Derivatives - IX

Pricing of options, that is calculation of premium, can be done under various methods. Black-Scholes Model and the Binomial Model are the most commonly used methodologies for theoretical calculation. If actual premium is different, derivative traders become active enough to make the actual price converge with the model outputs. However, the assumptions regarding interest rate and volatility may be different for some traders. Such traders are normally more active.

Many calculators are available for finding the theoretical premium for call and put options. Here is one such:

http://www.fintools.com/resources/online-calculators/options-calcs/options-calculator/

It will be interesting to modify various assumptions and look at the impact on option prices.

Derivatives - VIII

1) Futures contracts create obligations, not rights.

2) Only the option buyer gets rights.

3) Options seller is also known as writer.

4) Futures price = Cash price + carry charges

5) Cash price minus Futures price = Basis.

6) Maximum possible profit to the option seller = Premium

7) Neither intrinsic value nor time value can be negative.

8) Beta is a measure of systematic risk.

9) Longer the time to expiry, more will be the time value.

10) Short Futures = Long Put + Short call.

Derivatives - VII

The long and short of Hedging:

Hedging through futures may involve either buying or selling an asset in the futures market. Purchase in the Futures market is called as 'Long Hedge'. If hedging is done by selling in the futures market, it is called as 'Short Hedge'.

For example, you may have a lot of money with you and you may also want to buy a particular share. If you buy in the spot (cash) market, the price may go up immediately and you may get less number of shares. So, you buy from the futures market. Then, slowly as and when you make cash purchases, you unwind your futures position. This is 'long hedge'.

Similarly, if you have many shares to sell, you may sell them in the futures market so that the cash price is not brought down. This is 'short hedge'.

If there is no futures market for a particular item, you may enter into contracts for a similar product like diesel instead of aviation turbine fuel (ATF). This is called as 'Cross Hedge'. The assumption is the prices of diesel and ATF will move in a similar fashion.

Derivatives - VI

Hedging through Futures: Hedging means protecting one's portfolio from impact of market changes. This amounts to giving up or shedding risk.

Any asset (including an equity share) is subject to two kinds of risk: one is called Specific Risk that relates to its inherent risk and the other is Systematic Risk or Market Risk. If you own Tata Steel share, consequences of Tata Steel management's business style is the specific risk. Consequences arising from factors which affect all companies and not Tata Steel alone form the Market Risk or Systematic Risk.

If you want to give up specific risk without selling the share, you will have to 'diversify' your holdings (portfolio) so that you are less affected by factors that impact Tata Steel exclusively. If diversification is random and large enough, you may completely shed the specific risk of owning Tata Steel share.

But, diversification does not reduce market risk. One indicator of market risk in the equity market is what happens to a particular share's price when the index (say Nifty) moves up or down. This indicator or relationship is called 'beta'. Beta of a share is 1 if there is the same percentage change in the price of share as the change in index, say Nifty. If Nifty increases by 5% and the share's price also increases by 5%, we say that the beta of this share is 1. If the price of share goes up by 10%, it means beta is 2.

Nifty index can be bought and sold in the market. Suppose the Nifty index is now Rs.8,000. If Nifty moves up by 5%, Nifty index will be worth Rs.8,400. If you had shares worth Rs.4,000 when Nifty index was Rs.8,000 and beta of your shares is 2, your shares will be worth Rs.4,400 after Nifty has increased by 5%. This means that the increase in the value of your shares is the same as increase in the price of Nifty index.

Concept of 'beta' is made use of to hedge against market risk. In the example given above, if you sell one Nifty index in the Futures market (i.e. short one Nifty index futures), what you gain from owning shares would be offset by what you lose in the Nifty Futures sold. Similarly, if you lose from your share holdings, you will gain the same amount from the Nifty Futures sold. This is an example of 'perfect hedge'. Depending on your capacity and willingness to absorb market risk, you may opt for partial hedges.

When you own a collection (portfolio) of shares of different companies, beta of the portfolio is the weighted average beta of all shares, the weights being the market values of shares.

'Hedge Ratio' means the number of Nifty indices you need to short in order to neutralise or shed market risk totally. This is equal to Market value of portfolio multiplied by beta of portfolio and divided by value of Nifty index. (Note: Nifty index is taken as an example. Similarly, you can consider Sensex as an index or midcap index or any other index. It should however be noted that beta of a share will be different depending on the index. In addition, beta changes over time.)

Derivatives - V

Synthetic Options: A synthetic option is a combination of two or more options to yield a particular risk profile. That is, the risk profile that will be generated by one option is sought to be generated by combining multiple options. This enables greater flexibility in owning different risk profiles by withdrawing from certain options depending on evolving situations.

Different risk profiles and their synthetic options are given below:

1) Long Call = Long Put + Long Future

2) Short Call = Short Put + Short Future

3) Long Put = Long Call + Short Future

4) Short Put = Short Call + Long Future

5) Long Future = Long Call + Short Put

6) Short Future = Short Call + Long Put

Note: Above equations show the relationship among Call option, Put option and Futures. Cost in the form of premium is ignored. We are considering only the gross pay-off profile. Long means purchase, Short means sale.

Derivatives - IV

Options: An option contract is said to be ITM (in-the-money) if the option holder would exercise the option if it is the expiration day. Thus, a call option with strike price of Rs.40 is ITM if the ruling spot price is more than Rs.40. This means that the option holder will but the asset at Rs.40 and sell it at the prevailing price and thus make profit.

For a put option to be ITM, spot price has to be lower than the strike price. The following table explains the terms ITM, OTM (Out of - the - money) and ATM (at - the - money).

Situation                                                   Call option                                            Put option

1) Strike price > spot price                             OTM                                                 ITM

2) Strike price = spot price                             ATM                                                 ATM

3) Strike price < spot price                             ITM                                                   OTM


Premium: Premium is the price paid by the option buyer to the option seller.Premium is Value of the option.
Option's value consists of two elements namely intrinsic value and time value also known as extrinsic value.

Intrinsic value means the amount to which an option is ITM. Time value represents the additional profit potential that the remaining time to expiry of option is likely to create for the option holder. Hence, as time to expiry nears, time value drops.

Premium = Value = Intrinsic value + Time value. (If a call option premium = Rs.6, Strike price = Rs.40, Spot price = Rs.42, then Intrinsic value of the call option = Rs.2, time value = Rs.4)

Neither intrinsic value nor time value can be negative. They are either positive or zero.

For an OTM or ATM option, there is no intrinsic value. So, for an OTM or ATM, premium = time value.

Following consequences are note-worthy:

1) When an option is ATM, it commands the highest time value.
2) At the time of an option's expiry, the entire value is intrinsic only.
3) Fall in time value occurs at an accelerated pace as expiry draws near.
4) Extreme ITM or OTM option commands negligible time value.

Derivatives - III

Futures Contracts: A buyer gets into the Futures market in order to ensure that a particular asset will be available at the expected time of his need. Similarly, a seller participates in the Futures market to be in a position to dispose of an asset at a time convenient to him.

A manufacturer who needs a raw material for production two months from now may decide to ensure availability of the raw material with a definite price through a two-months Futures contract. What will be the price specified in this contract?

The manufacturer has two choices: 1) He can buy the raw material right now and preserve it for two months before using it or 2) He can get into the Futures contract in which case he will pay the price after two months. If he buys it right now, he has to pay the spot price, incur interest on this price for two months and also bear storage charges.

These two choices will involve the same cost because otherwise the costlier choice is no choice at all. (If the cost is different in these two choices, there will be 'arbitrage' possibility.)

So spot price + interest + storage charges = Futures price.

Sometimes, the asset under consideration may produce some income in the interval between now and the Futures period. A typical example is an equity share which may generate dividend in the intervening period. This income is to be deducted from cost to arrive at the Futures price. To calculate the Futures price more accurately, compounding at relevant interest rate has to be done for costs incurred and incomes received at different times.

Futures price will normally be higher than the present spot price. The difference between the spot price and the Futures price is called the 'Basis'. In a normal market , also called as 'contango' market, Basis is negative. If Futures price is less than present spot price, Basis is positive and such a market is called as 'backwardation' market.

Derivatives - II

Futures / Forward contracts are agreements to buy and sell (one party will buy and another will sell) an asset at a pre-determined price on a fixed future date. Agreements transacted through an exchange are called Futures contracts whereas agreements between two parties, that is a buyer and a seller, without the intervention of an exchange are known as Forward contracts.

Option contract is a right that the option buyer gets from the option seller also called the option writer to buy or sell an asset at a pre-determined price called the strike price during or at a particular time in future. Thus, the option buyer gets a right to buy or sell depending on the contract. Option contract that gives the right to buy an asset is known as call option; the contract that gives the right to sell an asset is called as put option. The option buyer purchases the right from the option writer by paying a price to the writer. This price is called the premium of the option. The day on which the option contract expires is called expiration day of the option. If the right to buy or sell can be exercised only on the expiration day, such an option is termed as 'European option'. If the right is exercisable on any day upto the expiration day, the option is called as 'American option'. So, the option buyer gets a wider window of time to exercise his / her option under American option.. Therefore, it stands to reason that American options attract higher premiums. In the Indian stock markets, only European options are allowed. Exercise day is the day on which the option is exercised. In case options are not exercised (this happens when the price movement is not favourable to the option buyer or the option holder), exercise day does not arise.

Swaps*
Another important class of derivative security are swaps, perhaps the most common of which are interest rate swaps and currency swaps. Other types of swaps include equity and commodity swaps. A plain vanilla swap usually involves one party swapping a series of  fixed level payments for a series of variable payments.
Swaps were introduced primarily for their use in risk-management. For example, it is often the case that a party faces a stream of obligations that are floating or stochastic, but that it will have to meet these obligations with a stream of fixed payments. Because of this mismatch between floating and fixed, there is no guarantee that the party will be able to meet its obligations. However, if the present value of the fixed stream is greater than or equal to the present value of the floating stream, then it could purchase an appropriate swap and thereby ensure that it can meet its obligations. (*Acknowledgement: Description of Swaps is taken from www.columbia.edu IEOR E4706: Financial Engineering: Discrete-Time Models °c 2010 by Martin Haugh)

Derivatives - I

What is a derivative? It is a contract whose value depends on an underlying asset. This means that a derivative does not have an independent value. It gains more value as the underlying asset gathers value.

What is an underlying asset? The underlying asset is the subject matter of derivative. Such an asset may be an equity share, a currency, a commodity, a fixed rate debt instrument or a loan (credit).

Derivatives can be broadly classified into financial derivatives and commodity derivatives.

In addition to classification based on type of underlying asset as above, we may classify derivatives in the following ways also:

1) Relationship between the underlying asset and the derivative: Forwards / Futures, Options and Swaps.

2) Market: Exchange-traded derivatives and Over the Counter (OTC) derivatives.

3) Purpose: Speculative, Hedge and Arbitrage

4) Payoff profile: In the Money (ITM), Out of Money (OTM) and At the Money (ATM) derivatives.

5) Payoff profile II: Linear and Non-linear derivatives.

Objective: Derivatives are normally considered as tools for Risk Management. When they are misused, knowingly or unknowingly, they have the potential to become what Warren Buffett calls as 'Financial Weapons of Mass Destruction'. Examples: 1) Nick Leeson of Barings Bank (1995), 2) Jerome Kerviel of SocGen (January, 2008), 3) Kweku Adoboli of UBS (Sept., 2011)