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Statistics and Financial Mathematics Question : Financial Mathematics The price of a forward contract on a share is given by F = Set where S, is the current share price, r is the risk-free rate of interest, and is the length of the contract A one-year forward contract on a non-dividend paying share is entered into when the share price is £40 and r = 10%. 0 What is the forward price and the initial value of the forward contract? 12) (ii) Six months later, the price of the share is £45 and the risk free rate is still r = 10% What are the forward price and the value of the forward contract? 12] (b) An asset currently has a price of £10. Suppose that six months future prices of : £11 £10.10 are available. If the risk free rate is r = 6%, show that a risk-free profit can be made in both cases [6] (c) Three friends Tom, Jerry, and Kate are members of an investment club. They each have a total of £10,000 to invest in three companies A, B, and C. On 1" Nov 2016, the following prices were available (E) 00 Share Call Put Strike price, K А 55 0.91 2.48 58 B 110 2.17 4.33 115 с 13 0.89 0.09 12.5 They made the following investments (not considering any dividends and commissions) . Tom bought 80 A shares, 2008 calls and saved the rest of the money in the bank Jerry bought 50 B shares, 400C puts and saved the rest of the money in the bank Kate bought 50 A shares, 100 B calls and spent the rest on Cshares The options expired after six months and the bank interest rate was 5% compounded continuously (assume that fractional numbers of shares may be purchased). If, at the end of six months, A shares were worth £59, B shares €108 and C shares £12, find the value of each of the three friends portfolios and hence the returns they made on their original investment of £10,000 [101

Statistics and Financial Mathematics Question : Financial Mathematics (a) The price of a forward contract on a share is given by F = Se where S, is the current share price, r is the risk-free rate of interest, and T is the length of the contract A one-year forward contract on a non-dividend paying share is entered into when the share price is £40 and r = 10%. What is the forward price and the initial value of the forward contract? [2] Six months later, the price of the share is £45 and the risk free rate is still r = 10%. What are the forward price and the value of the forward contract? [2] (b) An asset currently has a price of E10. Suppose that six-months future prices of : £11 (H) E10.10 are available. If the risk free rate isr = 6%, show that a risk-free profit can be made in both cases. [6] (c) Three friends Tom, Jerry, and Kate are members of an investment club. They each have a total of £10,000 to invest in three companies A, B, and C. On 1" Nov 2016, the following prices were available (E) Share Call Put Strike price, A 55 0.91 2.48 58 B 110 2.17 4.33 115 с 13 0.89 0.09 12.5 They made the following investments (not considering any dividends and commissions) Tom bought 80 A shares, 200 B calls and saved the rest of the money in the bank Jerry bought 50 B shares, 400C puts and saved the rest of the money in the bank Kate bought 50 A shares, 100 B calls and spent the rest on shares. . . The options expired after six months and the bank interest rate was 5% compounded continuously (assume that fractional numbers of shares may be purchased). If, at the end of six months, A shares were worth £59, B shares £108 and C shares £12, find the value of each of the three friends portfolios and, hence the returns they made on their original investment of £10,000 [10]