DRM-2 Futures Pricing

8/12/2019 DRM-2 Futures Pricing

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Forwards and FuturesMechanism, Hedging,

and Pricing



DERIVATIVES

A product whose value is derived from thevalue of another asset referred asunderlying asset.

Underlying Asset can be

– COMMODITIES, – T-BILLS,

– STOCKS,

– CURRENCIES,

– INDICES, etc. Basic products are: Forwards, Futures,

Options and Swaps

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Derivatives and Risk ManagementRajiv Srivastava



FORWARD CONTRACT Spot transaction is characterised by simultaneous

negotiation of price and settlement by exchange ofconsideration and delivery of asset.

Forward contract is a contract between two partiesto deliver the asset at a predetermined price at a

future date. First phase is fixing of price, and Second phase is settlement, Both phases are at different times.

In the absence of forward market one can not

hedge, and the results will be sub-optimal becauseof uncertainty. It is an Over-the-Counter (OTC) product with

terms negotiated between buyer and seller.

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HEDGING WITH FORWARD

Farmer Rice Mill

Supplier of Rice User of Rice

Farmer sells harvest 3 m forward for delivery at price of sayRs 20/Kg

Both supplier and user are assured of price and eliminateprice risk

Settlement: After 3 m farmer supplies and mill pays at Rs20/Kg

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LIMITATIONS OF FORWARD

SIZE OF MARKET OTC products have limited market size. There will be few hedgers. Finding counterparties with matching needs of timing, quality,

quantity and price is extremely difficult.FAIR PRICE??

Price discovery is not likely to be true.( Price of Rs 20/Kg would depend upon the negotiation power ofbuyer and seller. It is likely to be an unequal market for buyer andseller)

Exit Route:

Once entered it is difficult to make an early exit; requires consent ofthe counterparty

COUNTERPARTY RISK

Settlement is by delivery One of the parties would have strong incentive to default depending

upon the price at the time of harvest, the end of forward period.

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NEED FOR FUTURES

Need to increase the market size for discovery of fair price. – Speculators and Arbitrageurs (non-users) need to be

encouraged besides hedgers.

Delivery and price to be de-linked but not the process ofprice determination.

– Price must be governed by the physical market. To eliminate counterparty risk a mediator (An Exchange) needs

to come in.

Buyer Exchange Seller

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FEATURES OF FUTURES

Organised Exchange: Forwards are OTC whilefor Futures there exist an organised exchange.

Standardisation: Delivery and quantity of theasset are not fixed in forward contract. They are

tailor made. Futures contracts are standardisedquantity, quality,

delivery time, delivery centres.

Price quotation vs. Contract size

Tick size: Minimum movement of price.

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FEATURES OF FUTURES

Clearing House: Futures are through a clearinghouse, while forward contracts are done directly.

Margin Requirements: Margins have to bedeposited with clearing house. No margins are

required in a forward contract. Commission: to be paid separately. In forward

contracts spread between Bid – Ask exists.

Mark to the market: Futures contracts are markedto the market. Forwards are settled only once upon

maturity. Actual delivery is rare in futures while most

forward contracts are settled with delivery.

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Derivatives and Risk Management

Rajiv Srivastava





CBOT- WHEAT FUTURES

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FUTURES

Futures are forward contracts that are traded onEXCHANGE.

It is a contract between two parties (not known toeach other as Exchange works as interface) to

deliver the asset at a predetermined price at afuture date.

Fundamentally, futures contract is same as forwardin terms of pricing, applications etc but

mechanisms of trading, and settlement aresubstantially different.

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FUTURES Vs FORWARD

PARAMETER FUTURES FORWARD

Place Exchange OTC

Product Standardised Tailor-made

Initial Cashflow Margin required Nil

Settlement Daily by MTM Final

Closing out Offsetting, Easy,

Any time

Difficult

Delivery Rare Mostly

Liquidity Very high Very low

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TYPES OF FUTURES

Initially futures were used in merchandise businessonly. Financial futures came in to being in 1972 onthe International Money Exchange at CME.

Commodity:

Where the underlying asset is a commodity – Agricultural commodities like Wheat, Rice, Soya,

Coffee, Sugar, Rubber, Coconut, or

– Metals like Gold, Silver, Copper, Tin, Aluminum

Financial: Where the underlying is a financial asset.

– Stocks/Indices/Currencies/Interest Rate

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FINANCIAL FUTURES Currency:

– Where the underlying asset is a currency like $, Euro, £, ¥,Rs. etc.

– Currency futures trading started in August 2008.

Stocks:

– Where the underlying is a stock or index. Introduced inIndia on June 12, 2000 for Indices and on November 9,2001 on select individual securities, at NSE.

Interest Rate:

– Underlying is a Interest Rate (LIBOR, MIBOR). In Indialaunched on June 24, 2003 at NSE. Failed. Re-introduced

with a notional GOI security as underlying. – Short term interest rate futures began trading on July 4,

2011 at NSE with 91-day T Bill as underlying.

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CONTROLLED PRICE ANDHEDGE

Hedging is essential feature of futures.

Price variability gives rise to the risk of dealing inphysical commodities.

To eliminate risk of prices one is required to have

substantial control either on supplies or on thedemand of the commodity.

Govt. providing minimum support price to grainproducers is an expensive way to provide price

protection.

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COMMODITY FUTURES

Commodity futures exist on vast range ofcommodities – Agriculture, Energy, Metals,

Exchanges in India commenced trading in Nov 2003

• Multi Commodities Exchange (MCX), Mumbai

• National Board of Trade (NBOT), Indore

• National Multi Commodities Exchange (NMCE), Ahmedabad

• National Commodity and Derivatives Exchange(NCDEX), Mumbai

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TRADING WITH FUTURES

One can buy/sell futures contract on the exchange. Orders are matched in order of

Price - Time - Quantity. Price conditions

– Market order

– Limit order – Stop loss order

Time conditions – Good for the Day, GTD – Good Till Cancelled, GTC

– Immediate or Cancel, I/C (Partial match possible) Quantity

– Minimum Fill

– All or None

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SETTLEMENT

Three ways to Sett le Physical Settlement – Settlement by giving/

taking delivery – Prior intimation required. – Settlement is done on the basis of warehouse receipt.

– Warehouses are designated. Offsetting Before Maturity

– Buy first and sell later. – Sell first and buy later.

Close out - Cash Settlement, On Maturity

– Open positions on the expiry day considered closed withoffsetting contract at spot price. – Contracts are cash settled: Difference of price is

debited/credited – Closing price equals spot price

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SETTLEMENT BY DELIVERY

Delivery Notice Period Some days prior to maturity of the contract (usually

2 weeks) buyers/sellers must declare intentions totake/make delivery.

Delivery Notice Period required for delivery

preparation.DELIVERY LOGIC: Who can force delivery

Specified in the contract and determined by theexchange. – Option of the buyer

– Option of the seller – Both – Compulsory

Normally at the option of seller.

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MECHANISM/LOGISTICS

WAREHOUSE: Warehouses and places of delivery are designated.

ASSAYERS Suitable arrangement made for quality and quantity check,

(Assayers)TRANSFER Warehouse receipts are issued if quality/quantity found

acceptable. Warehouse receipts would be given to intending buyer to

receive delivery. Warehouse receipts are negotiable instruments.

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ASSIGNMENT

Mismatch between deliverable quantity among buyers andsellers gives rise to problem of assignment.

Process of finding willing counterparty (buyer willing to takedelivery) is called ASSIGNMENT. Exchange has to find somebuyer /seller who accepts delivery against the futures contract.Delivery notice to be assigned only to open positions.

METHODS OF ASSIGNMENT1. Display Notice and call for bids from willing buyers

(CBOT, Brazil, CME)2. Assign on some basis (COMEX, India)

– Random – First in first out (FIFO)

– Longest contract period Method of assignment is known through the contract

specifications. IMPLICATION: Assigned party loses opportunity to offset.

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OPTIONS TO SELLER/BUYER Those not needing delivery are expected to square up. Both seller/buyer have option to square up even after

intention to deliver/assignment till the last day of DeliveryNotice Period. This is not the case in stocks futures.

After expiry of Delivery Notice Period, delivery is assigned to

open long positions.DELIVERY RATE Delivery rate depends upon the spot price. Adjustment to the delivery price for quality, freight etc done. These are already specified in the contract before-hand.

Warehouse receipt is given to assigned buyer, who pays tothe exchange. Against receipt warehouse delivers. Exchange makes payment to seller.

World over delivery is about 1% of the contracts

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SETTLEMENT BYOFFSETTING

Normally settlement is done by offsetting contracts,before expiry of the contract, permitting participantsto nullify positions.

Buy first sell later or sell first and buy later. – 10 Dec Buy Gold Futures contract 12,680

– 15 Dec Sell Gold Futures contract 12,780

– Net Profit = 100 x Size of the contract

(in terms of price quotation)

This profit is calculated on daily basis (Marking to

the market, MTM). This helps an efficient discovery of price as all

participants monitor positions regularly and look foropportunities to make profit/contain losses.

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CASH SETTLEMENT Last day of trading all open positions are closed automatically

– All long positions are nullified by selling – All short positions are nullified by buying

The closing price is the spot price, ensuring that futures priceis equal to the spot price in the physical market

The difference of price of the initial contract and closing

contract are settled in cash. Spot price may be determined by polling and bootstrapping

Buy first sell later or sell first and buy later.10 Dec Initial position – Buy Gold Futures contract – 32,680 (Remains open till last day)20 Dec Last trading day

– Exchange Sells Gold Futures contract at spot price – 32,880 – Net Profit = 200 x Size of the contract (in terms of price

quotation)

This profit is calculated on daily basis (Marking To Market,MTM)

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MARGIN

Initial margin is deposited to open trade to coverthe settlement risk, the onus for which lies of theexchange. It is performance bond/good faith money

Payable upfront, refunded on closing out. Margin is commodity specific, exchange specific

and depends upon the volatility of asset price.Init ial Margin:

Meant to cover the largest possible loss in a day.Normally of the order of 5% – 10%.Maintenance Margin: Margin Call

Profit/loss on daily basis are credited/debited to themargin account.Can’t fall below certain level: Maintenance Margin

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MARKING-TO-MARKET(MTM MARGIN)

Exchange settles the contracts on daily basis. Computation of profit/loss as if the positions were

closed out. Actually the open position remains. Futures contracts are deemed settled and re-

written every day. All positions are brought to the same price each

day. Making good the loss or payment of profit on daily

basis.

Daily clearing price (different than closing price) isused in calculating the daily profit/loss. Final settlement price and daily settlement price

may be different. (Futures on currencies).

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MARKING-TO-MARKETEXAMPLE

Gold Contract Size 1 KgPrice quotation per 10 gms – For Gold in IndiaInitial Margin 5%

DAY ACTION Price Profit /Loss (+/-) Margin

Day 1 Bought 1 Gold Contract 32,300 1,61,500Day 1 Clearing Price 32,450 +150 +15,000 1,76,500

Day 2 Clearing Price 32,310 - 140 - 14,000 1,62,500Day 3 Clearing Price 32,470 +160 +16,000 1,78,500Day 4 Sold 1 Gold Contract 32,600 +130 +13,000 1,91,500

Amount in excess of 1,61,500 could be withdrawn atany time.

Aggregate profit is 30,000: Remains same asdifference of closing and opening values. This is split over series of daily cash flows over 4

days.

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OPEN INTEREST

Open Interest is the number of contractsthat are open on any given day.

It is an indicator of investors interest in the

contract. It rises initially and has to become zero on

the last day.

New positions are added to open interest

Offsetting position (closing the openposition) reduces open interest

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OPEN INTEREST

Open Interest is different than Volume.Day ACTIONS Open

Interest

Volume

1 A goes Long; B goes Short 50

C goes Long: D goes Short 100

150 150

2 E goes Long: F goes Short 100

(Two new contracts add to Open Interest)

250 100

3 B goes Long: H goes Short 50

(One party offsetting and second party

opening keeps Open Interest unchanged)

250 50

4 C goes Short: D goes Long 100

(Both parties closing reduces Open

Interest)

150 100

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PRICING AND

HEDGING



PRICINGFORWARDS & FUTURES

A derivative derives its price from the value ofanother asset referred as underlying asset

Underlying assets can be commodities, T-bills,stocks, currencies, indices, etc.

The spot price in the physical market mustdetermine the price of its futures contract

For pricing purpose there is no difference betweena forward contract and futures; both being

contracts for future delivery

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PRICING FORWARDCost of Carry

Suppose you needed 10 gms of Gold 3 monthslater.

The current price (called spot price, S0) of gold isRs 18,000 per 10 gms.

If you were to buy and the goldsmith were to selltoday cash would be paid against delivery.

Instead you wish to firm up the price today fordelivery of gold 3 months later (entering a forwardcontract) what price is appropriate?

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SELLER Asset is committed to bedelivered 3 months later

If he sold spot he would realiseRs 30,000

It would have grown to Rs30,900 (assuming 1% return

per month) after 3 months, ifhe invested the sum He would also incur some

costs in holding the asset forprospective buyer likeinsurance, rent etc for 3months, say ½% per month

Therefore he would charge aminimum of Rs 31,350 (30,000+ 900 + 450) to agree to enterin the forward deal and beindifferent

BUYER Asset is assured for delivery 3months later

If he bought spot he would partaway with Rs 30,000

If payment is deferred theamount would grow to Rs

30,900 (assuming 1% returnper month) after 3 months, ifhe invested

The buyer would also savesome costs like insurance, rentetc for 3 months, say ½% permonth

Therefore buyer would beindifferent to pay a maximumof Rs 31,350 (30,000 + 900 +450) to agree to enter in theforward deal.

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COST OF CARRY – Cost interest, Insurance, Rent etc form the cost ofcarrying, r (typically % per annum)

– Seller incurs it and buyer saves it For Buyer

– Maximum payable forward price, F

= Spot price + Cost of carrying for the forward period, TF ≤ S0 + S0 x r x T

For Seller

– Minimum acceptable forward price, F= Spot Price + Cost of carrying for forward period

F≥ S

0 + S0 x r x T The only way both can agree is

F = S0 + S0 x r x T = S0 (1 + r x T)

= 18,000 (1 + .015 x 3) = 18,810

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ARBITRAGECash and Carry

If forward price defied cost of carry model it offers arbitrage Arbitrage refers to risk free profit with no investmentCASH AND CARRY

Actual price = 31,600 ( > Theoret ical Forward Price 31,450)

ACTIONS Cash flow (Rs)

Today

Borrow at 1% pm for 3 months +30,000Buy 10 gms Gold Spot -30,000Sell Gold 3-m forward contract at 31,600 -Initial cash flow Nil

After 3 months

Realise from forward contract against gold +31,600

Pay expenses ½% -450Pay debt and Interest, 1% -30,900Net cash flow 150

Earn profit of Rs 150 without investment and without risk

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ARBITRAGEReverse Cash and Carry

REVERSE CASH AND CARRY

(If actual price were 31,250 ( < Theoretical Forward Price 31,350)

ACTIONS Cash flow (Rs)

Today

Sell spot 10 gms Gold +30,000

Invest at 1% pm for 3 months -30,000Buy Gold 3-m forward contract at 18,500 -Initial cash flow 0

After 3 months

Realise gold from forward contract and pay cash -31,250Saved expenses +450

Realise investment and Interest +30,900Net cash flow +100

Earn profit of Rs 100 without investment and without risk

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PRICING FORWARD

Process of arbitrage will govern the price of theforward contract for period ‘t’ (With short sellingpermitted)

Ft = S0 ert

If there is any dividend (benefit) accruing during theperiod then

Ft = (S0 – D) ert

where D = Present value of the benefit.

For securities providing known yield ‘y’ (incomeexpressed as % of price),

Ft = S0 e(r - y)t

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CONVERGENCE

Contango or backwardation, in either case thefutures price must converge to the spot price asmaturity approaches, as all cost of carry, benefits ofownership, storage costs, convenience yields etc.

tend to become zero.Convergence of price- Contango

Price

Futures

Spot

Maturity Time

Convergence of price- Backwardation

Price

Spot

Futures

Maturity Time

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LONG & SHORTPOSITIONS

ASSET When you have the asset you are called LONG on

Asset

When you do not have the asset you are calledSHORT on Asset

FUTURES

When you buy futures it is called LONG on Futures

When you sell futures it is called SHORT onFutures

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PAY OFF - ASSET LONG & SHORT

PAY OFF - ASSET POSITIONLong on Asset Short on Asset

Bought at S0, Currently at S Sold at S0 Currently at SIf S > S0 Gain S – S0 If S > S0 Loss S – S0 If S < S0 Loss S0 – S If S < S0 Gain S0 – S

Profit Profit

S0 S S0 S

Loss Loss

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PAY OFF - FUTURES LONG & SHORT

PAY OFF - FUTURES POSITIONLong on Futures Short on Futures

Bought at F0, Currently at F Sold at F0 Currently at FIf F > F0 Gain F – F0 If F > F0 Loss F – F0 If F < F0 Loss F0 – F If F < F0 Gain F0 – F

Profit Profit

F0 F F0 F

Loss Loss

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HEDGING PRINCIPLE

Futures offset the risk by taking of an oppositeposition in the future contracts to that of in thephysical market.SHORT HEDGE

LONG on asset – Go SHORT on futures

LONG HEDGESHORT on asset – Go LONG of futures

Loss in the physical market is expected to becompensated in the futures position, and viceversa,

This assures almost a steady and assured price.

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SHORT HEDGE Asset and Futures

PAY OFF – SHORT HEDGELong on Asset Short on Futures

Bought at S0, Sold at S Sold at F0 Bought at FIf S > S0 Gain S – S0 If F > F0 Loss F – F0 If S < S0 Loss S0 – S If F < F0 Gain F0 – F

Profit Profit

S0 S F0 F

Loss Loss

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SHORT HEDGE



SHORT HEDGEEXAMPLE

SITUATIONOwned asset 1 Kg of GoldNeed to sell after 3 monthsRisk – falling price of asset, Need to cover risk andprotect value

MARKET SCENARIOSpot price of Gold, S0 = Rs 30,000Futures price at Exchange F0 = Rs 31,350

HEDGING STRATEGY

Long on Asset - Go Short of Futures

Sell 3-m futures contract on gold now (Size 1 Kg)with intentions of buy the same futures contract atthe end of hedging period, after 3 months.

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SHORT HEDGE



SHORT HEDGEOUTCOME

After 3 months

Sell gold in spot market and offset position in futures.

The price of the futures now would be same as spot due toconvergence.

ACTIONS Spot price decreases

to Rs 29,000

Spot price increases

to Rs 33,000

Sell gold in spot market 29,000 33,000

Buy futures back infutures exchange

29,000 33,000

Initial futures contract

sold at

31,350 31,350

Cash flow from futuresexchange

2,350 -1,650

Effective Price 31,350 31,350

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LONG HEDGE Asset and Futures

PAY OFF – LONG HEDGELong on Futures Short on Asset

Bought at F0, Sold at F Sold at S0 Bought at SIf F > F0 Gain F – F0 If S > S0 Loss S – S0 If F < F0 Loss F0 – F If S < S0 Gain S0 – S

Profit Profit

F0 F S0 S

Loss Loss

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LONG HEDGE



LONG HEDGEEXAMPLE

SITUATIONShort on asset, To buy 1 Kg of GoldNeed to buy after 3 monthsRisk – rising price of asset, Need to cover risk andprotect value

MARKET SCENARIOSpot price of Gold, S0 = Rs 30,000Futures price at Exchange F0 = Rs 31,350

HEDGING STRATEGY

Short on Asset - Go Long of Futures

Buy 3-m futures contract on gold now (Size 1 Kg)with intentions of sell the same futures contract atthe end of hedging period, after 3months.

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LONG HEDGE



LONG HEDGEOUTCOME

After 3 months

Buy gold in spot market and offset position in futures.

The price of the futures now would be same as spot due toconvergence.

ACTIONS Spot price decreases

to Rs 29,000

Spot price increases

to Rs 33,000

Buy gold in spot market - 29,000 - 33,000

Sell futures back infutures exchange

+ 29,000 + 33,000

Initial futures contract

bought at

- 31,350 - 31,350

Cash flow from futuresexchange

- 1,350 +1,650

Effective Price 31,350 31,350

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PAYOFF AND



PAYOFF ANDEFFECTIVE PRICE

SHORT HEDGEValue of asset owned S0 Sell Asset SSold futures F0 Bought back futures F

– Pay off = (S – S0) + (F0 – F) = (S – F) - (S0 – F0)

– Price realised = S + (F0 – F) = F0

LONG HEDGE

Value of asset short S0 Buy Asset SBought futures F0 Sold futures F

– Pay off = (S – S0) + (F0 – F) = (S – F) - (S0 – F0) – Price paid = S + (F0 – F) = F0

(F = S due to convergence)

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PERFECT HEDGE

Profit/loss in position of asset is completely offsetloss/profit in position on futures.

PERFECT HEDGELong Hedge Short Hedge

Profit Long Future Profit Long Asset

F0 Price F0 Price

Short Asset Short Future

Loss Loss

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BASIS AND BASIS RISK

Basis is defined as difference between spot priceand futures price at any point of time.

As contract approaches maturity the basisdeclines.

It becomes zero on the maturity.

Effective price is

Price paid/realised = S + (F0 – F) = F0

Since S ≠ F when hedge is lifted price would be

S + (F0 – F) = F0 + (S– F)

= F0 + Basis when hedge is lifted

The price risk gets replaced by basis risk

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HEDGE



HEDGEFORWARD Vs FUTURES

Forward hedge is always a perfect hedge as it is acustomised contract. Price is fixed now. Futures hedge is seldom perfect. Hedging through

the futures does not exactly and completely offsetsthe gains/losses in the cash asset.

Perfect hedge is not possible due to – Difference in the asset: The underlying asset may not besame as that of the futures. (Gold Ornaments vs. Gold)

– Differences in timing: maturity of cash position andfutures contract may not coincide exactly. (Need tobuy/sell Gold at 2.5 m Contract available for 2 or 3 m)

– Differences in quantity/amount: The amount ofexposure may not match with amount of futures contract.(Need to buy/sell 2.50 Kg Gold Contract available inmultiples of 1 Kg.)

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OPTIMAL HEDGE RATIO

Futures price moves according to spot priceand principle of convergence applies.

Is the relationship of futures price and spotprice perfect.

Is co-efficient of correlation, ρ = 1?? When cross hedge (Hedging through

related asset but not the same asset) isused co-efficient of correlation ρ would not

be 1 nor would be the changes in the priceof futures, σf and spot, σs.Optimum Hedge Ratio h* = ρ σs/σf

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DRM-2 Futures Pricing

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