Derivative Module Lessons

The futures calculator is based upon the cost of carry model of forward pricing.  This model identifies the arbitrage free value a futures contract by identifying how much it costs to construct the contract synthetically.  That is, forming an equivalent position to the futures position by simultaneously borrowing (for the life of the future) and buying the underlying asset.  If there are additional costs (or revenues) received from holding this equivalent position for the life of the contract, these must also be added to or subtracted from the carry costs.

The following set of lessons elaborate upon the above theme. 

Regardless of whether one is trading options for risk management or speculative purposes, a view must be translated into a trading strategy.  In the following lessons you will learn about common option strategies and how views are translated into trading strategies.

The previous set of lessons exploit the option contract, that specifies what the option's terminal value is as a function of the underlying asset price.  In this current set of lessons we consider what the arbitrage free present value of an option is.

In order to understand the subtleties of option pricing we start by consider the present value of an option in a simple world where the underlying asset price can go up or down.

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Valuing options in the binomial world revealed deep insights about the arbitrage free price of an option.  The only drawback is that the world appears over simplified relative to real world asset price processes.  Things get a lot more realistic if the time to maturity is partitioned into smaller and smaller intervals.  Consider a single trading day, if at the end of the day IBM could only finish up or down by a fixed amount, such a representation of IBM's price process would be too simplistic.  But consider partitioning the day into two sub-partitions now the price can up, up; up, down; down, up or down, down; and so there are three or four possible terminal values depending upon whether up, down = down, up.  Three sub partitions expands this further and so on.  As a result, finer and finer sub partitions permit many more terminal price possibilities to be spanned and so now the model appears a lot more realistic.

In this module we explore what the implied arbitrage free price of an option is as we allow for more and more sub partitions and compare this to the Black Scholes option pricing model derived from a much more complex world where the underlying asset price dynamics is modeled as a "Brownian motion."

This module applies the Black Scholes option pricing model to identify the arbitrage free price of a European option.  It uses a numerical approximation to solve for the price of an American option.  A comprehensive set of lessons are provided below illustrate how the calculator is applied to real world option pricing problems as well as what type of information can be extracted from actual option prices.

This module serves as a simple introduction to exotic options.  It let's users explore what some of the most common exotic options are plus how they are valued in the context of a binomial tree.