QUESTION 1

Consider an asset with price S, at time ?, paying a dividend at a constant dividend yield, D. Dividends are paid at the end of each year and are immediately reinvested in the asset. The continuously-compounded risk-free rate of interest is r pa. Derive the forward price, K, of a contract issued at time f, with maturity at time 7 , to purchase one unit of the asset, where 7-f is an integer number of years. State any assumptions you make. [6]Give definitions of the "Greeks" that could be used as an aid to management in each of the following situations. State also the desired ranges for their numerical values and define any notation you use. (a) A hedge fund manager wishes to establish a delta-neutral position that would not need frequent rebalancing for part of his portfolio. (b) A derivatives trader is concerned that a change in the distribution of the daily price movements of particular shares might affect the values of the options he holds on those shares. (c) The trustee of a pension fund that purchased a large number of options last year as a means of hedging is concerned about changes in the value of the fund as the options approach their expiry date. [6]