Derivatives can be valued using risk neutral valuation. The spreadsheet Risk Neutral Valuation.xlsx simulates 10,000 values of stock price (assuming log normal distribution) at expiration of derivative. Each stock price results in a derivative payoff. These derivative payoffs are discounted and averaged to get derivative value. The formula in column C is set to price a European call with strike price of $50 but can be changed to price any other derivatives. Value the following derivative:

Current stock price = 20 + number of the first letter of your last name + number of the second letter of your last name. Assume A = 1, B = 2, and so on until Z = 26.

The derivative will expire after six months. Its payoff will equal the absolute difference between the price at that time and todays price, up to a maximum of $5. For example, if price today is $50 and the price at expiration is $47.2, you will get $2.8. If the price at expiration is $53.6, you will get $3.6. If the price at expiration is $30 or $90, you will get $5.

Risk-free rate is 5% per annum compounded continuously and stock volatility is 20% per annum.

How would you go about valuing the derivative theoretically - as in what are the steps? I know the excel sheet is not provided.