Examples

(i) Use of Low Discrepancy Sequences In the last section we made the distinction between the use of Monte Carlo for an occasional pricing and its routine use for calculating on-line prices or regular revaluation of a book. The same remarks apply to quasi-random numbers. There is no doubt that you need to be a lot more careful when setting up low discrepancy sequences. If you are using simulation for once-off calculations, it might be easier just to let your random number Monte Carlo simulations...

Introduction

i Price Volatility Apart from a few stray references, option theory has been developed to this point in the book with the assumption that stock price volatility remains constant. But it is very unlikely that a reader would have got this far without having heard that volatility is not constant. Before plunging into the subject we need to spend a couple of pages both defining the jargon and explaining the market observations which cause us to depart from the previous, well-ordered world of...

Options On Options Compound Options

Compound Option Payoff Diagram

i Definitions We will consider an option the compound option on an underlying option. Both the compound and the underlying options can be either put or call options, so that we have four options to consider in all. Half the battle in pricing these of compound underlying option option options is simply getting the notation straight, and this can be summarized as follows UNDERLYING OPTIONS Cu St, X, t Pu St, X, t Stock price at time t and volatility Value at time t of an underlying call put...

Extendible Options

i Consider a European call option with maturity at time t and strike price K at maturity, the holder has the choice of exercising or not exercising Longstaff, 1990 . Now suppose that an additional feature is added to this option the holder is given a third choice at maturity of extending the option to time T at a new strike price X, in exchange for a fee of k. The payoff of this extendible option at time t is The issues are best illustrated graphically. Figure 14.7 shows the value of the...

Binary Digital Options

i Recall the simple derivation of the Black Scholes formula which was given in Section 5.2. In its simplest form, this may be written F St max 0, St - X dST F St St - X dST where F ST is the lognormal probability distribution of ST. The two terms in this equation will now be interpreted separately, rather than together as they were before Reiner and Rubinstein, 1991b . ii Cash or Nothing Option Bet In the term fX F ST X dST, the factor X appears in two un- related roles as a constant...

Forward Contracts

i A forward contract is a contract to buy some security or commodity for a predetermined price, at some time in the future the purchase price remains fixed, whatever happens to the price of the security before maturity. Clearly, the market or spot price and the forward price will tend to converge Figure 1.3 as the maturity date is approached a one-day forward price will be pretty close to the spot price. In the last section we used the example of a forward currency contract this is the...

Applications

Jarrow Rudd Trees

i European Call Jarrow-Rudd Method u d-1 econsider the tree shown in Figure 7.4. From the specification of the option and equation 7.6 , the following parameters can be calculated Using these u and d factors, we can start filling in the stock prices on the tree shown just above each node . The intermediate values of St are not really necessary for a European option, since the option payoff only depends on the stock price at maturity however, they are shown for ease of understanding. The payoff...

Combinations Of Options

This is a book on option theory and many how to books are available giving very full descriptions of trading strategies using combinations of options. There is no point repeating all that stuff here. However, even the most theoretical reader needs a knowledge of how the more common combinations work, and why they are used also, some useful intuitive pointers to the nature of time values are examined, before being more rigorously developed in later chapters. Most of the comments will be confined...