OPTIONS

Terminology

Index options: These options have the index as the underlying. Some options are European while others are American. Like index futures contracts, index options contracts are also cash settled.

American Vs European: American can be Exercised anytime before expiry.

Stock options: Stock options are options on individual stocks. A contract gives the holder the right to buy or sell shares at the specified price.

Terminology

Buyer of an option: The buyer of an option is the one who by paying the option premium buys the right but not the obligation to exercise his option on the seller/writer.

Writer of an option: The writer of a call/put option is the one who receives the option premium and is thereby obliged to sell/buy the asset if the buyer exercises on him.

Terminology

Call option: A call option gives the holder the right but not the obligation to buy an asset by a certain date for a certain price.

Put option: A put option gives the holder the right but not the obligation to sell an asset by a certain date for a certain price.

Option price: Option price is the price which the option buyer pays to the option seller. It is also referred to as the option premium.

Terminology

Expiration date: The date specified in the options contract is known as the expiration date, the exercise date, the strike date or the maturity.

Strike price: The price specified in the options contract is known as the strike price or the exercise price.

ITM, ATM & OTM for Call & Put Options.A call (put) option is said to be in-the-money if the asset price is more (less) than the strike price, while it is out-of-the-money if the asset price is less (more) than the strike price. More so, an option is at-the-money if the strike price equals the price of the underlying asset.

Factors affecting Premium?

Price of the underlying stock.Strike price of the option.Time remaining until maturity.Volatility of the underlying stock: Volatility is the measure of uncertainty about the evolution of the price of the underlying stock Risk free interest rate: This is the rate of interest at which money can be lent or borrowed such that the money is certain to be repaid.

Long Forward Position- FuturesK

Short Forward Position-FuturesK

OptionsA call option is an option to buy a certain asset by a certain date for a certain price (the strike price)A put is an option to sell a certain asset by a certain date for a certain price (the strike price)

Long Call on Microsoft

Short Call on Microsoft

Long Put

Short Put

Payoffs from Options

K = Strike price, ST = Price of asset at maturity

Options Pricing- Black Scholes

Black-Scholes Model- Value of Call Option.

Value of Put Option.

Problems

The current price of shares of company XYZ is $100 and you would like to get an option to purchase one share of XYZ company stock for $95. The option expires in three months. We also assume that the stock pays no dividends. The standard deviation of the stocks returns is 50% per year, and the risk-free rate is 10% per year, calculate the value of the option.

d1 = [ln($100/$95) + (0.10 + 0.25/2) * 0.25]/ 0.50 * 0.25 = 0.43 d2 = 0.43 - 0.50 * 0.25 = 0.18 N(0.43) = 0.6664 N(0.18) = 0.5714

C(S,T) = $100* 0.6664 - $95 * e -(0.10* 0.25)* 0.5714

= 66.64 - 52.94 = $13.70

Options Pricing- Binomial

Options Pricing- BinomialProbability defined by,

P= (R-d)/(u-d)

R-Risk Free rate of returnD- Lower LimitU- Upper Limit

Put-Call Parity for European OptionsFor the prices c and p of respective European call and put options with the same exercise time t and the same strike price X >= 0 on the same asset, we have

where S is the present price of the underlying security.

Topics Pending..Strategies using Options.

Covered Call/Put, Straddle, Strangle, Butterfly, Bear Spread & Bull Spread..

Assumptions in Premium PricingOptions GreeksArbitrage opportunity using Options

Thank You..

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