The Intrinsic Bounds on the Risk Premium of Markovian Pricing Kernels

TL;DR

This paper derives intrinsic upper and lower bounds on the risk premium in Markovian financial markets by transforming the problem into a differential equation and analyzing its solutions.

Contribution

It introduces a method to determine bounds on the risk premium using market option prices under Markovian assumptions, linking finance with differential equations.

Findings

Derived explicit bounds on the risk premium.

Connected market option prices with differential equation analysis.

Provided a framework for risk premium estimation in Markovian models.

Abstract

The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk. The purpose of this article is to determine upper and lower bounds on the risk premium of an asset based on the market prices of options. One of the key assumptions to achieve this goal is that the market is Markovian. Under this assumption, we can transform the problem of finding the bounds into a second-order differential equation. We then obtain upper and lower bounds on the risk premium by analyzing the differential equation.