# Carr and Madan algorithm to avoid arbitrage in oprion prices

Hey in this text (https://arxiv.org/abs/1107.1834) in section 7 is described an algorithm which can delete options which generate an arbitrage. $$C_ij$$ is call option price with strike $$K_i$$ and maturity $$T_j$$ Unfortunately, it may happen that there are options with strike price $$K_i$$ and maturity $$T_j$$, but for $$T_{j+1}$$ there is no option with strike $$K_i$$. Or $$C_{i-1,j}$$ exists but there is no $$C_{i,j}$$ What to do in this case? Can I use this algorithm in some way? And what if I want to remove arbitrage from the put option? How to change the algorithm?