• Introduction:
          Some familiar financial instruments like - stocks, bonds, and currencies - are cash instruments. The value of such  instruments is determined directly by markets. The market price of a product is subject to fluctuations due to various factors effecting its demand & supply thereby associating itself to various risk factors.

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• Derivatives:
          In contrast to cash instruments, a derivative can be defined as something which derives its value from an underlying product being a stock, currency, commodity or anything that carries a market price. The price of a derivative rises and falls in accordance with the value of the underlying asset. So, derivative is a by-product of the core product which can be used to hedge, speculate & also undertake arbitrage activities.
  For example:
  1. Futures on the IBM  shares.
  2. Derivatives on the price of raw materials (e.g. natural gas futures and options).
  3. Call option on NIFTY index.

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• Time Value of Money:
          A $1 today is worth more than $1 in a year's time. This is because of all the things we can do with $1 over the next year. We could invest with banks or in risk free government bonds, which will give us the dollar with a little bit extra, the interest. There are several forms of interest rates available in a market; here we consider
  Simple interest: Is the interest you receive based only on the amount you initially invest?
  Continuously Compound Interest: Is the interest which you get interest on your interest?
          A sample calculation of simple and continuously compounded interest rates along with their formulae is given in Table1.

	Formula	Example
Principal	P	$100
Interest Rate %	r	5
Maturity	T	1 year
Simple Interest	(P * r * T) / 100	$ 5
Cont. Compound Interest	P - Pexp (r * T) / 100	$ 5.13

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• Forward Contract:
          A Forward contract is an agreement where one party promises to buy an asset from another party at some specified time in the future time and at some specified price. The asset could be a stock, commodity, currency, etc. No money changes hands until the delivery date or maturity of the contract. 
          Consider a future contract that obliges us to hand over an amount $F at time T to receive the underlying asset. Today's date is t and the price of the asset is currently $S(t), this is the spot price, the amount for which we could get immediate delivery of the asset. We know all of F, S(t), t and T, but is there any relationship between them? You might think not, since the future contract entitles us to receive an amount S (T) - F at expiry and this is unknown. However, by entering into a special portfolio of trades now we can eliminate all randomness in the future. This is done as shown in the Table 2.

Holding	Worth Today (t)	Worth at Maturity (T)
Buy Forward	0	S(T) - F
Sell Stock	-S(t)	-S(T)
Cash	+S(t)	S(t) χ e-r(T-t)

Since we began with a portfolio worth zero and we ended up with a predictable amount, that predictable amount should also be zero as there are 'no free lunches'.

F = S χ e^-r(T-t)

We can conclude that, this is the relationship between the spot price and the future price. It is a linear relationship; the future price is proportional to the spot price

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Contents

• Introduction
• Derivatives
• Time Value of Money
• Forward Contract