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Journal articles on the topic 'Risk-free rate'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Gadidov, Anda, and M. C. Spruill. "Drift and the Risk-Free Rate." Journal of Probability and Statistics 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/595741.

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It is proven, under a set of assumptions differing from the usual ones in the unboundedness of the time interval, that, in an economy in equilibrium consisting of a risk-free cash account and an equity whose price process is a geometric Brownian motion on , the drift rate must be close to the risk-free rate; if the drift rate and the risk-free rate are constants, then and the price process is the same under both empirical and risk neutral measures. Contributing in some degree perhaps to interest in this mathematical curiosity is the fact, based on empirical data taken at various times over an assortment of equities and relatively short durations, that no tests of the hypothesis of equality are rejected.

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2

Mayordomo, Sergio, Juan Ignacio Peña, and Eduardo S. Schwartz. "Towards a common Eurozone risk free rate." European Journal of Finance 21, no. 12 (May 15, 2014): 1005–22. http://dx.doi.org/10.1080/1351847x.2014.912670.

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3

KERIMOV, Pavlo. "Features of risk-free rate estimation in Ukraine." Fìnansi Ukraïni 2019, no. 285 (September 5, 2019): 61–74. http://dx.doi.org/10.33763/finukr2019.08.061.

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4

Cecchetti, Stephen G., Pok-sang Lam, and Nelson C. Mark. "The equity premium and the risk-free rate." Journal of Monetary Economics 31, no. 1 (February 1993): 21–45. http://dx.doi.org/10.1016/0304-3932(93)90015-8.

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5

Elul, Ronel. "Financial innovation, precautionary saving and the risk-free rate." Journal of Mathematical Economics 27, no. 1 (February 1997): 113–31. http://dx.doi.org/10.1016/0304-4068(95)00768-7.

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6

Yu, Han. "Research on Stock Return Rate." Frontiers in Business, Economics and Management 2, no. 1 (July 15, 2021): 8–15. http://dx.doi.org/10.54097/fbem.v2i1.28.

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There is a certain relationship among stock return rate, market return rate and risk-free interest rate, which is worth discussing, and it is helpful for us to analyze stocks and evaluate their prices. I have found that the market return rate and risk-free rate have correlation through multiple regression, and other stock's return rate can affect the target stock to some extent. The stock return rate is positively related to the market interest rate and inversely related to the risk-free interest rate.

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7

Martinka, Jozef, Peter Rantuch, Igor Wachter, and Karol Balog. "Fire Risk of Halogen-Free Electrical Cable." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 26, no. 42 (June 1, 2018): 21–27. http://dx.doi.org/10.2478/rput-2018-0002.

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Abstract This paper deals with the fire risk of a selected halogen-free electrical cable. The research was objected to a three-core power electric cable for a fixed installation CHKE J3x1.5 (cross section of each copper core was 1.5 mm2) with a declared class of reaction to fire B2ca, s1, d1, a1. The electrical cable was manufactured and supplied by VUKI, a. s., Slovakia. The fire risk of the electric cable was evaluated based on the heat release rate, total heat release, smoke release rate, total smoke release and effective heat of combustion. These parameters were measured using a cone calorimeter at 50 kW m−2 (specimens and cone emitter were placed horizontally during the test). The measured electrical cable showed a maximum heat release rate of nearly 150 kW m−2, a maximum average heat emission rate of almost 100 kW m−2, a total heat release of almost 130 MJ m−2, a maximum smoke release rate of almost 2.5 s−1, a total smoke release of more than 800 m2 m−2, an effective heat of combustion (cable as a whole) of nearly 9 MJ kg−1 and an effective heat of emission (polymeric parts of the cable) of 26.5 MJ kg−1.

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8

Boskovska, Diana. "Some problems in determining the free risk rate of return." IOSR Journal of Business and Management 14, no. 2 (2013): 70–73. http://dx.doi.org/10.9790/487x-1427073.

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9

Simozar, Saied. "Adjustment to Risk Free Rate/ Violation of Put-Call Parity." Applied Economics and Finance 6, no. 6 (October 17, 2019): 80. http://dx.doi.org/10.11114/aef.v6i6.4521.

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The present value of a forward contract for any asset that does not pay a dividend is calculated by discounting its forward price by the risk-free rate. We show that the discount function for assets that have a non-zero correlation with interest rates, has to be adjusted to account for the correlation between the asset and interest rates. Put-Call parity is also violated and needs to be adjusted as well for such assets. It is shown that the risk-free rate is asset dependent. The adjustment to the price is small for short dated forwards, but increases quadratically with time to maturity.

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10

Hutchison, Norman, Patricia Fraser, Alastair Adair, and Rahul Srivatsa. "The risk free rate of return in UK property pricing." Journal of European Real Estate Research 4, no. 3 (October 25, 2011): 165–84. http://dx.doi.org/10.1108/17539261111183407.

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11

Huggett, Mark. "The risk-free rate in heterogeneous-agent incomplete-insurance economies." Journal of Economic Dynamics and Control 17, no. 5-6 (September 1993): 953–69. http://dx.doi.org/10.1016/0165-1889(93)90024-m.

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12

Weil, Philippe. "The equity premium puzzle and the risk-free rate puzzle." Journal of Monetary Economics 24, no. 3 (November 1989): 401–21. http://dx.doi.org/10.1016/0304-3932(89)90028-7.

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13

Marini, François. "Financial intermediation in the theory of the risk-free rate." Journal of Banking & Finance 35, no. 7 (July 2011): 1663–68. http://dx.doi.org/10.1016/j.jbankfin.2010.11.009.

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14

Mello, Marcelo, and Roberto Guimarães-Filho. "Finite horizons, human wealth, and the risk-free rate puzzle." Economics Letters 85, no. 2 (November 2004): 265–70. http://dx.doi.org/10.1016/j.econlet.2004.04.014.

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15

Ilomäki, Jukka, and Hannu Laurila. "Real Risk-Free Rate, the Central Bank, and Stock Market Bubbles." Journal of Reviews on Global Economics 6 (August 23, 2017): 420–25. http://dx.doi.org/10.6000/1929-7092.2017.06.43.

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16

Borri, Nicola, and Giuseppe Ragusa. "Sensitivity, Moment Conditions, and the Risk-Free Rate in Yogo (2006)." Critical Finance Review 6, no. 2 (September 5, 2017): 381–93. http://dx.doi.org/10.1561/104.00000050.

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17

Grant, Simon, and John Quiggin. "The interaction between the equity premium and the risk-free rate." Economics Letters 69, no. 1 (October 2000): 71–79. http://dx.doi.org/10.1016/s0165-1765(00)00280-9.

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18

Cui, Xiaoyong, and Liutang Gong. "THE RISK-FREE RATE IN A FINITE HORIZON MODEL WITH BEQUESTS." Bulletin of Economic Research 67, no. 2 (July 3, 2012): 105–14. http://dx.doi.org/10.1111/j.1467-8586.2012.00456.x.

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19

Ito, Mikio, and Akihiko Noda. "The GEL estimates resolve the risk-free rate puzzle in Japan." Applied Financial Economics 22, no. 5 (October 20, 2011): 365–74. http://dx.doi.org/10.1080/09603107.2011.613761.

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20

Wagenvoort, Rien J. L. M., and Sanne Zwart. "UNCOVERING THE COMMON RISK-FREE RATE IN THE EUROPEAN MONETARY UNION." Journal of Applied Econometrics 29, no. 3 (July 31, 2013): 394–414. http://dx.doi.org/10.1002/jae.2335.

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21

Zhang, Tongbin. "Stock prices and the risk-free rate: An internal rationality approach." Journal of Economic Dynamics and Control 127 (June 2021): 104103. http://dx.doi.org/10.1016/j.jedc.2021.104103.

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22

Kim, Jin Yeop, Ji Hun Lim, Il Gyo Jeong, Moon Kyu Ham, and Sun-Joong Yoon. "Listing of RFR (Risk-Free Rate) Futures in Korean Financial Markets." Asian Review of Financial Research 34, no. 2 (May 30, 2021): 167–203. http://dx.doi.org/10.37197/arfr.2021.34.2.6.

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23

Diana Boskovska, Diana Boskovska. "The free risk rate of return and factors that affect its assessment." IOSR Journal of Business and Management 9, no. 4 (2013): 88–92. http://dx.doi.org/10.9790/487x-0948892.

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24

Ludwig, Alexander, and Alexander Zimper. "Biased Bayesian learning with an application to the risk-free rate puzzle." Journal of Economic Dynamics and Control 39 (February 2014): 79–97. http://dx.doi.org/10.1016/j.jedc.2013.11.007.

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25

Menkveld, Albert J., Asani Sarkar, and Michel van der Wel. "Customer Order Flow, Intermediaries, and Discovery of the Equilibrium Risk-Free Rate." Journal of Financial and Quantitative Analysis 47, no. 4 (April 20, 2012): 821–49. http://dx.doi.org/10.1017/s0022109012000245.

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AbstractMacro announcements change the equilibrium risk-free rate. We find that Treasury prices reflect part of the impact instantaneously, but intermediaries rely on their customer order flow after the announcement to discover the full impact. This customer flow informativeness is strongest when analyst macro forecasts are most dispersed. The result holds for 30-year Treasury futures trading in both electronic and open-outcry markets. We further show that intermediaries benefit from privately recognizing informed customer flow, as their own-account trading profitability correlates with customer order access.

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26

Bianconi, Marcelo, Scott MacLachlan, and Marco Sammon. "Implied volatility and the risk-free rate of return in options markets." North American Journal of Economics and Finance 31 (January 2015): 1–26. http://dx.doi.org/10.1016/j.najef.2014.10.003.

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27

Hin, Lin Yee, and Nikolai Dokuchaev. "On the implied volatility layers under the future risk-free rate uncertainty." International Journal of Financial Markets and Derivatives 3, no. 4 (2014): 392. http://dx.doi.org/10.1504/ijfmd.2014.062395.

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28

Frankfurter, George M., and Wai K. Leung. "FURTHER ANALYSIS OF THE PUT-CALL PARITY IMPLIED RISK-FREE INTEREST RATE." Journal of Financial Research 14, no. 3 (September 1991): 217–32. http://dx.doi.org/10.1111/j.1475-6803.1991.tb00659.x.

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29

Nozari, Milad. "Information content of the risk-free rate for the pricing kernel bound." Journal of Asset Management 22, no. 4 (February 23, 2021): 267–76. http://dx.doi.org/10.1057/s41260-021-00209-1.

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30

Klemperer, W. David, James F. Cathcart, Thomas Häring, and Ralph J. Alig. "Risk and the discount rate in forestry." Canadian Journal of Forest Research 24, no. 2 (February 1, 1994): 390–97. http://dx.doi.org/10.1139/x94-052.

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One of the most common ways to account for investment risk is to add a risk premium to the risk-free discount rate when computing present values of expected revenues which are uncertain. Using certainty-equivalent analysis, we show that the correct risk premium for short-term investments can easily be in the commonly used 7-percentage-point range. But for such risk premiums to be appropriate for long-term forestry investments, the necessary certainty-equivalent conditions often seem to be unreasonably restrictive. Results suggest that the appropriate risk premium may decline with lengthening payoff period for many forest investments. Limited empirical data provide tentative support, but more research is needed to resolve the issue. We review policy implications and suggest areas for further research.

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31

Luo, Yulei, Jun Nie, and Eric R. Young. "Ambiguity, Low Risk-Free Rates and Consumption Inequality." Economic Journal 130, no. 632 (April 17, 2020): 2649–79. http://dx.doi.org/10.1093/ej/ueaa045.

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Abstract Macroeconomists failed to predict the Great Recession, suggesting that the existing macroeconomic models may have been misspecified. Bearing in mind this potential misspecification or ‘model uncertainty’, how do agents’ optimal decisions change? Furthermore, how large are the welfare costs of model misspecification? To shed light on these questions, we develop a tractable continuous-time general equilibrium model to show that a fear of model misspecification reduces both the equilibrium interest rate and the relative inequality of consumption to income, making the model’s predictions closer to the data. Our quantitative analysis shows that the welfare costs of model uncertainty are sizable.

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32

Mukherji, Sandip. "IMPACT OF THE RISK-FREE RATE ON REQUIRED RETURNS AND ALPHAS OF STOCKS." Journal of International Finance and Economics 17, no. 3 (December 1, 2017): 41–48. http://dx.doi.org/10.18374/jife-17-3.4.

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33

Lally, Martin. "Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt." Accounting Research Journal 20, no. 2 (December 2007): 73–80. http://dx.doi.org/10.1108/10309610780000691.

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34

Palandri, Alessandro. "Risk-free rate effects on conditional variances and conditional correlations of stock returns." Journal of Empirical Finance 25 (January 2014): 95–111. http://dx.doi.org/10.1016/j.jempfin.2013.12.002.

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35

Van Heerden, Chris. "The Eminence Of Risk-Free Rates In Portfolio Management: A South African Perspective." Journal of Applied Business Research (JABR) 32, no. 2 (March 1, 2016): 569. http://dx.doi.org/10.19030/jabr.v32i2.9597.

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The traditional Capital Asset Pricing Model (CAPM) suggests that the minimum return required by an investor should be equal to the return of a risk-free asset (Reilly & Brown, 2003), which should be stable (Reilly & Brown, 2006), not influenced by external factors (Harrington, 1987), and certain (Bodie, Kane & Marcus, 2010). Evidence, however, suggests that risk-free asset returns vary (Brunnermeier, 2008), and that “there is really no such thing as a truly riskless asset” (Brigham & Ehrhardt, 2005:312). The pioneering studies of Mehra and Prescott (1985) and Weil (1989) only justified the size of the equity premium and risk-free rate puzzle but failed to provide a consensus on the specifications for the most ideal risk-free rate proxies. The results from this paper accentuated the problem of selecting a risk-free rate proxy, as all proxies under evaluation exhibited a level of risk and volatile returns. No regularities between the pre-, during and post-financial crisis regarding the choice of most ideal risk-free rate proxy were found. Overall findings suggested that the ideal proxies are the 3-month T-Bill rate and the 3-month NCD rate for the pre-, during and post-financial crisis periods, respectively.

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36

ILOMÄKI, JUKKA. "RISK-FREE RATES AND ANIMAL SPIRITS IN FINANCIAL MARKETS." Annals of Financial Economics 11, no. 03 (September 2016): 1650011. http://dx.doi.org/10.1142/s2010495216500111.

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We show analytically that animal spirit excess profits for uninformed investors fall (increase) when the risk-free rate rises (falls). In the theoretical analysis, we examine the expected returns of risk-averse, short-lived investors. In addition, we find empirically that the local risk-free rates explain 14% of the changes in the animal spirit excess profits in the global stock markets for the last 29 years when the animal spirits is characterized as a product of the trend-chasing rule.

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37

Wada, Kenji. "The Knightian uncertainty and the risk premium and the risk free rate puzzles in Japan and the U.S." Economics Letters 95, no. 3 (June 2007): 386–93. http://dx.doi.org/10.1016/j.econlet.2006.11.012.

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38

Trifonov, Nikolai Yu. "Development of the Risk Accumulation Method for Calculating the Capitalization Rate." Economics of Contemporary Russia, no. 1 (March 29, 2021): 7–14. http://dx.doi.org/10.33293/1609-1442-2021-1(92)-7-14.

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Risk build-up method is the most used for calculating the capitalization rates. With the help of the literature analysis, the origin of this method is considered. The method was based on the relationship between risk and profitability of a stock in exchange trading, proven statistically. Later, when formulating the build-up method, this idea was transferred without any justification to the valuation of enterprises that do not list their securities on stock exchange. In other words, the formulas traditionally used in the application of the build-up method are empirical in nature and not precise.It is more accurate to write them down by analogy with Irwin Fisher's equation of returns. Based on the principle of dependence, one of the main ones for the valuation procedure, the essence of which is that the value of the valuation subject depends on its economic location, a set of four independent risks is given for use in the build-up method in general case: risk-free rate, country risk premium, branch risk premium, and subject risk adjustment. It is noted that the numerical value of these parameters used in the method fundamentally depends on the monetary unit used in the calculation (the valuation currency). Recommendations are given on finding a risk-free rate for various currencies, on calculating country risk premium, branch risk premium, and subject risk adjustment. The article is intended for academics, lecturers, and practitioners in such areas as corporate finance, business microeconomics, valuation, and investment analysis.

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39

DeJong, Douglas V., and Daniel W. Collins. "Explanations for the Instability of Equity Beta: Risk-Free Rate Changes and Leverage Effects." Journal of Financial and Quantitative Analysis 20, no. 1 (March 1985): 73. http://dx.doi.org/10.2307/2330678.

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40

Bansal, Ravi, and Wilbur John Coleman. "A Monetary Explanation of the Equity Premium, Term Premium, and Risk-Free Rate Puzzles." Journal of Political Economy 104, no. 6 (December 1996): 1135–71. http://dx.doi.org/10.1086/262056.

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41

Hall, Jason. "Comment onRegulation and the Term of the Risk Free Rate: Implications of Corporate Debt." Accounting Research Journal 20, no. 2 (December 2007): 81–86. http://dx.doi.org/10.1108/10309610780000692.

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42

Lally, Martin. "Rejoinder: Regulation and the Term of the Risk Free Rate: Implications of Corporate Debt." Accounting Research Journal 20, no. 2 (December 2007): 87–88. http://dx.doi.org/10.1108/10309610780000693.

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43

Lustig, Hanno, and Adrien Verdelhan. "Does Incomplete Spanning in International Financial Markets Help to Explain Exchange Rates?" American Economic Review 109, no. 6 (June 1, 2019): 2208–44. http://dx.doi.org/10.1257/aer.20160409.

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We assume that domestic (foreign) agents, when investing abroad, can only trade in the foreign (domestic) risk-free rates. In a preference-free environment, we derive the exchange rate volatility and risk premia in any such incomplete spanning model, as well as a measure of exchange rate cyclicality. We find that incomplete spanning lowers the volatility of exchange rate, increases the risk premia but only by creating exchange rate predictability, and does not affect the exchange rate cyclicality. (JEL E32, F31, F44, G15)

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44

Brooks, Chris, and Frank Skinner. "What will be the risk-free rate and benchmark yield curve following European monetary union?" Applied Financial Economics 10, no. 1 (February 2000): 59–69. http://dx.doi.org/10.1080/096031000331932.

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45

Kamal, Javed Bin. "Optimal Portfolio Selection in Ex Ante Stock Price Bubble and Furthermore Bubble Burst Scenario from Dhaka Stock Exchange with Relevance to Sharpe’s Single Index Model." Financial Assets and Investing 3, no. 3 (September 30, 2012): 29–42. http://dx.doi.org/10.5817/fai2012-3-3.

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The paper aims at constructing an optimal portfolio by applying Sharpe’s single index model of capital asset pricing in different scenarios, one is ex ante stock price bubble scenario and stock price bubble and bubble burst is second scenario. Here we considered beginning of year 2010 as rise of stock price bubble in Dhaka Stock Exchange. Hence period from 2005 -2009 is considered as ex ante stock price bubble period. Using DSI (All share price index in Dhaka Stock Exchange) as market index and considering daily indices for the March 2005 to December 2009 period, the proposed method formulates a unique cut off point (cut off rate of return) and selects stocks having excess of their expected return over risk-free rate of return surpassing this cut-off point. Here, risk free rate considered to be 8.5% per annum (Treasury bill rate in 2009). Percentage of an investment in each of the selected stocks is then decided on the basis of respective weights assigned to each stock depending on respective ‘β’ value, stock movement variance representing unsystematic risk, return on stock and risk free return vis-à-vis the cut off rate of return. Interestingly, most of the stocks selected turned out to be bank stocks. Again we went for single index model applied to same stocks those made to the optimum portfolio in ex ante stock price bubble scenario considering data for the period of January 2010 to June 2012. We found that all stocks failed to make the pass Single Index Model criteria i.e. excess return over beta must be higher than the risk free rate. Here for the period of 2010 to 2012, the risk free rate considered to be 11.5 % per annum (Treasury bill rate during 2012).

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46

Gubareva, Mariya, and Maria Rosa Borges. "Interest rate, liquidity, and sovereign risk: derivative-based VaR." Journal of Risk Finance 18, no. 4 (August 21, 2017): 443–65. http://dx.doi.org/10.1108/jrf-01-2017-0018.

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Purpose The purpose of this paper is to study connections between interest rate risk and credit risk and investigate the inter-risk diversification benefit due to the joint consideration of these risks in the banking book containing sovereign debt. Design/methodology/approach The paper develops the historical derivative-based value at risk (VaR) for assessing the downside risk of a sovereign debt portfolio through the integrated treatment of interest rate and credit risks. The credit default swaps spreads and the fixed-leg rates of interest rate swap are used as proxies for credit risk and interest rate risk, respectively. Findings The proposed methodology is applied to the decade-long history of emerging markets sovereign debt. The empirical analysis demonstrates that the diversified VaR benefits from imperfect correlation between the risk factors. Sovereign risks of non-core emu states and oil producing countries are discussed through the prism of VaR metrics. Practical implications The proposed approach offers a clue for improving risk management in regards to banking books containing government bonds. It could be applied to access the riskiness of investment portfolios containing the wider spectrum of assets beyond the sovereign debt. The approach represents a useful tool for investigating interest rate and credit risk interrelation. Originality/value The proposed enhancement of the traditional historical VaR is twofold: usage of derivative instruments’ quotes and simultaneous consideration of the interest rate and credit risk factors to construct the hypothetical liquidity-free bond yield, which allows to distil liquidity premium.

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47

MAI, JAN-FREDERIK. "PRICING-HEDGING DUALITY FOR CREDIT DEFAULT SWAPS AND THE NEGATIVE BASIS ARBITRAGE." International Journal of Theoretical and Applied Finance 22, no. 06 (September 2019): 1950032. http://dx.doi.org/10.1142/s0219024919500328.

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Assuming the absence of arbitrage in a single-name credit risk model, it is shown how to replicate the risk-free bank account until a credit event by a static portfolio of a bond and infinitely many credit default swap (CDS) contracts. This static portfolio can be viewed as the solution of a credit risk hedging problem whose dual problem is to price the bond consistently with observed CDSs. This duality is maintained when the risk-free rate is shifted parallel. In practice, there is a unique parallel shift [Formula: see text] that is consistent with observed market prices for bond and CDSs. The resulting, risk-free trading strategy in case of positive [Formula: see text] earns more than the risk-free rate, is referred to as negative basis arbitrage in the market, and [Formula: see text] defined in this way is a scientifically well-justified definition for what the market calls negative basis. In economic terms, [Formula: see text] is a premium for taking the residual risks of a bond investment after interest rate risk and credit risk are hedged away. Chiefly, these are liquidity and legal risks.

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48

Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 01 (May 2006): 79–120. http://dx.doi.org/10.2143/ast.36.1.2014145.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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49

Cairns, Andrew J. G., David Blake, and Kevin Dowd. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk." ASTIN Bulletin 36, no. 1 (May 2006): 79–120. http://dx.doi.org/10.1017/s0515036100014410.

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It is now widely accepted that stochastic mortality – the risk that aggregate mortality might differ from that anticipated – is an important risk factor in both life insurance and pensions. As such it affects how fair values, premium rates, and risk reserves are calculated.This paper makes use of the similarities between the force of mortality and interest rates to examine how we might model mortality risks and price mortality-related instruments using adaptations of the arbitrage-free pricing frameworks that have been developed for interest-rate derivatives. In so doing, the paper pulls together a range of arbitrage-free (or risk-neutral) frameworks for pricing and hedging mortality risk that allow for both interest and mortality factors to be stochastic. The different frameworks that we describe – short-rate models, forward-mortality models, positive-mortality models and mortality market models – are all based on positive-interest-rate modelling frameworks since the force of mortality can be treated in a similar way to the short-term risk-free rate of interest. While much of this paper is a review of the possible frameworks, the key new development is the introduction of mortality market models equivalent to the LIBOR and swap market models in the interest-rate literature.These frameworks can be applied to a great variety of mortality-related instruments, from vanilla longevity bonds to exotic mortality derivatives.

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Qudratullah, Mohammad Farhan. "Zakah Rate In Islamic Stock Performance Models: Evidence From Indonesia." IQTISHADIA 13, no. 1 (June 15, 2020): 107. http://dx.doi.org/10.21043/iqtishadia.v13i1.6004.

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Abstract:

<p>There are three models commonly used to measure the performance of Islamicstocks, named Treynor Ratio, Sharpe Ratio, and Jansen Index. One component of the three models is risk-free returns which are usually approached with interest rates, whereas interest rates are prohibited in the concept of Islamic finance. This paper will approach a risk-free return with zakat-rate on the Islamic capital market in Indonesia from January 2011 - July 2018, then compare it with a model that uses interest rates. The results obtained by the model with interest rates and zakah-rate in this third model have very high suitability values, so that zakah-rate can be used as an alternative substitute for interest rates in measuring the Islamic stock performance. Beside not contradicting the concept of Islamic economics, calculation of models with zakah-rate is simpler than models with interest rates.</p>

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