This paper studies the problem of option pricing in an incomplete market, where the exact replication of an option may not be possible. In an incomplete market, we suppose a situation where a hedger wants to invest as little as possible at the beginning, but he/she wants to have the expected squared loss at the end not exceeding a certain constant. We study this problem when the log of the underlying asset price process is compound Poisson, which converges to a Brownian motion with drift. In the limit, we use the mean-variance approach to find a hedging strategy which minimizes the expected squared loss for a given initial investment. Then we find the asymptotic minimum investment with the expected squared loss bounded by a given upper bound. Some numerical results are also provided.
Bibliographical noteFunding Information:
This research was supported by a Korea University Grant.
- Bounded loss
- Compound Poisson processes
- Option pricing
- Weak convergence