Derivative

Derivative


Derivatives are financial instrument whose values depend on the value of the other, more basic un-derlying assets.

1. They do not value of their own.

2. They derive their value from another assets or multiple of assets.

A stock index like nifty is also a derivative on multiple assets as the value of the index is derived from the basket of stocks that constitute the index.

Motivation to use derivatives



The real motivation to use derivatives is that they are useful in relocating risk either across time or across individuals with different risk bearing preferences.

Types of derivatives

Derivatives are basically classified into two based upon mechanism that is used to trade on the them. They are the over the counter derivatives and exchange traded derivatives. The OTC deriva-tives are the between two private party and designed to suite the requirement of parties con-cerned. The exchange traded one are standardized one where the exchange sets the standard for trading by providing the contract specifications and the clearing corporation provides the trade guarantee and the settlement activities.

Futures

A future contract is agreement to buy or sell an asset at the certain future time for a certain price.



The future contract is similar to a forward contract conceptually but differs in mechanism the contract is executed. The attributes on which the future contracts differs from forwards are

Attributes Forwards Futures

Contract type Privately trade Exchange traded

Contract term Customized Standard

Price transparency Poor Good

Price discovery Poor Good

Liquidity Poor Good

Credit risk High low

Type of futures

The type of futures that are traded fall into four fundamentally different categories. The underlying asset traded may be a physical commodity foreign currency, an interest earning asset or an index, usually a stock index . As we are going to see the index based future in-troduced in the market, we shall restrict our discussion to index based futures.



Risk Management in futures

As the futures are exchange traded, clearing corporation of exchange by granting cre-dit guarantee nullifies the counterparty risk. Also the strict margining system followed in the future market worldwide, reduces the default risk associated with futures. The general margining system that is follows in the future market is as follows.

Depending on the position taken an initial margin is charge on the investor . this is deter-mined by exposure limit assigned by the investor. This can be interpreted as an advance payment made to take larger position. For example exposure limit is 33 times the base capi-tal given by the investor, then it means that an initial margin of 3.33 is required.

More than the initial margin collected, the net profit or loss on a position is paid out to or in by investor on the very same day in the form of daily mark to market (MTM). The MTM is made compulsory to remove any default on large losses if the position is accumulated for several days. Calculating the net loss associated with a postion does the calculation of MTM margin. This is paid up each evening after trading end. The focus is on calculating the net loss on all contracts enterd by the clients.



Purpose of future markets

Traditionally future market are recognized to meet the folloeing the needs,

Price discovery: the future market helps in revealing information about the future cash mar-ket prices thereby serving the social purpse by helping people make better estimates of future prices So that they can make their inevestment decision more widely.

Hedging: Future are traded as a substitute for a cash market transaction, thereby reducing the risk of the investor for his position in the cash market.



Pricing of the futures

Future price is linked to spot price of underlying commodity. There is a strong correlation between futures and spot prices of the underlying asset. The difference is due to the cost of carrying it till the specified expiry date , the demand supply gaps, various market and eco-nomic forces. Future price immediately incorporate and absorb any information related to the underlying asset.

Future price can be written as

Future price = cash price + cost-of- carry

Price of stock index future = Spot Index + cost of funding- Dividend income



Feature of nifty index futures

NSE offers index based and scrip based futures in more than 200 stocks.

Features NSE

Underlying Index S&P CNX NIFTY

Trading cycle Maximum 3 month, the near month (one), the next month (two)and the far month (three)

Expiration Last Thursday of expiry month

Contract Size 50 and multiple thereof

Settlement Cash

System Screen



Future trading Strategies



Arbitrage and NIFTY futures

Arbitrage is the opportunity of taking advantage of the price difference between two mar-ket. An Arbitrageur will buy at the cheaper market and the sell at costlier market. It is possi-ble tp arbitrage d between nifty in the future market and cash market > If the future prices given bellow other than equilibrium price then the strategy to be followed is

Note: the arbitrage opportunity arising when the future price is underpriced to cash price is not feasible, If the arbitrageur does not hold the script or borrowing of script is not possible in the market. This is because the delivery in the spot market comes before the delivery in the future market.



hedging with Nifty Futures

Case 1

Short hedge

Let us assume that an investor is holding a portfolio of the following s script as given bellow on 1st December 2007.

Company

Beta

Amount of Holding (in Rs)

Infosys 1.55 400000



Bhel 2.06 200000

LT 1.75 375000

Reliance 2.15 225000

Bharti Airtel 1.95 150000

Total Value of Portfolio 1350000



Trading strategy to be followed



The investor feels that the market will go down in the next two month and want to protect him from any adverse movement. To achieve this the investor has to go short on 2 month nifty futures i.e. he has to sell June nifty. The strategy is called short hedge.

Formula to calculate the no. of futures for hedging purpose is



Beta of adjusted value of portfolio / nifty index level



Beta of the above portfolio = (1.55*400000)+(2.06*200000)+(1.75*375000)+(2.15**225000)+(1.95*150000) / 1350000



1.82556 (round to 1.83)



Applying the formula to calculate the no of contracts

Assume nifty future to be 5733 on 1st December, 2007

= (1350000*1.83) / 5733

= 430.926 units

Since the nifty contract is 50 units the investor has to sell 8.618 or 9 contracts.

Short hedge

Stock market Future market

1st November Holds Rs 1350000 in stock port-folio Sell 9 Nifty contract at 5733

20th December Stock portfolio fall by 6% to Rs 1269000 Nifty Future falls by 5% to 5466.35

Profit / Loss Loss – Rs 81000 Profit – Rs 128992.50

Net Profit - 128992.50 – 81000

47992.50



Case 2

Long Hedge

Let us assume that an investor feels that the market is at beginning of a bull run. He is ex-pecting to get 1500000 in 2months. Waiting two month to invest could mean that He might miss bull run altogether. An alternative to missing the market move is to use nifty future market. The investor could simply buy an amount of nifty futures Contract that would be equal lent to Rs 1500000. This strategy called long hedge.

Let’s assume that on 1st December 2007 The nifty Futures stand at 5733. He expect to get Rs. 1500000 By Jan End . He has 2 months Jan Nifty in December. The No. of contract he should buy is 1500000/ (5733*50) = 5.232 (round to 5 Contract)





Stock Market Future Market

1st December The investor Expect Rs 1500000 in two months Buys 5 contracts at 5733

15th Jan 1500000 Become available for investment The market has risen and Nifty Futures stand at 5865

The investor will invest Rs 1500000 in the market but will not get the same amount of shares as on 1st December 2007 Future Profit: Rs 33000.00





Speculation with NIFTY futures

Futures contract allow the speculator to speculate on the movement of the direction of the futures price. Other than the direct speculation where the speculator takes a view on the market and trades accordingly, in the futures contract on can speculate on the spread available between the quotes of the futures contract of two different calendar periods.

Important terms in futures



Basis: It is the current cash price of the underlying asset minus the price of particular futures contract for the same asset

Basis = Current Cash Price — Futures Price

Contango: This is the situation where the futures price is above the expected future spot price.

Normal Backwardation: This is the situation where the futures price is below the expected future spot price

Backwardation: A Market is said to be in backwardation at a given moment if the cash price exceed future price or if a nearby futures price exceeds a distant futures price.



Calendar Spread: A Calendar spread Is a position at one maturity which is hedged by an offsetting position at a different maturity: for example, a short position in a one month contract coupled with a long position in the two month contract. If the underlying asset rises, one leg of the spread loses mon-ey while the other gains money resulting in a hedged position.



Open Interest: It is the total number of net open contracts available at any point of time

Option Feature

In other contracts, the focus is on underlying asset and each counterpart has right and obligation (r&O) to perform. For example, in futures contract, the buyer has the right and obligation to buy; and seller, the right and obligation to sell.

Option contract differs from others in two respects. The primary focus is on r&o, not on underlying asset. Second, the r&o are separated, with buyer taking the right without obligation (r w/o 0) and sel-ler taking the obligation without right. Thus, the distinguishing feature of option is the right-without-obligation for the buyer.

In option contract, what the buyer buys is the right, not the underlying asset; and what the seller sells is the right, not the underlying asset.

The privilege of r w/o o has a price, called the option price (or premium) and is paid by the buyer to the seller upfront. In return for receiving the option price from buyer, the option seller grants the privilege of r w/o o. It should be noted that option price is totally different from the price of underlying asset.

Option Type

Option type defines the nature of buyer’s right, which can be

• . Right to buy the underlying asset, which is called the call option; or

• . Right to sell the underlying asset, which is called the put option.

The buyer will exercise his right only if it Is favorable to him. If It is not, he will not exercise his right because he has no obligation. Thus, the underlying asset moves from to another only when the option is exercised. When it moves from one counterpart to another, its price (in cash) must move in the opposite direction. The amount of price in cash is fixed at the time of contract and is called the strike price (K) or exercise price.



Note: that option price is the price of the privilege of r&o whereas strike price is the price of underlying asset. Further, option price is paid by the buyer to seller with certainty whereas the strike price paid only if the option is exercised at the discretion of the buyer.

We can see from the exhibit above that option seller is actually buying the asset if the option exercised is put option. We may say that the option seller is actually underwriting the risk on the underlying asset, and he may be seller or buyer of the underlying asset. For this reason, the option seller is called option writer.

The buyer’s privilege of r w/o o has a limited life, called the expiration date (7), after which the option expires.

Option Style

Option style defines when can the buyer exercise his right on the underlying asset. If he can exercise only on the expiration date of the option, it is European style; if he can exercise any-time during option life, it is American-style







The option contract can now be formalized. It specifies the following.

• . Underlying asset

• . Nature of buyer’s r w/o o (ie, option type)

• . Price of r w/o o (ie, option price)

• . Exercise time (le, option style)

• . Price of underlying asset in exercise (ie, strike price)

• . Expiration date of option







Option Status

Option status defines the benefit to buyer from exercising the option. The status could be as fol-lows.

• . Profit from exercise: the status is called in-the-money (itm)

• • Loss from exercise: the status is called out-of-the-money (otm)

• • No Profit, No Loss: when the status is called at-the-money (atm)

Given his right without obligation, the buyer will exercise only those options that yield profit and let all others expire. In other words, only tm options are exercised; and otm and atm options expire unexercised.

4 The market convention is to call exercise for buyer and assignment for writer. In other words, buyer makes the exercise and it becomes assigned to writer.

The option status naturally depends on the market price of the underlying asset (S), strike price (K) and option type. It is important to note that option price is not taken into account in determin-ing option status. In other words, exercising ttm option does not necessarily result in net profit; and exercise profit and net profit are not synonymous. We can only say it will be exercised. The following example illustrates the point.

Current market price of under lying asset (5): 100

Price of call option (C):

9

Price of put option (P):

7



Type K Status Exercise Benefit Profit

Call 90 itm [ Yes 10 1

Call 100 atm No 0 -9

Call 110 otm No 0 -9

Put: 90: otm No 0 -7

Put 100 atm No 0 -7

Put 110 itm Yes 10 3





Option Exposures

In cash and futures market, we have only two exposures: buy asset (long) or sell asset (short). Since there are two option types, and each can be bought or written, we have a total of four expo-sures as follows





Exposure Meaning Implication Exposure on exer-cise

Long Call (lc) Buying call Right to buy underlying as-sets Long underlying asset

Short call(sc)

Writing call

Obligation to sell underlying asset

Short underlying asset



Long put (lp)

Buying put

Right to sell underlying as-sets

Short underlying asste



Short put (sp) Writing put Obligation to buy underlying asset Long underlying asset





Thus, ‘long’ option means having the right, and “short’ option means having the obligation. Fur-ther, Sc and Ip result in the same exposure in the underlying asset, namely long, when the option Is exercised. Similarly, long call and short put result in long underlying asset when exercised. There is a crucial difference, however. When you are long on option, you control the exercise. When you are short on the option, you cannot control the exercise.









Option Payoff

Given that “long” means buying option and that the buyer has r w/o o, the long option has “limited loss and unlimited profit.” If the market moves unfavorably, the buyer will not exercise his option, and his loss will be limited to the option price paid. If the market moves favorably, the buyer will exercise his option and the profit will be proportional to extent of price move.

Similarly, for short option (ie, for option writer), the payoff is “limited profit, unlimited loss”:

profit is limited to the option price received and the loss is proportional to the extent of price move.



Option Payoff

The “limited loss, unlimited profit” for long options is inappropriate or even erroneous. We should always consider three jointly: payoff, its size and its probability. Never consider them in isolation. For example, the loss may be limited but its size may be large or its probability high or both. In such a case, the limited loss is actually a guaranteed loss. Similarly, the profit may be unlimited but its probability is so low that it may never occur.







Option is a Wasting Asset



The unusual and important feature of option is that it loses value over time. It loses part or total value over time regardless of whether the price move is favorable or unfavorable. This is called time-decay in option value, which favors the option writers and works against option buyer. For this reason, option buyer should not stay with option until expiration date, but should get out of it either through exercise or sale in option market.

Option Price

Option price consists of three components:

o o Intrinsic value (iv)

o o Leverage (I)

o o Option value (ov)



Intrinsic Value

Intrinsic value (iv) is the benefit to buyer from exercise. It is the positive difference between mar-ket price of the underlying asset (5) and strike price (K) of option.

iv (call) = S — K :buyer pays (ie, outflow) cash amount K and receives (ie, inflow) asset worth S

lv (put) = K — S :buyer gives asset (ie, outflow) worth S and receives (ie, inflow) cash amount K

The above expression needs some modification. Since option buyer has the right without obliga-tion, he will exercise only if there is benefit. If there is not benefit, he will not exercise. Therefore,

iv (call) = Maximum[O, S — K]

iv (put) = Maximum[O, K — 5)

Leverage

Leverage refers to the interest on strike price during option life. Let us examine call. The call buy-er has the right to buy asset by paying a fixed price of K. By postponing the exercise until expira-tion date, the can deposit K and earn interest at the market rate (r). Therefore, the call price must be increased by the interest earned on K duping option life. This is roughly the cost-of-carry im-plicit between cash and futures price.

For put option, the leverage works in the reverse. In exercise of put option, it is the put buyer who receives cash amount K from put writer. By postponing the exercise until expiration date, the put buyer is deprived of earning interest on K. Therefore, the put price must be lowered by this amount.

How to quantify leverage component? Since by definition, K is payable at expiration date, we will have to use the discounted price of K, and deduct it from K.

L = K – Ke-rt

where t- is the (annualized) market interest rate and T, the option life (in years) and e, the base of natural logarithm to compute the continuous discounting factor. As time passes, leverage compo-nent shrinks and totally disappears at expiration date.



Option Value

Option value (ov) accounts for the option feature, which is right without obligation for the option buyer. It is the price of this privilege and accounts for limited loss for option buyer in case the market moves unfavorable to him.

Option value is linked to the volatility (or risk) of the underlying asset. Statistically, it is calcu-lated as the standard deviation of log price relatives. This is the only component in option price that requires fairly sophisticated amount of math and statistics. As time passes, the option value becomes less and less and disappears at expiration date. For example, the option feature is more valuable in 30-day option than in 10-day option, because the chance of favorable move in 30 days is much higher than in 10 days. At expiration, there is no chance of price moving favorably in fu-ture because the option expires now. This decay on option value over time is the reason why the option is a wasting asset.

As the expiration date approaches, both I and ov components decay and disappear; and at expira-tion, only iv remains. The decay is smooth for I but more complicated and curvy for ov. We can now summarize the components in option price, before and at expiration, as follows.

Before expiration:

Call Price = Intrinsic Value + Leverage + Option Value

Put Price Intrinsic Value — Leverage ÷ Option Value (Leverage is negative) At Expiration

Call Price and Put Price = Intrinsic Value

Since intrinsic value and leverage can be readily calculated, we can restate the above as follows for option price before expiration.

Call Price = Maximum [0, S - K) + (K — Ke-rt) + ov

Put Price = Maximum[O, K — 5] — (K — Ke-rt) + ov

The above two equations show the option price determinant. They are as follows.

5: Current market price of the underlying asset, which is readily obtained from cash market

K: Strike price, which is fixed by option contract

r: Interest rate on risk-free assets such as treasury bill, which is obtained from money market

T: Option life, which is fixed by option contract

ov: This is determined by volatility of underlying asset in a complex manner

Of the five price determinants above, only volatility or ov is not readily observed. It has to be computed statistically and involves some amount of subjective estimation. All others can be objec-tively determined and same to all market participants.







Disclaimer: Although all precautions has been taken care to write this documents. However au-thor is not responsible for any information.

© 2007 Indux Investment