**Option**, a financial derivative, is a contract between a buyer and a seller of an underlining asset such as a stock, commodity, bond, index, futures and etcetera. This contract gives the buyer of the option the right but not the obligation to buy or to sell the underlining asset at a later day at an agreed price. The seller (underwriter) of the option in return gets to collect a payment called the premium from the buyer.

Trading **Stock Options** concepts

If a trader believes that the price of a stock will increase in the future, he might want to purchase a **call option**. If the stock goes higher than the strike price, the trader will have the right to purchase the stock at a cheaper price. However, if the stock price at expiration is lower than the exercise price, the call option will expire worthless. *It is important to note that actual stock shares rarely exchange hands. Those that purchase call or put options will often sell them back to the issuer or another call or put buyer before expiration at a profit or expire worthless.*

If a trader believes that the price of a stock will decrease in the future, he might want to purchase a **put option**. If the stock goes lower than the strike price, the trader will have the right to sell the stock at a higher price. However, if the stock price at expiration is higher than the exercise price, the put option will expire worthless.

If a trader believes that the price of a stock will decrease in the future, he might want to write a **call option**. The trader selling a call has an obligation to sell the stock to the call buyer at the buyer’s option. If the stock price decreases, the short call position will make a profit in the amount of the premium. If the stock price increases over the exercise price by more than the amount of the premium, the short will lose money, with the potential loss unlimited.

If a trader believes that the price of a stock will increase in the future, he might want to write a **put option**. The trader selling a put has an obligation to buy the stock from the put buyer at the buyer’s option. If the stock price at expiration is above the exercise price, the short put position will make a profit in the amount of the premium. If the stock price at expiration is below the exercise price by more than the amount of the premium, the trader will lose money, with the potential loss being up to the full value of the stock.

Options can be bought or written via an online broker (not all let you write them). There are several different brokers with different pricing structures. Options are often priced per contract plus a premium.

*Here are some examples of option orders placed in a brokerage account.*

Buy 10 Contracts of GS Jan 2011 **puts** at strike 75 (In this case your betting that Goldman Sachs will drop in price, you are buying 10 contracts, 1000 shares of Goldman Sachs. This put option will expire on January 2011. You can exercise the *option* is GS drops below 75. However, you don’t need to wait for Goldman to drop below 75 before making money. If Goldman Sachs drops in price from the day you purchased the *options* significantly, your put *options* will go up in value and therefore you can just sell that back at a gain. If the VIX goes up in price significantly, *options* prices usually follow. The key is to sell the *option* before time decay kicks in and devalue it)

Write 10 Contracts of GS August 2010 c**alls** at strike 170 (In this case you are betting that Goldman Sachs will not increase in value past 170 by writing 10 call contracts, 1000 shares of Goldman Sachs. This call *option* will expire on August 2010. If by August 2010 Goldman Sachs not above 170 or the *option* was not exercised, the *option* will expire worthless and you will keep the premium. If however Goldman is $200 a share, you will be forced to sell your shares for $170 a share.)

*Strategies for Trading Options*

Bear Call Spread – It is an *option strategy* used when a trader is moderately bearish on the underlying security utilizing call options. The trader buys equal quantities of out-the-money *call option* and sells a in-the-money *call option*.

Bear Put Spread – It is an *option strategy* used when a trader is moderately bearish on the underlying security utilizing put options. The trader buys equal quantities of in-the-money *put option* and sells out-the-money *put option*.

Bull Call Spread – It is an *option strategy* used when a trader is moderately bullish on the underlying security utilizing call options. The trader buys equal quantities of in-the-money *call option* and sells out-the-money *call option*

Bull Put Spread – It is an *option strategy* used when a trader is moderately bullish on the underlying security utilizing *put options*. The trader buys equal quantities of out-the-money *put option* and sells in-the-money *put option*.

Butterfly Spread – It is an *option strategy* that focuses on reducing risk. Example is long one X1 call, short two X2 calls, and long one X3 call where a trader can profit if the stock price on the expiration date is near the middle exercise price, X2 while at the same time protected if it falls.

Collar – Is an *option strategy* that contains an investment risk by buying a *put option* and writing a *call option*.

Covered Call – It is an *option strategy* in which a trader will write *call options* on a stock that they own or plan to own. This way, if the call *option* is triggered, the trader sells his shares at a gain, but if the stock drops in value, the trader profits from the *option* premium paid to him.

Iron Condor – It is an *option strategy* in which a trader uses an equal quantity of Bull put spread + Bear call spread with identical expiration days.

Long Straddle – It is an *option strategy* when a trader buys both a *put *and *call option* at the same strike price with the same strike day. The trader is betting high volatility, with limited down side (cost of both *options*) but unlimited upside.

Long Strangle – It is an *option strategy* when a trader buys both a *put *and *call* *option* at the different strike price with the same strike day. The trader is betting high volatility, with limited down side (cost of both *options*) but unlimited upside.

Short Straddle – It is an *option strategy* when a trader sells both a *put* and *call option* at the same strike price with the same strike day. The trader is betting low volatility, with limited upside (premium of both *options*) but unlimited downside.

Short Strangle – It is an *option strategy* when a trader sells both a *put* and *call option* at a different strike price with the same strike day. The trader is betting low volatility, with limited upside (premium of both *options*) but unlimited downside.

*Valuation Models for Options*

Black Scholes – Was the first mathematical model for evaluating stocks and derivatives based on…..

**Call option** C = (the price of the underlyning stock * the standard normal cumulative distribution function * delta 1) – {strike price * E ^- (continuously compounded risk free interest rate * time in years until the expiration of the option) * the standard normal cumulative distribution function * delta 2}

**Put option** p = {strike price * E ^- (continuously compounded risk free interest rate * time in years until the expiration of the option) * the standard normal cumulative distribution function * negative delta 2} – (the price of the underlyning stock * the standard normal cumulative distribution function * negative delta 1)

Delta 1 = {log (stock price / strike) + ((continuously compounded risk free interest rate + implied volatility for the underlying stock^2/2)* time in years until the expiration of the option)} / (implied volatility for the underlying stock * square root of time in years until the expiration of the option)

Delta 2 = delta 1 – (implied volatility for the underlying stock * square root of time in years until the expiration of the option)

Stochastic volatility models are options model that further break down implied volatility based on the underline stock price. The implied volatility for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility is stochastic (varying both for time and for price of the underlying security).