Derivatives 3
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Transcript of Derivatives 3
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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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
of Futures
I. Pricing of Futures contracts
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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Session-3 Futures pricing and Application
of Futures
I. Pricing of Futures contracts
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
of Futures
I. Pricing of Futures contracts
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
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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Session-3 Futures pricing and Application
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