## Introduction to options pricing

Another form of volatility that affect options is historic volatility , also known as statistical volatility. This measures the speed at which underlying asset prices change over a given time period. Historical volatility is often calculated annually, but because it constantly changes, it can also be calculated daily and for shorter time frames. It is important for investors to know the time period for which an option’s historical volatility is calculated. Generally, a higher historical volatility percentage translates to a higher option value.

## Introduction to Options - CME Group

Retail price setting process includes a series of decisions a retailer makes while determining the price of merchandise. As said earlier, there is no universal way to set the price of merchandise but one thing should be noted in this regard that regardless of the price setting process used, the price of merchandise should meet the cost of obtaining the supplies and expenses to operate the retail firm.

### Introduction to the Mathematics of Finance: Arbitrage and

Options are financial derivatives that represent a contract by a selling party—or the option writer—to a buying party—or the option holder. An option gives the holder the ability to buy or sell a financial asset with a call or put option respectively. This is done at an agreed price on a specified date or during a specified time period. Holders of call options seek to profit from an increase in the price of the underlying asset, while holders of put options generate profits from a price decline.

At a price level of 98, the 97 call is now in the money, and the payoff is \$6. At 655, the payoff is \$8, at 657 the payoff is \$5 and at 659 the payoff would be \$7.

Following factors have direct or indirect influence on retail pricing. Three are usually basic pricing options before a retailer. Each has its own merits and demerits.

Gross margin, commonly known as gross profit is an important performance measure in retailing. It indicates the retailer a measure (estimate) of how much profit it is making on merchandise sales without considering the expenses associated with running a store. In other words, gross margin is the difference between Net sales and the Cost of goods sold.

The point of difference between initial markup and maintained markup is that initial markup percentage depends on planned retail operating expenses, profit, reductions and net sales while on the other hand, maintained markup represents some additional costs from original retail values caused by discounts, shortages, Inventory theft, markdowns and added markups. The maintained markup percentage can be viewed as:

It simply means setting the merchandise prices simply to beat the competitor 8767 s price by charging price that is below the prevalent market rate. This policy is advisable only when retailer follows an optimum inventory plan, procure merchandise at right time and at right (minimum best possible) price to gain the benefits of cash payment, trade discount, bulk buying etc.

The main advantage of demand oriented pricing strategy is to set the merchandise prices as per customer response towards the product offered. The Gap decides to test the Koutons 8767 T-shirt in five markets at different prices. Figure presents the pricing test 8767 s results. It is clear from column 5 that a unit price of Rs. 65 is by far the most profitable (,75,555).

Setting the retail price of merchandise is a complicated, but the most important aspects of managerial decision making. If the price is set too low, retailer may not be able to cover its store expenses. If the merchandise is priced too high retailer may price himself out. Therefore, price setting is a complex activity and no formula has been developed so far to set the price correctly.

This policy allows a retailer to set the merchandise price above the current market rate. This policy seems to be straight forward and simple but must be applied carefully.

There are two facets to the option premium: The option s intrinsic value  and  time value. The intrinsic value is the difference between the underlying asset s price and the strike price. The latter is the in-the-money portion of the option s premium. The intrinsic value of a call option is equal to the underlying price minus the strike price. A put option s intrinsic value, on the other hand, is the strike price minus the underlying price. The time value, though, is the part of the premium attributable to the time left until the option contract expires. The time value is equal to the premium minus its intrinsic value.

This reduced rate will not be applicable to a customer who places order for a few items. A reduced price (discounted rate) is offered if one buys 5 kg or more instead of 6 kg or two shirts instead of one. It is helpful in clearing out the merchandise and generates quick revenue for a retail firm.

With the emergence of various retail formats and enhanced competition, it is not practical for a retailer to sell all the merchandise items at their actual prices. Therefore, retailers compute the initial mark up, maintained mark up and gross margin during their normal course of business.

Options are  derivative contracts that give the buyer the right, but not the obligation, to buy or sell the  underlying  asset at a mutually agreeable price on or before a specified future date. Trading these instruments can be very beneficial for traders. First, there is the security of limited risk and the advantage of  leverage. Secondly, options provide protection for an investor s portfolio during times of market volatility.

Under such markdowns, prices are reduced to clear out the seasonal retail merchandise, such as 8766 Ludhiana woolen sales 8767 in the last months of winter season are very common in North Indian states like Haryana, Punjab, and Delhi etc.

First, we introduce the factors in the model. For all the factors listed below, only volatility is not known.  There are many types of volatilities. Then which volatility should be used is a critical question in option pricing model. We will further discuss this part in the next few chapters.

Now that we have the probability for each price point, we can start pricing options with different strike prices. First, you need to know the payoff for each strike price at the defined price level.

There are some details we need to pay attention to about the input of BSM model. Firstly, the model works in continuous time, rather than discrete time. Therefore the risk-free rate r has to be modified to the continuous form. Secondly, the time to expiration should be converted to year. The volatility is the annual volatlity.