TITLE:
An Approach to Calculate a Call Option Value on A Nontraded Underlying Asset Considering Its Risk Measures
AUTHORS:
Rafael A. Rodríguez
KEYWORDS:
Volatility, Real Options, Binomial Trees, Binary Approximations, Risk Measure
JOURNAL NAME:
Journal of Financial Risk Management,
Vol.13 No.4,
December
27,
2024
ABSTRACT: It is proposed an approach to calculate the suitable parameters for a binomial tree with a specific structure that allow us to calculate a call or put option on a nontraded underlying asset based on the risk perception for the beginning of the evaluation, time t0, and for the expiration time t1. Although there is not enough information to define with certainty the value of a non-traded underlying at t0, as it is usual, the specific structure of the binomial tree allows us to consider the risk involved at t0 and it effectively replicates the expected value and variance of the underlying asset at t1. An optimization model calculates the suitable parameters for the binomial tree in order to minimize the difference between the probability mass function (pmf) of the underlying asset at the future time modeled by the binomial tree and the one considered for the underlying asset. The results of the proposed method confirm the feasibility of its application no matter the shape of the pmf at t0 and t1. Also, the result of the model is checked with an academic case where the risk of the underlying asset at t0 is included.