** ****Futures Calculator Module**

Welcome to the Futures Calculator from FTS. This module will let you learn price futures and/or infer information from current futures prices. Information that can be inferred from futures prices is carry cost information and this module will let you answer the following questions:

What is the implied constant continuous dividend yield from a stock index?

What is the current financial cost of carry in for a 6-month offshore deposit for any major currency?

What is the arbitrage free futures price given current prices in the spot markets?

You will learn to answer these questions by first becoming acquainted with how the futures calculator works and secondly working through the generic online support lessons.

**Elements of the Module Screen **

There are two sides to the calculator divided by the vertical red line.

**Left Side of Calculator (Below Underlying)**

In the module to the left you can see two primary calculator screens. The underlying arbitrage free price is computed from the cost of carry model. This model prices out what the cost of constructing the future synthetically is. That is, what is the cost of recreating the future's contract in the spot market by borrowing, buying the underlying asset and holding it over the life of the futures contract.

A. Beside Underlying: Select whether you are working with an Index, Currency or Commodity

The elements of the cost of carry are: the spot market price of the underlying asset, the financial cost of borrowing this spot price (i.e., interest rate), any storage cost incurred for holding the underlying asset and if the underlying pays a dividend then this is a reduction in the cost of carry.

Thus, the left side of the calculator lets you compute the arbitrage free futures price from the inputs to the cost of carry model:

i. The underlying asset price (Labeled Spot).

ii. The interest rate or financial cost of carry (Labeled Interest Rate).

iii. If the underlying asset pays a dividend then enter the constant continuously compounded equivalent of this dividend yield. If the underlying pays no dividend over the life of the future's contract then enter 0. (Labeled Dividend Yield)

iv. The life or maturity of the future (Labeled Maturity).

v. If the future is a financial future, such as a stock index future, the storage cost is zero. If the future is a commodity future such as wheat, the storage cost is non zero (Labeled Storage Cost).

**Using the automated recovery of price data **

From the drop down you can automatically retrieve some data from the web. For example, CME S&P 500 Futures refers to the S&P500 index futures. When retrieving data from the web use the following sequence:

a. Enter the maturity of the future (or at least approximate maturity date getting the maturity month correct initially.

b. Click on Futures Price to retrieve the Futures price from the web for the maturity month. If you get an error here check that the month you put in is trading. To see this, select the Option Menu item (Expand bottom window). This will let you see which web page is being parsed.

c. Click on Spot Value to retrieve the spot price of the underlying if available.

d. Click on Interest Rate to retrieve the interest rate for the maturity you have entered.

e. If any values do not come in enter them from the site or source that you can access.

f. If the underlying pays a dividend enter the continuously compounded equivalent approximation of the dividend yield (e.g., a reasonable approximation is to take the natural logarithm of the dividend yield). This number of course can also be inferred from the market price (see below when we cover the right hand side of the screen).

g. Usually you do not enter an estimate for storage costs, but you may infer it below if dealing with a future defined on some commodity. For financial futures you can ignore this field.

Click on Calculate to compute the predicted price. You can contrast the predicted price with the current futures price. This lets you adjust field values to match the predicted price. For example, on the S&P500 index you will know the interest rate but you probably do not know the dividend yield. Hence you can enter a number to see whether this moves towards the market price or away from it. That is, you can do sensitivity analysis this way. Alternatively, you can let the calculator solve for these values directly by using the right side of the calculator as described below.

**Right Side of the Calculator (Below Contracted Price)**

The right side of the futures calculator provides different information. It lets you infer information from the futures price.

Field 1: Contracted Price -- this is the price that you either paid or the price that you want to work with. Alternatively, it could be the price at the time of the spot market closing even though the futures market is still open for trading and so the futures price is constantly being updated.

If you select Contract Value and you have entered a Contracted Price then the number that appears when you hit calculate is the difference between the theoretical price (Left side of the screen) and the Contracted Price. After this you can ignore Contracted Price and the remaining implied values work from the Futures Price Number. For example, to see how this works delete the current price and enter the theoretical price (from the left side of the screen).

Now click beside Implied Interest Rate, and Calculate. You will see the same interest rate as is displayed in the left side of the screen. This means that if you now click on the Futures Price button to bring in the current futures price and Spot Value button to bring in the current spot price of the underlying you can estimate the implied financial cost of carry given your Div Yield estimate (and Storage Cost estimate) if relevant.

**Applying the FTS Futures Module to Real World Markets **

One of the potential real world difficulties with futures contracts is to learn how they are quoted. This must be understood before it is possible to infer information from price. To learn about how futures contracts are quoted click on Futures Contracts.

**Specific Applications**

i. Determining the arbitrage free price of a stock index futures contract. To work through this example click on Example 1 now.

ii. Inferring the market's estimate of the constant continuous dividend yield for the underlying stock index. To work through this example, click on Example 2 now.

iii. The final example, extends the arbitrage free price
of a futures contract to the problem of pricing a currency forward
contract. This is useful for inferring information about foreign yield
curves. To work through the application of the covered interest rate
parity approach to the arbitrage free price of a currency forward contract
click on Example
3 now. This illustrates how to apply the Futures Calculator to a
USD/Euro forward contract.

(C) Copyright 2003, OS Financial Trading
System