Options

Presented by Vishakh S

Vishnu Sankar SNeethu Satheesh

What are options?

• An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time.

What is the single most importantcharacteristic of an option?

• It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.

Every option has four specific features:

1. It relates to a specific stock or other security, called the “underlying” security.”

2. It is a right to buy (call) or sell (put), and every option controls 100 shares of stock.

3. A specific “strike” price is the fixed price at which the option can be exercised.

4. Every option has a fixed expiration date. After that date, the option is worthless.

Two types of Options:• Call Option: Gives the holder right to buy an assets at certain price within the specific

period of time.• Put Option: Gives the holder right to sell an assets at certain price within the specific

period of time.

CALL AND PUT OPTIONS

• A call option is a financial contract between two parties, the buyer and the

seller of this type of option. It is the option to buy shares of stock at a

specified time in the future. Often it is simply labelled a "call". The buyer of

the option has the right, but not the obligation to buy an agreed quantity of a

particular commodity The buyer pays a fee (called a premium) for this right.

• Put Option is just opposite of the Call Option which gives the holder the

right to sell shares. A put becomes more valuable as the price of the

underlying stock depreciates relative to the strike price.

Merits Of Option

• Options protect downside risk to the buyer• The buyer of the option limits losses to the

premium paid on the purchase of the options• Eg. If I buy a nifty 2900 put at Rs 34, my loss is

limited to Rs 34 while gain potential is limitless • If the price goes above Rs 2900 I do not

exercise the option limiting my loss to the premium paid.

Option Terminology

• Call option: An option to buy a specified number of shares of a security within some future period.

• Put option: An option to sell a specified number of shares of a security within some future period.

• Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold.

• Option price: The market price of the option contract.

• Expiration date: The date the option matures.• Exercise value: The value of a call option if it

were exercised today = Current stock price - Strike price.Note: The exercise value is zero if the stock price is less than the strike price.

• Covered option: A call option written against stock held in an investor’s portfolio.

• Naked (uncovered) option: An option sold without the stock to back it up.

• In-the-money call: A call whose exercise price is less than the current price of the underlying stock.

• Out-of-the-money call: A call option whose exercise price exceeds the current stock price.

• LEAPS: Long-term Equity AnticiPation Securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years.

Consider the following data:

Strike price = $25.Stock Price Call Option Price

$25 $3.00 30 7.50 35 12.00 40 16.50 45 21.00 50 25.50

Exercise Value of Option

Price of stock (a)

Strike price (b)

Exercise valueof option (a)–(b)

$25.00 $25.00 $0.0030.00 25.00 5.0035.00 25.00 10.0040.00 25.00 15.0045.00 25.00 20.0050.00 25.00 25.00

Market Price of Option

Price of stock (a)

Strike price (b)

Exer.val. (c)

Mkt. Price of opt. (d)

$25.00 $25.00 $0.00 $3.0030.00 25.00 5.00 7.5035.00 25.00 10.00 12.0040.00 25.00 15.00 16.5045.00 25.00 20.00 21.0050.00 25.00 25.00 25.50

Time Value of Option

Price of stock (a)

Strike price (b)

Exer.Val. (c)

Mkt. P of

opt. (d)

Time value

(d) – (c)$25.00 $25.00 $0.00 $3.00 $3.0030.00 25.00 5.00 7.50 2.5035.00 25.00 10.00 12.00 2.0040.00 25.00 15.00 16.50 1.5045.00 25.00 20.00 21.00 1.0050.00 25.00 25.00 25.50 0.50

Call Time Value Diagram

What happens to the premium of the option price over the exercisevalue as the stock price rises?

• The premium of the option price over the exercise value declines as the stock price increases.

• This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.

What are the assumptions of theBlack-Scholes Option Pricing Model?

• The stock underlying the call option provides no dividends during the call option’s life.

• There are no transactions costs for the sale/purchase of either the stock or the option.

• RRF is known and constant during the option’s life.

• Security buyers may borrow any fraction of the purchase price at the short-term risk-free rate.

• No penalty for short selling and sellers receive immediately full cash proceeds at today’s price.

• Call option can be exercised only on its expiration date.

• Security trading takes place in continuous time, and stock prices move randomly in continuous time.

Black-Scholes Option Pricing Model

funds invested of

cost yOpportunit

potential upside

of Value

price

Call

)()( 21 dNe

XdNSC

rt

Where C: current price of a call option S: current market price of the underlying stock X: exercise price r: risk free rate t: time until expiration N(d1) and N (d2) : cumulative density functions for d1 and d2

Example Current stock price: 50 exercise price : 55Risk free rate: 6.25% time to expiration: 6 monthsVolatility: 40% What is the call price?

Solution

0851.02828.0

0713.00953.05.04.0

5.04.05.00625.05550lnd

2

1

3679.0

5.04.00851.0d 2

N(d1) = 0.4661 N(d2) = 0.3564

30.4$]3564.0[55

]4661.0[50

)()(price Call

)5.0)(0625.0(

21

e

dNe

XdNS

rt

What impact do the following para-meters have on a call option’s value?

• Current stock price: Call option value increases as the current stock price increases.

• Exercise price: As the exercise price increases, a call option’s value decreases.

• Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.)

• Risk-free rate: Call option’s value tends to increase as rRF increases (reduces the PV of the exercise price).

• Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).

Six basic strategies

Six option strategies are especially interesting in the way they allow you to leverage capital, reduce risks, and control shares of stock.

These six are:

1. Covered call. 2. Ratio write. 3. Variable ratio write. 4. Insurance put. 5. Collar. 6. Synthetic stock.

Six basic strategies

These strategies share a few common themes and attributes. These are:

- They can be constructed with conservative goals in mind: reducing or eliminating risk and hedging long positions in your portfolio.

- The positions either eliminate risk or generate income.

- The level of capital placed at risk can be controlled by offsetting long and short positions, or limited by selecting modestly priced options.

Covered call

A covered call has two parts: - ownership of 100 shares of stock - 1 short call

A “short” call is created by selling it. When you sell a call you receive cash.

A short transaction is sequenced as “sell-hold-buy” instead of the more familiar long position, “buy-hold-sell.”

Covered call

A covered call becomes profitable if the underlying security remains at or below the strike.

In that case, the call will expire worthless, or it can be closed (bought) at a lower price.

If the underlying security moves above the strike, the call will be exercised and your stock will be called away.

Being exercised is profitable as long as your original cost of the stock was lower than the strike. In that case, you earn a capital gain, the option premium, and any dividends during your holding period.

Ratio write

The ratio write is an expansion of the covered call. Instead of 1 call per 100 shares, you write more calls than you can cover.

For example, if you own 200 shares and sell 3 calls, you create a 3:2 ratio write. If you own 300 shares and sell 4 calls, you create a 4:3 ratio write.

Although this strategy is higher-risk than a covered call, some or all of the exposed calls can be closed to avoid exercise.

Variable ratio write

This a further expansion of the covered call. In the variable ratio write, you use two different strikes.

For example, the stock price is $49 and you own 300 shares. If you sell two $50 calls and two $52.50 calls, you have created a variable ratio write.

Insurance putThis strategy protects your stock position against the risk of loss. A put is the

right to sell stock at a fixed price.

For example, you bought stock at $45 and it is now worth $49. You sell a 50 put and pay 2 ($200).

If the stock falls below 50, you can exercise the put and sell it at the fixed strike of 50. However, because the put cost you $200, your breakeven is $48 per share.

In this example, the insurance put locks in profits of at least $300 – the strike less cost of the put, minus your original basis: $50 - $2 - $45 = $300

Collar

A collar is a three-part strategy that combines the covered call with the insurance put. It consists of:

100 shares of stock1 short call1 long put

Collar

A collar costs little or nothing to open. The short call should be higher than the current price, and the long put should be lower. The cost of the long put is all or mostly paid for by the short put.

The collar is a smart strategy when you want to protect paper profits, and you are willing to have shares called away at the call’s strike.

Synthetic stock

This is a strategy similar to the collar. But both options are opened at the same strike price.

When you open a long call and a short put, it creates a synthetic long stock position, because the options grow in value as the stock rises, mirroring price changes point for point.

When you open a short call and a long put, it creates a synthetic short stock position, because the options grow in value as the stock falls, mirroring price changes point for point.