TABLE OF CONTENTS In several of the preceding chapters reference has been made to the use of options in creating engineered payoff profiles. In each of the examples used option premia were taken as given by the market. This chapter looks at how those prices, at least to an extent, can be calculated. In addition it considers and explains several different frameworks that are available for the calculation of option premia.
In Chapter 6 reference was made to the well-known and oft-cited Black and Scholes (B&S) option pricing model. The current chapter will explain how the B&S model can be applied and will develop alternative pricing approaches: lattice frameworks and Monte Carlo simulation. The overall objective in introducing these alternative pricing frameworks is to develop a good intuitive understanding of their strengths and weaknesses, whilst at the same time developing an operational framework that will enable the reader to generate payoff profiles, under a variety of market outcomes for a variety of instruments. The framework will also provide a springboard from which more complex models can be analysed and from which hedge parameters can be obtained.
The B&S model is introduced in Section 11.2 and will be examined in the context of pricing regular stock or equity options. The binomial and trinomial model will be used to examine the pricing of regular stock options, too, but will also demonstrate how the flexibility offered by these frameworks might lend itself to pricing options with non-standard payoff profiles. The Monte Carlo method will...
