ScottishEnergy is currently trading at 116. You look at your computer screen and find out that there are European puts and calls for ScottishEnergy available, expiring in 120 days, with exercise prices both at 110. Treasury-Bills trading with risk-free annual rates of returns at 1%. You also understand that ScottishEnergy will not issue any dividends within the next 120 days. You estimate the uncertainty for ScottishEnergy is around 38% per year. Use Black-Scholes-Merton formula to answer the following,

(a) Compute and explain the probabilities of ScottishEnergy calls and puts would be exercised at expiry; compute the fair European calls and puts for ScottishEnergy. Explain the equations you use to compute the put calls and puts.

(b) Continue with (a). Explain how a ScottishEnergy put writer could create a risk-free hedge portfolio to hedge his/her positions in writing such puts. Including the explanations of hedge ratio for puts in your answer.

(c) Continue with (b). Now it is 40 days later, and it is understood that the uncertainty about ScottishEnergy is estimated 27% per year and ScottishEnergy is trading at 120. Show and explain in details of how the put writer should do with such new information.