Forward and Future

7/27/2019 Forward and Future

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FORWARD AND FUTURE

CONTRACT

Prepared by:

JANAK



WHAT IS FORWARD AND FUTURE

CONTRACT?

forward contract or simply a forward is a non-standardizedcontract between two parties to buy or to sell an asset at aspecified future time at a price agreed upon today. This is incontrast to a spot contract, which is an agreement to buy or sell an

asset today.

futures contract is a standardized contract between two parties to buy or sell a specified asset of standardized quantity and quality

for a price agreed upon today (the futures price) with delivery and payment occurring at a specified future date, the delivery date.The contracts are negotiated at a futures exchange, which acts asan intermediary between the two parties.



PAYOFF CHART



PRICING OF FORWARD AND FUTURE

We can find fair futures price by adding cost of carrying the

asset into the current market price (spot price) and then

converting this resultant Present Value (PV) into Future Value

(FV).

F = (S + C) erT

F = (Fair) Futures price

S = Spot price C = Cost of carrying

e = Euler’s number

r = Risk free interest rate

T = Life of the contract



Example:

A trader enters into a 6 months contract to buy 500

quintal of barley. Barley is selling in the spot market

for Rs.13 per kg. The risk free interest is 4 % and costof storing barley is 50 paisa per kg. What should be

the fair futures price for this deal?



Solution:

S = Spot price = Rs. 13

C = Cost of carrying = Rs. 0.50

r = Risk free interest rate = 4 %

T = Life of the contract = 6 months

F = (S + C) erT

= (13 + 0.50) × e0.04 × 0.5

= 13.50 × 1.02020

= 13.7727

The fair futures price for this deal should be Rs. 13.7727 per kgor fair contract value of Rs. 688635 (13.7727 × 500 × 100).

The prices of these contract depend upon the spot prices of the

underlying asset, cost of carrying assets into the future and

relationship with spot prices.



VALUATION OF FORWARDS AND FUTURE

While creating forward contracts, delivery price of a futuredate is derived in such a way that both the parties (long &short) have no profit-no loss situation. At this stage the valueof the contract remains zero to both the parties. On a laterstage, there may be a positive value or negative value of the

contract due to change in market conditions. This situationarises because while entering into contract there was no profitno loss situation but as the time passes, one of the party to thecontract will be in gain and the other will be in loss. So it isimportant for the businesses to value the forward contract

daily or on periodic basis.

Valuation of forward contract is find out by finding the present value of the difference between new forward contract price and the old forward contract price.



Formula:

flong = (F0 – K) e-rT fshort = (K - F0) e-rT

f = Forward value of the contract (long or short)

F0 = Forward price of the asset if it is created today K = Delivery price

r = Risk free rate of interest

T = Life of the forward contract

While entering a forward contract, the delivery price (K) is set equal to theforward price (F0) and the value of the contract (f) comes at zero.

Delivery price (K) remains constant with the time but the forward price (F0)changes and so the value of the contract also changes.

So to find out K on the date of contract and F0 for a later date, we need tofind out F0 because even K= F0 on the date of contract.

F0 = (S0) erT

F0 = Forward price of the asset if it is created today

S0 = Spot price of the asset on day “0”

r = Risk free rate of interest

T = Life of the forward contract



Example:

Mr. A has entered into 1 year forward contract to purchase an

asset (non- income generating) when the spot price was Rs.

120 and the interest rate at 10% p.a. After 6 months the interestrate rise to 11% and spot price falls to Rs. 110 What is the

value of the forward contract in present?



Solution:

First we need to find out value of K and then we can proceed to find thevalue of F0 and then we can find the value of the forward contract by taking

the Present Value of the difference between F0 and K. Valuation ofForwards.

As we know K = F0 on the date of contract, we find K with theformula of F0

F0 = S0 × erT

F0 = 120 × e0.10 × 1 = 132.62

After six months, the forward prices of the same asset will be:

F0 = 110 × e0.11 × 0.5 = 116.21

Value of the contract will be: flong = (F0 – K) e-rT

flong = (116.21 – 132.62) × e.-0.11 × 0.5 = -15.53

The present value of the contract is -15.53 or a loss of Rs. 15.53 for Mr. A



EQUITY FORWARD WITH DIVIDEND YIELD



Example:

A portfolio manager expect to purchase a portfolio of stock in90 days in order to hedge against a potential price increase overthe next 90 days. She decide a take long position on a 90 dayforward contract on the S&P 500. the index is currently at1145rs. The continuously compounded dividend yield is

1.75%. The risk free rate is 4.25%

A. Calculate the no arbitrage forward price on this contract

B. If is now 28 days seen a portfolio manager enter the forwardcontract the index value at 1225.Calculate the value of thecontract . 28 days in the contract.

C. See at expiration index value 1233 . calculate the value of theforward contract.



Solution:

A. e^rc = (1+r)n

= In( 1+r)= In (1+0.0425)

= In(1.04162)

= 4.16%

No Arbitrage

Ft-0 = STe^-d(T-t) * e^r(T-t)

F0= SOe^(r-d)t

=1145*e^(0.0416-0.0175)90/365=1145*e^1.0059

=1151.83



B.Ft = st*e^(r-d)(T-t)

F28 = 1225*e^(0.0416-0.0175)(90/365- 28/365)

= 1230.03

Vt= (ft-k)*e^-r(T-t)

= (1230.03- 1151.83)*e^-0.0416(90/365-28/365)

= 77.65

C.Vt= (st-k)

=(1235-1151.83)

= 83.81

Benefit to long because answer is Positive.



PRICING OF CURRENCY

FORWARD



Example:

Suppose you are the US based importer , a good you import

from UK you expect the value of the pound to increase theagainst the US dollar over the next 30 days. You will be

making the payment within 30 days and want to hedge

currency hedge us risk free rate 5.5%, UK risk free rate =

4.5%. current spot rate is $1.5%

A. Present your hedging strategy

B. Calculate no arbitrage price at day 0

C. Moving forward 10 days the spot rate is 1.53$. interestrate are unchanged. Calculate the value of your forward

position.



Solution:

A. Hedging Strategy

If we Import Long strategy

If we Export Short strategy

B. Compounding Interest rate:

US UK

RC= In (1+r) RC= In(1+r)= In(1+0.055) =In( 1+0.045)

=0.0535 = 0.0440

= 5.35% = 4.40%

Fto= ste^(r-d)(T-t)= So*e(rus-ruk)*t

= 1.5e(0.0535-0.0440)30/365

=1.5*1.0008

=1.50117



C.

Ft= st.e(r-d)(T-t)

F10= 1.53*e^(0.0535-0.0440)(30/365- 10/365)

=1.53*1.0005

= 1.5308

Value at maturity

Vt=(ft-k)*e^-r(T-t)

= (1.5307-1.50117)*e^-0.535(30/365-10/365)

= 0.0295

Forward and Future

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