Derivatives 3

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9/23/2010 12:22:12 AM [email protected] 1

Derivatives

Fifth Trimester-

Session-3Futures pricing and Application

of Futures

Prof Bhaskar [email protected]


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Session-3 Futures pricing and Application

of Futures

Session Details

. Pricing of Futures prices Price convergence at delivery date

Future prices in practice

Currency futures

Hedging and Speculation with

Interest futures Hedging and speculation with interest futures

Summary


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of Futures

I . Pricing of Futures prices

Meaning

Pricing of futures are essential in understanding

the price of underlying asset at the future date

The basic purpose of futures pricing is toeliminate risk-less profit through arbitraging


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of Futures

I. Pricing of Futures contracts

The important characteristics of perfect market are

a. Presence of large number of buyers and sellersb. Decisions taken is based on economic logic

c. Perfect information to all participants

d. Absence of Transaction cost

e. Absence of any market restrictionsf. Absence of restriction on free contracting

between parties.


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of Futures


Arbitrage- Its roleMeaning. It is a Process by which Risk-less profit

is obtained by buying and selling of same scrip in

different prices in different markets

Eg- Infosys is trading at 12,500 and 12600 at mumbai

and Ahmedabad stock exchange simultaneously


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of Futures


Cost of carry model

The cost of carry or carrying cost is the total cost to carry a

storable goods forward in time

The various cost involved are

Storage costFinancing Cost

Insurance and Transportation cost


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of Futures

I. Pricing of Futures contractsCash and carry model

Assumptions made

Spot price of gold per 10 gms 4000Futures prices of gold per 10 gms 4500

Interest rate per annum 10%

Transactions

Borrow Rs 4000 for one year at 10% 4000

buy 10 gms of gold in spot market -4000deliver 10 gms of gold against futures 4500

Contract repay loan with interest -4400

Risk-less profit 100


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of Futures

I.Pricing of Futures contractsReverse Cash and Carry ModelAssumptions made

Spot price of gold per 10 gms 4200

Futures prices of gold per 10 gms 4500

Interest rate per annum 10%

,

Transactions

Sell 10 gms of gold shor 4200

lend Rs 4200 for one year @ 10% - 4200

buy 10 gms of gold in futures market

Collect proceeds from loan 4620Accept deliver 10 gms of gold

against futures - 4500

Risk-less profit 120


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of Futures


To develop theory of future pricing, we will

Use the following notations

F= Future price

P= Cash Market price

r = Financing CostY = Cash yield.

Total Profit = F+ yP- (P + rP)


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of Futures

1. Pricing the Futures Contracts

Profits = Total proceeds Total outlay

Total Profit = F+ yP- (P + rP)

The equilibrium futures price is the price that ensure

that the profit from the arbitrage is zer0. Therefore

0 = F+ yP- (P + rP) or

F = P + P( r-y )

So future price is equal to cash price plus function of cashprice and finance cost and cash yield.


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of Futures

I. Pricing the Futures Contracts

Future prices could be at a premium or at discount

to the spot prices. , depending upon the value of the

P(r-y).(r-y) denotes difference between cost of financing and

the cash yield. Which is called as Net Financing

cost or Cost of Carry

Carry Future prices

Positive (y>r) will sell at discount to cash price

Negative (y


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of Futures

II. Price convergence at delivery date

. At the delivery date future price will be equal to

the cash price HOW ?

As delivery date approaches financing cost approaches =0

yield that can be earned by holding investment = 0

Hence Cost of carry approaches to Zero

Thus future price will approach are will be equal

to cash price


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of Futures

III. Future prices in practice

Why future rates will not be equal to

Cash price in reality.

1. Lending and borrowing rates will be different2. Restriction on short selling

3. Different Tax treatment of cash and future

transactions.

4. Transaction cost-cost of entering and closing

the contract.


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of Futures

VI Currency futures

Receivable in a currency A.

The bank will like to hedge the currency value if the

currency value drops. The bank should take a future

position such that future generate a positive cash flowwhenever the asset declines in value

Derivatives 3

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