to introduce the reader to the premium setting of annuities within life insurance. This is done using a hypothetical annuity contract offered to 36-year-olds in Sweden. The contract provides an annual pension from age 65 until either the individual's death or age 90, after which payouts cease. The analysis employs life tables using real-life data to estimate mortality, discounting to decide present values, and calculates fair and risk-adjusted premia for lump sum and annual payment options using theory and simulations. Ultimately, we found that the method used was insufficient given the data. This is due to the last decades' rise in life expectancy, requiring us to use other methods to acquire accurate premia. / <p>Detta arbete omfattar 3,0 hp och är en del av kursen Matematisk kommunikation (MM7020), 7,5 hp.</p>

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Obligationer är grundläggande för kapitalmarknadens funktion, och på senare tid kräver investerare möjligheten att diversifiera sina portföljer utefter miljömässiga och klimatfrämjande ändamål. Gröna obligationer omfattas av osäkerheter som exempelvis risker för greenwashing och obefintlig reglerad tillsyn över det öronmärkta kapitalet. Gröna certifieringar sägs motverka dessa risker och integreras därför i studien. Sedan gröna företagsobligationer introducerades på marknaden har det även florerat rykten om att investerare avstår en del av sin avkastning för att investera enligt sina gröna preferenser. Den gröna premien har undersökts i många utföranden, men alltför sällan på den svenska primärmarknaden. Studien använder sig av en matchningsmetod tillsammans med en hypotesprövning och korrelationsanalyser för att undersöka förekomsten av en grön premie. Matchningsparen består av likvärdiga gröna och konventionella företagsobligationer. Resultaten visar att det förekommer en svagt positiv premie för gröna obligationer och att gröna certifieringar har en stor betydelse för fortsatt marknadseffektivitet och minskad informationsasymmetri. Slutsatsen blir därmed att gröna företagsobligationer emitterade av svenska fastighetsföretag inte nämnvärt lönar sig ekonomiskt, men kommer med andra fördelar såsom en riskdiversifierad investeringsportfölj. / Bonds are fundamental to the functioning of the capital market, and more recently investors have been seeking the possibility to diversify their portfolios by making more environmental and climate conscious investments. Green bonds are accompanied by uncertainties, for example risk of greenwashing and insufficient regulations and supervision of the earmarked capital. Green certification has the possibility of minimising these risks and has therefore been integrated into this study. Since green certification has been introduced into the market, rumour has it that investing in green bonds results in losing part of one's profit margin. The green premium has been examined in many ways, but all too rarely in the Swedish primary market. To investigate if a green premium exists the study uses a matching method, together with a hypothesis test and correlation analysis. The matching method consists of equal parts of green and conventional corporate bonds.  The results show a slightly more positive premium of green bonds, and that green certification is both meaningful and important for continued market efficiency and reduced information asymmetry. The conclusion is therefore that green corporate bonds issued by Swedish real estate companies are not financially advantageous but do bring other benefits such as a risk-diversified investment portfolio.

The green bond market has gained significant traction over the past few years. In 2019, issuers released $320 billion worth of green bonds, compared to $490 billion in 2023 (Yamaguchi &amp; Ramos, 2024). This study applies the widely used metric Value-at-Risk (VaR) to better understand the risk profile of this relatively new financial instrument. The study forecasts volatility using an ARMA(1,1)-GARCH(1,1) model to simulate VaR. The thesis employs regression analysis to explore higher downside risk and a green premium in the primary Nordic bond market for green bonds. The findings reveal that green bonds carry higher downside risk, as evidenced by significantly larger VaR values for green-labeled bonds. Additionally, the study identifies a lower yield to maturity associated with green bonds compared to conventional bonds, indicating a green premium in the primary Nordic bond markets. This research contributes to the growing body of literature on green finance, providing valuable insights for investors regarding the risks and yields associated with green bonds. The findings of this study are essential since ESG is a crucial topic for today’s investors, and a green premium encourages firms to invest in more sustainable projects. If proof of investors willingness to pay a premium for sustainability was confirmed, firms might undertake more climate-friendly projects. Further research should explore alternative risk metrics and apply these metrics across different regions.