EXplain the following;

Involuntary unemployment

Cyclical unemployment

Technological unemployment.

Voluntary unemployment.

5 A bond market consists of the following four government bonds, with prices (per 100 nominal) and redemption yields (in % per annum) as per the table below: Term Annual Price Redemption Discount coupon % yield % p.a. factor 1 year 3.00 101.03 1.95 0.98087 2 year 4.00 102.05 2.93 3 year 4.75 103.21 3.60 4 year 5.50 105.36 4.02 0.85153 In each case, coupons are paid annually and the next one is due to be paid in a year's time. Redemption yields are annually compounded. Discount factors are shown for years 1 and 4. The discount factor for year n is the decimal price of a zero coupon bond of duration . (i) Complete the table above by calculating the discount factors applicable to the yield curve for years 2 and 3. [2] Consider a 2-year European Put option on the 4-year government bond shown above. The strike price of the option is 100 (per 100 nominal) and the applicable forward yield volatility is 25% per annum. The option is exerciseable immediately after the bond pays its second annual coupon. (ii) (a) Show that the 2-year forward price of the 4-year government bond is 100.45. (b) Calculate, using a forward modified duration of 1.85 and a forward yield of 3.25%, the volatility of the price in (a). (c) Estimate, using the Black model, the price of the option. [7]4 The "speed" of a derivative is defined as its third order sensitivity to movements in the price of the underlying, i.e. of _a'7 as agg : Where S is price of the underlying asset, I is the gamma of the option and I is the option price. Let OVI where I'is the strike and / is the risk-free rate (continuously compounded) (1) (a ) Derive a formula for the gamma of a European Call option of maturity I years based on a non income bearing security S with volatility o. [Note: You may use the result that the delta of the option is Maj).] (b) Hence show that the "speed" of the option is given by: [4] (ii) Sketch graphs for this European Call option at time I from expiry, showing how the following vary with the price of the underlying asset: (a) price delta (c) gamma (d) "speed" [6] A dealer, who is in charge of hedging a portfolio of options on the US$-Euro exchange rate, has just discovered the formula for "speed" and thinks it would be a good indicator to monitor, on the basis that reducing the absolute level of portfolio "speed" would result in a more stable gamma hedge. (iii) Discuss this proposal. [4]