Option Pricing Model for Incomplete Market

TL;DR

This paper introduces an analytic stochastic optimization method using Bellman equations to determine option prices and optimal trading strategies in incomplete markets, aiming for practical applicability.

Contribution

It develops a new algorithm based on dynamic programming for pricing options and managing risk in incomplete markets, which is practical and effective.

Findings

Provides a formalism for option pricing in incomplete markets

Develops an algorithm for optimal trading strategies

Addresses risk reduction in option writing

Abstract

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces total risk inherent in writing the option. The basic purpose of paper is to present an effective algorithm that can be used in practice. Keywords: option pricing, incomplete market, transaction costs, stochastic optimization, Bellman equation.