I am reading this book by Mark S. Joshi. Can you help me make sense of one of the exercise questions? Here is the question (from page 40 of the book):
Exercise 2.5 Suppose no-arbitrage bounds for an option price show that the price lies between $L_1$ and $L_2$ in a world without transaction costs. What can we say about the bounds if we take transaction costs into account?
Here are the solutions (from page 474):
Exercise 2.5 Increasing transaction costs can only decrease the number of arbitrage portfoliois, so the bounds will be at least as wide.
I don't understand why the bounds will be at least as wide. I understand that transaction costs make it harder to find an arbitrage. Shouldn't decreasing the number of arbitrage portfolios act to decrease the no-arbitrage price range?