Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-07T20:34:02.171Z Has data issue: false hasContentIssue false
This chapter is part of a book that is no longer available to purchase from Cambridge Core

13 - Option pricing

David C. M. Dickson
Affiliation:
University of Melbourne
Mary R. Hardy
Affiliation:
University of Waterloo, Ontario
Howard R. Waters
Affiliation:
Heriot-Watt University, Edinburgh
Get access

Summary

Summary

In this chapter we review the basic financial mathematics behind option pricing. First, we discuss the no arbitrage assumption, which is the foundation for all modern financial mathematics. We present the binomial model of option pricing, and illustrate the principles of the risk neutral and real world measures, and of pricing by replication.

We discuss the Black–Scholes–Merton option pricing formula, and, in particular, demonstrate how it may be used both for pricing and risk management.

Introduction

In Section 12.4 we discussed the problem of non-diversifiable risk in connection with equity-linked insurance policies. A methodology for managing this risk, stochastic pricing and reserving, was set out in Sections 12.5 and 12.6. However, as we explained there, this methodology is not entirely satisfactory since it often requires the insurer to set aside large amounts of capital as reserves to provide some protection against adverse experience. At the end of the contract, the capital may not be needed, but having to maintain large reserves is expensive for the insurer. If experience is adverse, there is no assurance that reserves will be sufficient.

Since the non-diversifiable risks in equity-linked contracts and some pension plans typically arise from financial guarantees on maturity or death, and since these guarantees are very similar to the guarantees in exchange traded financial options, we can use the Black–Scholes–Merton theory of option pricing to price and actively manage these risks. When a financial guarantee is a part of the benefits under an insurance policy, we call it an embedded option.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×