A trader creates a long butterfly spread from options with strike prices of $90, $100, and $110 per share by trading a total of 20 option contracts (buy 5 contracts at $90, sell 10 contracts at $100 and buy 5 contracts at $110). Each contract is written on 100 shares of stock. The options are worth $15, $18, and $22 per share of stock, respectively.
a) What is the value of the butterfly spread at maturity as a function of the then stock price?
b) What is the profit of the butterfly spread at maturity as a function of the then stock price? Make sure to derive the exact range of then stock prices where the trade is profitable.