An Optimization Approach for pricing of Discrete European Call options Based on the Preference of Investors

Abstract

Firstly, a method for measuring the risk aversion of investors was proposed based on the prospect theory. Secondly, under a sole hypothetical condition in which the risk aversion degree for different assets is the same in a market, the pricing of discrete European options was given based on the objective probability. Thirdly, it was proven that the European option price obtained was a non-arbitrate price. And then, both for the binomial tree, which is a complete market, and for the trinomial tree, which is an incomplete market, pricing European options were discussed by implementing the method provided in this paper. Lastly, an illustration is used to demonstrate how to estimate preference parameters from market data and how to calculate options prices. The result states that the method in this paper is the same as the traditional risk-neutral methods in a complete market, but it is different from the traditional risk-neutral methods in an incomplete market, and more, the price obtained in this paper is affected by the objective probability and also contains the risk attitude of the investors.

Keywords

• discrete European option
• pricing
• risk aversion
• objective probability