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8 - Martingale option pricing

Published online by Cambridge University Press:  02 December 2010

Joseph L. McCauley
Affiliation:
University of Houston
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Summary

Introduction

Betting is risky, and for noise traders financial markets are formalized gambling casinos. The idea of a bet is to take a risk in order to try for a big win. A hedge on the bet reduces the risk, reducing both the possible win and the possible loss. Buying stocks in both rain and beach umbrellas reflects the idea of a hedged bet. Options provide a more direct way of hedging a bet on a stock, bond, or FX. Even money, however, is risky, as inflation can occur and a currency can be degraded systematically by the policies of the government in charge.

A stock, bond, or a foreign currency is a risky paper “asset” because the price fluctuates freely against your local currency. A bank deposit in the local currency, CD, or money market account is called “risk free” in financial math texts. Obviously, that idealization ignores the riskiness of the local currency (which reflects a nation's financial and fiscal policies) against necessary imports like oil and food. The riskiness of the Dollar as the world's default reserve currency is discussed in Chapter 9. Here, we will write as if a local currency could be “risk-free.” We will ignore inflation and consider only local bank interest rates. In truth, because of market instability, nothing in finance is risk-free.

A bond is a loan at a fixed interest rate, and fluctuates in price in anticipation of changes in future money market interest rates.

Type
Chapter
Information
Dynamics of Markets
The New Financial Economics
, pp. 176 - 187
Publisher: Cambridge University Press
Print publication year: 2009

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