Derivatives

DERIVATIVESPRESENTED BYSIMRAN KAUR

DERIVATIVESO Derivatives are instruments which

include (a) security derived from a debt instrument, share, loan, risk instrument or contract for differences or any other form of security and (b) a contract that derives its value from the price/index of prices of underlying securities

O Variants of derivatives are Forwards, Futures and Options

3 CATEGORIES OF PARTICIPANTS

O HedgersO SpeculatorsO Arbitrageurs

HEDGERSO Hedgers face risk associated with the

price of an assetO They use futures or options markets

to reduce/eliminate this risk

SPECULATORSO Speculators wish to bet on future

movements in the price of an assetO Futures and options contracts can

give them an extra leverage, that is, they can increase both the potential gains and potential losses in a speculative venture

ARBITRAGEURSO Arbitrageurs are in business to take

advantage of a discrepancy between prices in two different markets

O If, for example, they see the futures price of an asset getting out of line with the cash price, they will take offsetting positions in the two markets to lock-in a profit

ECONOMIC FUNCTIONS OF DERIVATIVES

O They help in the discovery of the future as well as current prices

O They transfer risk to those who have an appetite for them

O The underlying cash markets witness high trading volumes

O Speculative trades shift to a more controlled environment

O They help increase savings and investment in the long run

FORWARD CONTRACTO Forward contract is an agreement to

buy(long position) or sell(short position) an asset/security on a specified date for a specified price; settlement happens at the end of the period

O Other contract details like delivery date, price and quantity are negotiated bilaterally by the parties to the contract

FEATURES OF FORWARD CONTRACT

O They are bilateral contracts and, hence, exposed to counterparty risk

O Each contract is customer designed, and, hence, is unique in terms of contract size, expiration date and asset type and quality

O The contract price is generally not available in public domain

O On the expiration date, the contract has to be settled by delivery of the asset

LIMITATIONS OF FORWARD CONTRACT

O LiquidityO Counterparty risk (possibility of

default by any one party to the transaction)

FUTURE CONTRACTS/FUTURES

O Future contracts/Futures is an agreement between two parties to buy/sell an asset/security at a certain time in future; it follows daily settlement

O Futures are standardized and stock exchange traded

O It may be offset prior to maturity by entering into equal and opposite transaction

STANDARDIZED ITEMS IN FUTURES

O Quantity of the underlyingO Quality of the underlyingO The date/month of deliveryO The units of price quotation and

minimum price changeO Location of settlement

TERMINOLOGY IN FUTURES

O SPOT PRICE: The price at which an instrument/assets trade in the spot market

O FUTURE PRICE: The price at which the futures contract trade in the future market

O CONTRACT CYCLE: The period over which a contract trades

O EXPIRY DATE: The last day, specified in the futures contract, on which the contract will be traded, at the end of which it will cease to exist


O CONTRACT SIZE: The amount of asset that has to be delivered under one contract

O BASIS: The futures price minus the spot price

O COST OF CARRY: The relationship between futures price and spot prices can be summarized in terms of the cost of carry. This measures the storage cost plus the interest that is paid to finance the asset, less the income earned on the asset


O INITIAL MARGIN: The amount that must be deposited in the margin account at the time a futures contract is first entered into

O MARKING TO MARKET: In the futures market, at the end of each trading day, the margin account is adjusted to reflect the investor’s gain or loss depending upon the futures closing price


O MAINTENANCE MARGIN: This is somewhat lower than the initial margin. This is set to ensure that the balance in the margin account never becomes negative

PAYOFF FOR THE FUTURES

O Payoffs is the likely profit/loss that should accrue to the market participant with change in the price of the underlying asset

O Futures contracts have linear payoffsO Linear payoffs implies losses as well

as profits for both the buyer and seller of futures are unlimited

PRICING FUTURESO The Cost-of-Carry ModelO Pricing equity index futuresO Pricing stock futures

COST OF CARRY MODEL

O Cost of carry model explains the dynamics of pricing that constitute the estimation of the fair value of futures

O According to this model, using discrete compounding, where interest rates are compounded at discrete intervals, the price of the contract is defined as

F = S + C

COST OF CARRY MODEL

O Other formulae for the model includeF = SF = S

TERMS IN COST OF CARRY MODEL

O F = future priceO S = spot priceO C = holding costs or carry postsO r = cost of financingO T = time till expirationO e = 2.71828

PRICING EQUITY INDEX FUTURES

O Index futures is a future contract that gives the owner the rights/obligations to buy/sell the portfolio of stocks characterized by the index

O The differences between commodity and equity index features are : (i) There are no costs of storage involved in holding equity and (ii) equity comes with a dividend stream


O GIVEN EXPECTED DIVIDEND AMOUNT: The pricing of index futures is also based on the cost-of-carry model, where the carrying cost is the cost of financing the purchase of the portfolio underlying the index, minus the present value of dividends obtained from the stocks in the index portfolio


O GIVEN EXPECTED DIVIDEND YIELD: If the dividend flow throughout the year is generally uniform, it is useful to calculate the annual dividend yield

F = SWhere F = futures price, S = spot price, r = cost of financing, q = expected dividend yield, T = holding period

PRICING STOCK FUTURES

O Stock futures is a future contract that gives its owner the right/obligation to buy/sell the stocks(shares)

O The main difference between commodity and stock futures are that (i) There are no costs of storage involved in holding stock and (ii) Stocks come with a dividend stream


WHEN NO DIVIDEND EXPECTED: The pricing of stock futures is based on the cost-of-carry model, where the carrying cost is the cost of financing the purchase of the stock, minus the present value of dividends obtained from the stock. If no dividends are expected during the life of the contract, pricing futures on that stock is very simple. It simply multiplies the spot price by the cost of carry


WHEN DIVIDENDS ARE EXPECTED: When dividends are expected during the life of the futures contract, pricing involves reducing the cost of carry to the extent of the dividends. The net carrying cost is the cost of financing the purchase of the stock, minus the present value of dividends obtained from the stock

OPTIONS/OPTIONS CONTRACT

O Option/option contract is a contract that gives the holder the right but not the obligation to buy/sell an asset/security

O The purchase of option requires an up front payment

TERMINOLOGY IN OPTIONO STOCK OPTIONS: Options on individual

stocksO BUYER OF AN OPTION: One who by

paying the option premium buys the right but not the obligation to exercise his option on the seller/writer

O WRITER OF AN OPTION: One who receives the option premium and is thereby obliged to sell/buy the asset if the buyer exercises the option on him

TERMINOLOGY IN OPTIONO CALL OPTION: It gives the holder the

right but not the obligation to buy an asset by a certain date for a certain price

O PUT OPTION: It gives the holder the right but not the obligation to sell an asset by a certain date for a certain price

O OPTION PRICE/PREMIUM: Price that the option buyer pays to the option seller

TERMINOLOGY IN OPTIONO EXPIRATION DATE: The date specified

in the options contract is known as the expiration date, the exercise date, the strike date or maturity

O STRIKE PRICE: The price specified in the options contract

O IN-THE-MONEY OPTION: Option that would lead to a positive cashflow to the holder if it were exercised immediately

TERMINOLOGY IN OPTIONO AT-THE-MONEY OPTION: Option that

would lead to zero cashflow if it were exercised immediately

O OUT-OF-THE-MONEY OPTION: Option that would lead to a negative cashflow if it were exercised immediately

O INTRINSIC VALUE OF AN OPTION: The amount of option in ITM(In-the-money option)

TERMINOLOGY IN OPTIONO TIME VALUE OF AN OPTION:

Difference between its premium and its intrinsic value

OPTIONS PAYOFFO The optionality characteristics of

options results in a non-linear payoffO Non-linear payoff implies the losses

for the buyer of the option are limited but profits are potentially unlimited; profits to the writer of the option are limited to the option premium but losses are potentially unlimited

O Option premium is the price that the option buyer pays to the option seller

BLACK-SCHOLES OPTION PRICING

O Black and Scholes start by specifying a simple and well known equation that models the way in which stock prices fluctuate

O Also called Geometric Brownian Motion

O It implies that stock returns will have a lognormal distribution, meaning that the logarithm of the stock’s return will follow the normal (bell-shaped) distribution


O The option’s price is determined by only two variables that are allowed to change: time and the underlying stock price

O The other factors, namely, volatility, exercise price and risk free rate do affect the option’s price but they are not allowed to change


Black-Scholes formulae for the prices of European calls and puts on a non-dividend paying stock are C = SN(N( P = Xwhere

TERMS IN BLACK-SCHOLES OPTION PRICING

O N() is cumulative normal distributionO N(O σ is a measure of volatilityO X is the exercise priceO S is the spot priceO T is the time to expiration measured

in years

FACTORS AFFECTING OPTION PRICES

O STOCK PRICE: The payoff from a call option will be the amount by which the stock prices exceeds the strike price

O STRIKE PRICE: In the case of a call, as the strike price increases, the stock price has to make a larger upward move for the option to go in-the-money

O TIME TO EXPIRATION: Both put and call options become more valuable as the time to expiration increases

FACTORS AFFECTING OPTION PRICES

O VOLATILITY: The volatility of a stock price is a measure of how uncertain we are about future stock price movements

O RISK FREE INTEREST RATE: The affect of the risk free interest rate is less clear cut

O DIVIDENDS: They have the effect of reducing the stock price on the ex-dividend date. This has a negative affect on the value of call options and a positive effect on the value of put options

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Economy & Finance

Derivatives