1. (30) Price a 2y 3.8% semi-annual pay bond, callable at 102, assuming rate volatility is 15% and yields are as below. Once you have priced this bond, calculate its annualized yield to call. T y(0,t) 0.5 1.2% 1.0 3.2% 1.5 4.5% 2.0 5.3% 2. (15) Calculate and interpret daily 99 and 95 historical Value at Risk for the data set provided. 3. (20) Using a binomial tree, approximate the price of an up-and-out knock-out barrier option given the following terms. This option is exotic, and therefore path dependent. A Knock-out barrier option only pays out if the underlying asset's price does not 'reach or breach' the pre- defined barrier. Once it is out, it's out for good. S $100 K $100 50% r 10.0% T 2y 0.5y Barrier $200 4. (10) Price a European call using the Black Scholes model then price a put using put-call parity. S $100 K $80 14% r 2.5% T 0.5y 5. (25) In one page, explain what risk is.