Consider a perpetual American put option with exercise price E and infinite expiry time. Suppose that the volatility is sigma and the risk free rate is r. In terms of the parameters E, r and sigma, write down the price V(S) of this option, and write down a formula for the exercise boundary S_f. Compute explicit formulae for the following Greeks: partial differential V/partial differential S, partial differential V/partial differential E, partial differential V/partial differential sigma, partial differential V/partial differential r. Determine whether these functions are always positive, always negative or of indeterminate sign. Give brief financial explanations of your results (a few sentences for each). Compute formulae for: partial differential S_f/partial differential E. partial differential S_f/partial differential r, partial differential S_f/partial differential sigma. Determine whether these functions are always positive, always negative or of indeterminate sign. Give brief financial explanations of your results (a few sentences for each). Consider a perpetual American put option with exercise price E and infinite expiry time. Suppose that the volatility is sigma and the risk free rate is r. In terms of the parameters E, r and sigma, write down the price V(S) of this option, and write down a formula for the exercise boundary S_f. Compute explicit formulae for the following Greeks: partial differential V/partial differential S, partial differential V/partial differential E, partial differential V/partial differential sigma, partial differential V/partial differential r. Determine whether these functions are always positive, always negative or of indeterminate sign. Give brief financial explanations of your results (a few sentences for each). Compute formulae for: partial differential S_f/partial differential E. partial differential S_f/partial differential r, partial differential S_f/partial differential sigma. Determine whether these functions are always positive, always negative or of indeterminate sign. Give brief financial explanations of your results (a few sentences for each)