Pricing of Barrier Options on Underlying Assets with Jump-Diffusion Dynamics: A Mellin Transform Approach

Marianito R Rodrigo

doi:10.3390/math8081271

Abstract

A barrier option is an exotic path-dependent option contract where the right to buy or sell is activated or extinguished when the underlying asset reaches a certain barrier price during the lifetime of the contract. In this article we use a Mellin transform approach to derive exact pricing formulas for barrier options with general payoffs and exponential barriers on underlying assets that have jump-diffusion dynamics. With the same approach we also price barrier options on underlying futures contracts.

Highlights

A European call option is a financial contract that gives the holder the right, but not the obligation, to buy an underlying asset from the writer at an agreed strike price on a predetermined expiry date.A European put option is similar but gives the right to sell instead
An investor who already owns shares of a certain stock may insure against a temporary fall in the share price by deciding to buy a put option to minimize the risk of a potential loss
The primary objective of this article is to employ a Mellin transform approach to price barrier options with general payoffs when the underlying is modeled by the jump-diffusion dynamics (3)

Summary

Introduction

A European call option is a financial contract that gives the holder the right, but not the obligation, to buy an underlying asset from the writer at an agreed strike price on a predetermined expiry date. A European put option is similar but gives the right to sell instead. Examples of the underlying asset, or the underlying, are stocks or futures contracts. An investor who believes that the share price for a certain stock is going to rise within the month may invest by buying a call option on that stock. An investor who already owns shares of a certain stock may insure against a temporary fall in the share price by deciding to buy a put option to minimize the risk of a potential loss

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