AS463_Lec07 - ACTSC 463/863 Property and Casualty Loss...

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1 ACTSC 463/863 Property and Casualty Loss Reserving
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2 Discounting Loss Reserves
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3 Discounting > Process of recognizing the time value of money • Required in Canadian reporting • Outstanding reserves can be invested • $1 of future payments requires <$1 of reserve today – basic theory > However, actuaries like to make things more complicated • Is the discounted reserve sufficient?
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4 Discounting > A number of questions • How to determine the interest rate to use? • How to determine the timing of future payments? • Other considerations? – Provisions for adverse deviation (PFADs) - Claims development - Interest rate - reinsurance
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5 Discounting - Rate > Interest Rate • Currently the market rate of return on the assets supporting the liabilities – Market rates can be volatile which creates income volatility (can be significant) – This could change under IFRS – risk free rate? – Asset-liability matching – simple to determine – If no hedging strategy need to determine how to segregate your asset portfolio and select a rate - Reinvestment rates are a consideration – Options for segregating assets lead to hedging options
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6 Discounting - Rate > Interest Rate Methodologies Internal rate of return model – If assets and liabilities are perfectly matched – discount rate should be the same as the balance sheet yield – If not matched – reinvestment risk – Discount rate produced varies from balance sheet yield to extent of mismatch – ? = ° +? ° ) (1+²) ° ³ ?´1 – ?³ = ³µ¶·¶¸¹?³º???»³¼¶·??³½?³¶ºº?»º³»?¶»³¾¿½¼?À?³¹¶º?³?¸ − ?·½Á –  ? = ??¹?ºº³¹¶º?³?¸ − ?·½Á³Á?»?À¿¶Á¸³¶»³»??³?¸À³½?³Ã½¸»?³» – Ä ? = ??¾?¹»?À³·½ºº³¾¶ÅÃ?¸»³?¸³Ã½¸»?³» – À = À?º¹½?¸»³¿¶»?
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7 Discounting - Rate > Interest Rate Methodologies • Duration Weighted Yield – ? = ? ° ×± ° ײ ° ? ° ×± ° – ? = ?³?´??µ¶·????????·¸´¹´¶º?·»????·¼??¹? – ½ ¾ = ¸´¹´¶º?·»????·¿´¹³?·µÀ·¸µ¶?·¶ – Á ¾ = ?³?´??µ¶·µÀ·¸µ¶?·¶ –  ¾ = ¸´¹´¶º?·»????·¼??¹?·?µ·Ã´?³???¼·µÀ·¸µ¶?·¶ Balance Sheet Value Weighted – ? = ? ° ײ ° ? ° – ? = ¸´¹´¶º?·»????·¿´¹³?·????????·¸´¹´¶º?·»????·¼??¹? – ½ ¾ = ¸´¹´¶º?·»????·¿´¹³?·µÀ·¸µ¶?·¶ –  ¾ = ¸´¹´¶º?·»????·¼??¹?·?µ·Ã´?³???¼·µÀ·¸µ¶?·¶
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8 Discounting – Cash Flows > Timing of future payments • Common methods for determining a payment pattern – Paid to paid method - Calculate triangle of paid to ultimate paid for each accident year and development point - Make selections and apply to outstanding – Implied LDF - Use the loss development factors to derive percentage paid - % °??? = 1 ±²?²³´?µ?¶ ·¸¹
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9 Discounting – Cash Flows Accident Year Paid Losses LDF to Ultimate Ultimate
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AS463_Lec07 - ACTSC 463/863 Property and Casualty Loss...

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