# Option volatility pricing advanced trading strategies and techniques

The exercise priceor strike price is the price at which the underlying will be delivered should the holder of an option choose to exercise his right to buy or sell. The date after which the option may no longer be exercised is the expiration date. The premium paid for an option can be separated into two components, the intrinsic value and the time value. The additional amount ofpremium beyond the intrinsic value which traders are willing to pay for an option is the time value, sometimes also referred to as the option's time premium or extrinsic value.

An option's premium is always composed of precisely its intrinsic value and its time value. If the option has no time value,its price will consist solely of intrinsic value. The option is trading at parity. Any option which has a positive intrinsic value is said to be in-the-money by the amount of the intrinsic value. An option which has no intrinsic value is said to be out-of-the-money.

An option whose exercise price is identical to the current price of the underlying contract is said to option volatility pricing advanced trading strategies and techniques at-the-moneysuch an option is also out-of-the-money since it has no intrinsic value.

The distinction between an at-the-money and out-of-the-money option because an at-the-money option has the greatest amount of time premium and is usually traded very actively.

When a trader makes an opening trade on an exchange, the exchange may require the trader to deposit some amount of marginor good faith capital. If he purchases options, not only must he be right about market direction, he must also be right about market speed. The two most common considerations in a financial investment are the expected return and carrying costs.

And, in fact, dividends are an additional consideration in evaluating options on stock. The goal of option evaluation is to determine, through the use of theoretical pricing models, the theoretical value of an option. The trader can then make an intelligent decision whether the option is overpriced or underpriced in the marketplace, and whether the theoretical edage is sufficient to justify going into the marketplace and making a trade.

In its original form, the Black-Scholes Model was intended to evaluate European options no early exercise permitted on non-dividend paying stocks. Shortly after its introduction, realizing that rnost stocks do pay dividends, Black and Scholes added a dividend cornponent. InFischer Black rnade slight rnodifications to the rnodel to allow for the evaluation of options on futures contracts.

And inMark Garman and Steven Kohlhagen made several other modifications to allow for the evaluation of options on foreign currencies. The futures version and the foreign currencyversion are known officially as the Black Model and the Garman-Kohlhagen Model, respectively.

But the evaluation rnethod in each version, whether the original Black-Scholes Model for stock options, the Black Model for futures options, or the Garman-Kohlhagen Model for foreign currency options, is so similar that they have all come to be known as simply the Black-Scholes Model.

In order to calculate an option's theoretical value using the Black-Scholes Model, we need to know at a minimum five characteristics of the option and its underlying contract.

Black and Scholes also incorporated into their model the concept of the riskless hedge. That is, whatever option position we take, we must take an opposing market position in the underlying contract. The correct proportion of underlying contracts needed to establish this riskless hedge is known as the hedge ratlo. If we assume at prices are distributed along a normal distribution curve, the value of an underlying contract depends on where the peak of the curve is located, while the value of an option depends on how fast le curve spreads out.

When price changes are assumed to be normally distributed, the continuous compounding of these price changes wiU cause the prices at maturity to be lognormally distributed. It assumes at the volatility of an underlying instrument is constant over the life of the option, but that this volatility is continuously compounded. These two assumptions mean that the possible prices of the underlying instrument at expiration ofthe option are lognormally distributed.

Summarize the most irnportant assurnptions governing price movement int the Black-Scholes Model:. He might then look at the difference between each option's theoretical value and its price in marke lace selling any options which were overpriced relative to the theoretical value, and buying any options which were underpriced.

The purchase or sale of a theoretically mispriced option requires us to establish a hedge by taking an opposing positlon in the underlying contract. When this is done correctly, for small changes in the price of the underlying, the increase decrease in the value of the optlon position will exactly offset the decrease increase in the value of the opposing position in the underlying contract. Such a hedge is unbiased, or neutralas to the direction of the underlying contract.

The number which enables us to establish a neutral hedge under current market conditions is a by-product of theoretical pricing model and is known as the hedge ratio or, more commonly, the delta. The steps we have thus far taken illustrate the correct procedure in using an option theoretical value:.

The gamma sometimes referred to as the curvature of an option, is the rate at which an option's delta changes as the price of the underlying changes. If an option has a gamrna of 5for each point rise fal1 in the price of the und. Since vega is not a Greek letter, a common alternative in academic literature, where Greek letters are preferred, is kappa K. The sensitivity of an optio 's theoretical value to a change in interest rates is given by its rho P.

As time passes,or as we decrease our volatility assumption,call deltas move away om 50,and puts deltas away from As we increase our volatility assumption, cal1 deltas move towards 50, and put deltas towards option volatility pricing advanced trading strategies and techniques The theta of an at-the-money option increases as expiration approaches.

A short-term, at-the-money option will a1 ways decay more quickly than a long-term, at-the-money option. As we increase decrease our volatility assumption, the theta of an option will rise fall. Higher volatility means there is greater time value associated with the option, so at each day's decay wil1 also be greater when no movement occurs. The various positions and their respective signs are given in Figure The positive or negative effect of changing market conditions is summarized in Figure An option's elasticitysometimes denoted with the Greek letter omega or less commonly the Greek letter lambdais the relative percent change in an option's value for a given percent change in the price of the underlying contract.

The elasticity is sometimes referred to as the option's leverage value. The greater an option's elasticity, the more highly leverage the option. Spreading is simply a way of enabling an optlon trader to take advantage of theoretlcally mispriced options, while at the same time reducing the effects of short-term changes in market option volatility pricing advanced trading strategies and techniques so that he can safely hold an optlon positlon to maturity.

At option volatility pricing advanced trading strategies and techniques point the intelligent trader will have to consider not only the potential profit, but also the risk associated with a strategy. Even when he incorrectly estimates the inputs, the experienced trader can survive if he has constructed intelligent spread strategies which allow for a wide margin of error. A backspread is a delta neutral spread which consists of more long purchased options than short sold options where all options expire at the same time.

A call backspread consists of long calls at a higher exercise price and short calls at a lower exercise price.

A put backspread consists of long puts at a lower exercise price and short puts at a higher exercise price. If he foresees a market with great upside potential, he will tend to choose a call backspread; if he foresees a market with great downside potential he will tend to choose a put backspread. He will avoid backspreads in quiet markets since the underlying contract is unlikely to move very far in either direction. A trader who takes the opposite side of a backspread also has a delta neutral spread, but he is short more contracts than long, with all options expiring at the same time.

Such a spread is sometimes referred to as a ratio spread or a vertical spread. A straddle consists of either a long call and a long put, or a short call and a short put, where both options have the same exercise price and expire at the same time. If both the call and put are purchased, the trader is said to be long the straddle; if both options are sold, the trader is said to be short the straddle.

Like a straddle, a strangle consists of a long call option volatility pricing advanced trading strategies and techniques a long put, or a short call and a short put, where both options expire at the same time.

If both options are purchased, the trader is long the strangle if both options are sold, the trader is short the strangle. To avoid confusion a strangle is commonly assumed option volatility pricing advanced trading strategies and techniques consist of out-the-money options.

When both options are in-the-money, the position is sometimes referred to as a guts. A butterfly consists of options at three equally spaced exercise prices, where all options are of the same type either all calls or all puts and expire at the same time.

If the ratio is other than option volatility pricing advanced trading strategies and techniques x 2 x 1, the spread is no longer a butterfly.

Time spreads, sometimes referred to as calendar spreads or horizontal spreads, consist of opposing positions whlch expire in different months. The most common type of time spread consists o.

The most common type of time spread consists of opposing positions in two options option volatility pricing advanced trading strategies and techniques the same type either both calls or both puts where both options have the same exercise price. When the long-term option is purchased and the short-term option is sold, a trader is long the time spread; when the short-term option is purchased and the long-term option is sold, the trader is short the time spread.

If we assume that the options making up a time spread are approxjmately at-the-money, time spreads have two important characteristics:. These two opposing forces, the decay in an option's value due to the passage of time and the change in an option's value due to changes in volatility, give time spreads their unique characteristics.

When a trader buys or sel1s a time spread, he is not only attempting to forecast movement in the underlying market. If we are considering stock options with different expiration dates,we mut consider two different forward prices. Andthese two forward prices may not be equaly sensitive to a change in interest rates. Therefore, a long short call time spread in the stock option market must have a positive negative rho.

Therefore, a long short put time spread in the stock option market must have a negative positive rho. In a time spread, if a dividend option volatility pricing advanced trading strategies and techniques is expected between expiration of the short-term and long-term option, the long-term option will be affected by the lowered forward price of the stock.

Hence, an increase in dividends, if at least one dividend payment is expected between the expiration dates, will cause call time spreads to narrow and put time spreads to widen. A decrease in dividends will have the opposite effect, with call time spreads widening and put time spreads narrowing. The effect of changing interest rates and dividends on stock option time spreads is shown below:. A diagonal spread Is similar to a time spread, except that the options have different exercise prices.

A Christmas tree also referred to as a ladd is a term which can be applied to a variety of spreads. The spread usually consists of three different exercise prices where all options are of the same type and expire at the same time. In a long short call Christmas tree, one call is purchased sold at the lowest exercise price,and one call is sold purchased at each of the higher exercise prices.

In a option volatility pricing advanced trading strategies and techniques short put Christmas tree, one put is purchased sold at the option volatility pricing advanced trading strategies and techniques exercise price, and one put is sold purchased at each of the lower exercise prices. Such spreads therefore increase in value if the underlying market either sits still or moves very slowly. Short Christmas trees can be thought of as particular types of backspreads, and therefore increase in value with big moves in the underlying market.

It is possible to construct a spread which has the same characteristics as a butterfly by purchasing a straddle strangle and selling **option volatility pricing advanced trading strategies and techniques** strangle straddle where the straddle is executed at an exercise price midway between the strangle's exercise prices.

All options must expire at the same time. Because the position wants the same outcome as a butterfly, it option volatility pricing advanced trading strategies and techniques known as an iron butterfly. Another variation on a butterfly, known as a condorcan be constructed by splitting the inside exercise prices. Now the position consists of four options at consecutive exercise prices where the two outside options are purchased and the two inside options sold a long condoror the two inside options are purchased and the two outside options sold a short condor.

As with a butterfly, all options must be of the same type all calls or all puts and expire at the same time.

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