microsoft powerpoint - pricing of forwards

8/7/2019 Microsoft PowerPoint - Pricing of Forwards

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Pricing of Forward and Future

Dillip KhuntiaDillip KhuntiaDillip KhuntiaDillip Khuntia

Master of Finance & ControlMaster of Finance & ControlMaster of Finance & ControlMaster of Finance & Control

Utkal UniversityUtkal UniversityUtkal UniversityUtkal University


2/21

Investment Asset:- Asset Held for investment

purpose by significant number of investor. Eg; Stocks, Bonds etc.

-

Consumption.

Eg; Copper, Oil, etc.

2MFC


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Short Selling

Involves Selling of Assets that is not owned.

Margin Account is maintained with the

Broker.

3MFC


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PricingPricingPricingPricing

4MFC


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Assumptions

No Transaction Cost

Same Tax for all.

Interest Rate on Borrowing = Interest Rate on

Lending; i.e. at Risk-free Rate of Interest.

Advantage of Arbitrage Opportunities.

5MFC


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Forward PricesForward PricesForward PricesForward Prices

Stocks with No Income:-

F0

= S= S= S= S0000

eeeerTrTrTrT

Where

T = Time to Maturity r = Risk-free Interest rate

F0

= Forward Price

S0 = Spot Price

6MFC


7/21

Stocks with Known Income:-

F0

= (S= (S= (S= (S0000

I)eI)eI)eI)erTrTrTrT

Where T = Time to Maturity

=

F0

= Forward Price

S0

= Spot Price

I = Known Income

7MFC


8/21

Stocks with Known Yield:-

F0

= S= S= S= S0000

eeee((((rrrr----q)Tq)Tq)Tq)T

Where T = Time to Maturity

=

F0

= Forward Price

S0

= Spot Price

q = Average Yield

8MFC


9/21

Value of Forward ContractsValue of Forward ContractsValue of Forward ContractsValue of Forward Contracts

The value of a forward contract at the time of

entering into the contract is zero.

a er s age, ue o uc ua on n e orwarprice, the value of the forward contract change,

i.e. either positive or negative.

9MFC


10/21

Notations

K= Delivery Price

T = Time to maturity

r = Risk-free interest rate

F0

= Forward Price

f= Value of forward contract today.

10MFC


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Value of forward Contract on an Asset

With No Income;

f = S0

Ke-rT

With a Known Income I

f = S0

I - Ke-rT

With a Known Yield (q)

f = S0e-qT - Ke-rT

12MFC


13/21

Future Prices of Stock - Indices A stock index can be usually be regarded as an asset that

pays dividend.

Here paid is considered as known yield rather than knownincome.

Thus Price of Stock Index Future

F0

= S0e(r-q)T

Where, r = risk-free interest rate

q = Known yield from stock index future

T = Time to maturity

F0 = Price of Future contract

S0 = Spot price 13MFC


14/21

Index Arbitrage

If, F0

> S0

e(r-q)T, Profit can be made by buying

the stocks underlying the index at the spot price and

.

If, F0

S0e(r-q)T, Profit can be made by selling the

stocks underlying the index at the spot price and

buying futures contract. (Corporation Holding)

This strategy is known as INDEX ARBITRAGE14MFC


15/21

Forward & Futures Contract on Currencies

The holder of the foreign currency can earn

interest at a risk-free rate prevailing in foreign

countr .

F0

= S0e(r rf

)T

For known yield q

F0

= S0e(r q)T

15MFC


16/21

Forward & Futures Contract on Commodities Storage cost & Carries cost are taken into

account while determining the Price of Futures

on Commodities

In the absence of storage cost and income

F0 = S0er

With storage cost U

F0

= (S0

+U)erT

Storage costs net of income(u) are proportional

to the price of the commodity

F0 = S0e(r+u)T 16MFC


17/21

Consumption Commodities No income, Significant Storage Cost

Price

F0

(S0+U)erT

orF

0 S

0e(r+u)T

Where,u = Storage cost as proportion of spot price.

17MFC


18/21

Convenience YieldLet; U = Present value of Storage cost.

y = Convenience YieldF

0eyT = (S

0+U)erT

Or

F0eyT = S0e(r+u)T

or

F0 = S0e

(r+u-y)T

Where,

u = Storage cost as proportion of spot price.

18MFC


19/21

The CostThe CostThe CostThe Cost----ofofofof----CarryCarryCarryCarry

Cost of Carry (c) = (Storage Cost)

+

(Interest Paid to Finance the Asset)

-(Income Earned on the Asset)

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20/21

For non-dividend paying stockc = r (as no storage and no income)

For Stock Index

c = r q (as income is earned at q rate)

c = r rf(rf = risk-free interest rate of foreign

country)

For Commodity

c = r q + u ( Income q and storage cost u)

20MFC


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Future Price for investment asset

F0

= S0ecT

Future Price for consumption asset

F0 = S0e(c-y)T

Where, c = cost of carry

y = convenience yield

21MFC

microsoft powerpoint - pricing of forwards

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