The questions are attached below.

4 One form of the Black-Scholes partial differential equation is: (i) State the context in which this formula applies, indicating what s and f represent. (You are not required to state the Black-Scholes assumptions.) (ii) What do / and o represent? What assumptions are made about these quantities in this equation? (iti) State the names and give the mathematical definitions of the 'Greeks' that appear in this equation. (iv) What boundary condition would you need to use in order to solve this equation when applied to a European call option with a strike price K ? 5 An investor buys, for a premium of 187.06, a call option on a non-dividend-paying stock whose current price is 5,000. The strike price of the call is 5,250 and the time to expiry is 6 months. The risk-free rate of return is 5% pa continuously compounded. The Black-Scholes formula for the price of a call option on a non-dividend-paying share is assumed to hold. (i) Calculate the price of a put option with the same time to maturity and strike price as the call. [2] The investor buys a put option with strike price 4,750 with the same time to maturity. Calculate the price of the put option if the implied volatility were the same as that in (i). [You need to estimate the implied volatility to within 1% pa of the correct value.] [7] [Total 9] 6 The solution to the Black-Scholes equation for the price V (assuming a risk-free force of yle interest r ) of a European put option maturing u years from now with strike price K on a stock that pays dividends at force q whose current spot price is $ is: V = Ke-""D(-d2)-Se-qu@(-dj) where dj,d2 = - _log(5/X) +(r-qthe ju JVu (i) Show that the hedge ratio A = av as is given by A = -e-9"