The Pricing of A Moving Barrier Option

TL;DR

This paper derives an analytical formula for pricing a barrier option with a special moving barrier, accounting for time-dependent risk-free rate, dividend rate, and volatility, and establishes put-call parity under certain conditions.

Contribution

It introduces a novel analytical pricing formula for barrier options with a specific moving barrier and extends the put-call parity to this context with time-dependent parameters.

Findings

Derived an explicit pricing formula for the moving barrier option.

Established put-call parity for the specific moving barrier case.

Demonstrated the impact of time-dependent rates and volatility on barrier option pricing.

Abstract

We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relation with risk free rate, dividend rate and stock volatility.