Page 55 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Derivatives & Risk Management

Notes whether the underlying asset is held for investment or for consumption. Assets underlying
individual stock futures are for investment purpose, whereas those like rice futures (commodity)
are exclusively for consumption.
The basic principle of futures pricing involve the requirement of 'no arbitrage opportunities'.
The price of a future is determined via arbitrage arguments. The future price represents the
expected future value of the underlying discounted at the risk free rate-as any deviation from
the theoretical price will afford investors a riskless profit opportunity and should be arbitraged
away.
Thus, for a simple, non-dividend paying asset, the value of the future, F(t), will be
found by discounting the present value S(t) at time t to maturity (T) by the rate of risk-free
return (r).



F(t) S(t) (1 r) T t ...(5.1)

or, with continuous compounding
F(t)  S(t)e r(T t) ...(5.2)
This relationship may be modified for storage costs, dividends, dividend yields, and convenience
yields.
In a perfect market, the relationship between futures and spot prices depends only on the above
variables. In practice, there are various market imperfections (transaction costs, differential
borrowing and lending rates, restrictions on short selling) that prevent complete arbitrage. All
of these are discussed at the end of this unit. Thus, the futures price in fact varies within arbitrage
boundaries around the theoretical price.

Did u know? What is the concept of basis?
The relationship between the futures market price and the cash price is called basis. In
formula:
Basis = Cash Price – Futures Price
The difficulty with basis is not computing it 'after the fact', but the problem is encountered
when basis must be estimated 'ahead of time'.

Self Assessment

Fill in the blanks:
1. The value of the futures position at time T may be greater or less than the ……………..of
the forward position, depending on the path that futures price follows over the life of the
contract.
2. A …………. contract is a standardized agreement to buy or sell a commodity at a date in
the future.
3. The basic principle of futures pricing involve the requirement of …………….
4. The future price represents the expected future value of the underlying discounted at the
………………….
5. The relationship between the futures market price and the cash price is called
…………….

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