PLEASE answer each question with clear step!

A commercial bank wants to sell a new derivative security. If ST is the stock price at expiration, this new derivative will pay max{lnSTK,0}, where K is the strike price. Suppose that stock returns follow a geometric Brownian motion with annual mean return =4% and annual volatility =20%. The risk-free rate of return is r=3% per year, the contract expires in one year, and the initial stock price is 10 . You have been hired as an analyst to price this new derivative. Proceed in steps: a. Write down the SDE for the stock price, using BP, the Brownian motion under the objective probability measure. b. Rewrite the SDE for the stock price, using BQ, the Brownian motion under the risk-neutral measure. State which theorem you are using here. c. Use Ito's lemma to find the stochastic differential equation for lnSt under the risk-neutral measure. Integrate the SDE for lnSt to find the risk-neutral distribution of lnST at t=0, where T is the time to expiration. d. Express the price of the derivative (at t=0) as a risk-neutral expectation. A commercial bank wants to sell a new derivative security. If ST is the stock price at expiration, this new derivative will pay max{lnSTK,0}, where K is the strike price. Suppose that stock returns follow a geometric Brownian motion with annual mean return =4% and annual volatility =20%. The risk-free rate of return is r=3% per year, the contract expires in one year, and the initial stock price is 10 . You have been hired as an analyst to price this new derivative. Proceed in steps: a. Write down the SDE for the stock price, using BP, the Brownian motion under the objective probability measure. b. Rewrite the SDE for the stock price, using BQ, the Brownian motion under the risk-neutral measure. State which theorem you are using here. c. Use Ito's lemma to find the stochastic differential equation for lnSt under the risk-neutral measure. Integrate the SDE for lnSt to find the risk-neutral distribution of lnST at t=0, where T is the time to expiration. d. Express the price of the derivative (at t=0) as a risk-neutral expectation