Suppose that there are two farms in a Norfolk postcode which have known flood risks (i.e. both the farmers and any insurer know their elevation above sea level and have the same projections about sea level rise). There are also three possible but as yet unknown states of the world: under Scenario 1 there will be no sea level rise into the future, and therefore both farms will be valued at £1 million. Under Scenario 2, sea level rise will be moderate, causing the present valuation of one of the farms to be cut to £500,000, whereas the other farm, located slightly higher, is still valued at £1 million. Finally, under Scenario 3 the sea level rise will be severe and both farms will suffer reduced valuations. Under Scenario 3 the present valuation of both farms would be £250,000. Scenario 1 is seen by all people as having a 25% likelihood, Scenario 2 is perceived as having a 50% likelihood and Scenario 3 as having a 25% likelihood. (a) Calculate the expected present value of each of the two farms. (7 marks) (b) How would a risk-neutral insurer need to price an individual policy for each of the two farms so as to break even in expectation? Suppose that the policy would pay out £0 to both farmers in Scenario 1, pay £500,000 only to the low-lying farmer in Scenario 2, and pay out £750,000 to both farmers in Scenario 3 (i.e. full insurance). The two farmers can be charged different prices! Assume that both farmers are risk-averse and would therefore want to buy the policies at these actuarially fair prices. (8 marks) 2 Page 3 EC301 2021/22 Turn over (c) Scenario 3 presents a challenge to the insurer because it would need to make payouts to both farmers. What if it doesn’t have reinsurance? Let your answers to b be denoted by P1 and P2. Suppose the insurer were constrained in that it could only pay out the sum total of collected premia out to the two farmers. I.e. rather than £750,000 to each farmer, it could only pay out (P1 + P2)/2 to each of them. Would both consumers still want to buy the policies at P1, P2, respectively if they were able to anticipate the insurer’s constraint? What would the farmers’ risk premia need to be?
