Pricing of Call Options with The Down-and-Out Barrier using the Fuzzy Approach Agustina, F (1), Sidarto, K. A (2*) and Sumarti, N (2*)
1. Doctoral Program of Mathematics, Faculty of Mathematics and Natural,
Institut Teknologi Bandung,
Jl. Ganesha, 10, Bandung, 40132, Jawa Barat, Indonesia
2. Industrial and Financial Mathematics Group, Faculty of Mathematics and Natural,
Institut Teknologi Bandung,
Jl. Ganesha, 10, Bandung, 40132, Jawa Barat, Indonesia
*kuntjoroadjisidarto[at]gmail.com
*novriana[at]itb.ac.id
Abstract
An Option is an investor^s tool that is used for speculation or hedging purposes. The concept of fuzziness can be used to describe the options pricing parameters. In this paper, we apply fuzzy set theory to price down-and-out call options by setting the volatility and asset price parameters as the fuzzy number. We calculate the risk-neutral probabilities, which are represented as fuzzy numbers. Under fuzzy probabilities, the risk-neutral probabilities of down-and-out call options are determined for the Ritchken trinomial model and the bino-trinomial model. Using these models, the obtained tree will pass the barrier exactly at one or more nodes. Numerical simulations show that, when the membership degree of the fuzzy set numbers increases, the fuzzy price range gradually decreases in length. With this membership degree, financial investors can narrow option price intervals and make investment decisions.
