Derivatives: Valuation and Risk Management

By David A. Dubofsky; Thomas W. Miller Jr. | Go to book overview

CHAPTER 16

Arbitrage Restrictions on Option Prices
In Chapter 15, we presented option strategies based on the value of options at expiration. In Chapters 17 and 18, we will discuss two particularly important models that can be used to calculate option prices before the option expiration date.However, before those two specific models are presented, it is important to realize that basic option values before expiration must obey a set of pricing restrictions, regardless of the specific option-pricing model employed. Therefore, in this chapter, we present the upper and lower boundary prices for call and put options.We close this chapter with a particularly important relationship is known as put-call parity. Note that this important relationship, the subject of Section 16.4, can be studied independently of the other pricing restrictions.To begin, recall that a fundamental assertion of modern finance is that arbitrage cannot persist. Arbitrage is a trade, or a set of trades, that produces a positive cash flow at one or more dates and zero cash flows at all other dates. In well-functioning markets, options, like any other security, cannot be priced such that arbitrage opportunities exist. If the chance to realize a riskless arbitrage profit were to appear, investors would immediately move to exploit it, and in the process, prices would correct themselves. This chapter also establishes important concepts concerning the early exercise decision for American options on equities.1We make the following assumptions in deriving the arbitrage restrictions described in this chapter:
a. No commissions or transactions costs.
b. All trades take place at a single price (i.e., there is no bid-ask spread, and trading does not affect the market price).
c. No taxes.
d. No margin requirements and no short sale restrictions. Investors receive the full amount of written options and shares sold short.2
e. Investors can trade in the stock and options markets instantaneously. Investors get immediate notice of option assignments.
f. Dividends are received on the ex-dividend day, and the ex-day stock price decline equals the dividend amount.
g. Investors prefer more wealth to less, and they are quick to take advantage of any arbitrage opportunities that appear.

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