Why Do Bees Swarm How Honey Bees Move Their Hives

Bees usually swarm in the spring, but occasionally do so in summer or even in fall. Why do bees suddenly decide to get up and move en masse? Its actually normal bee behavior. Bees Swarm When the Colony Gets too Large Honey bees are social insects (eusocial, technically), and the honey bee colony functions much like a living organism. Just as individual bees reproduce, the colony must reproduce, too. Swarming is the reproduction of a honey bee colony, and it occurs when an existing colony subdivides into two colonies. Swarming is essential to the bees survival. If the hive becomes overcrowded, resources will be scarce and the colonys health will begin to decline. So every now and then, a bunch of bees will fly out and find a new place to live. What Happens During a Swarm When the colony gets too crowded, the workers will start making preparations to swarm. Worker bees tending to the current queen will feed her less, so she loses some body weight and is able to fly. Workers will also start raising a new queen by feeding a chosen larva large quantities of royal jelly. When the young queen is ready, the swarm begins. At least half of the colonys bees will quickly leave the hive, prodding the old queen to fly with them. The queen will land on a structure and workers will immediately surround her, keeping her safe and cool. While most bees tend to their queen, a few scout bees will begin searching for a new place to live. Scouting may only take an hour or so, or it can take days if a suitable location proves difficult to find. In the meantime, the large cluster of bees resting on someones mailbox or in a tree may attract quite a bit of attention, especially if the bees have alighted in a busy area. Once the scout bees have chosen a new home for the colony, the bees will guide their old queen to the location and get her settled. Workers will start building honeycomb and resume their duties raising brood and gathering and storing food. If the swarm occurs in spring, there should be ample time to build the colonys numbers and food stores before the cold weather arrives. Late seasons swarms dont bode well for the colonys survival, as pollen and nectar may be in short supply before theyve made enough honey to last the long winter months. Meanwhile, back in the original hive, the workers that stayed behind tend to their new queen. They continue to gather pollen and nectar and to raise new young to rebuild the colonys numbers before winter. Are Bee Swarms Dangerous? No, actually quite the opposite is true! Bees that are swarming have left their hive, and dont have brood to protect or food stores to defend. Swarming bees tend to be docile, and can be observed safely. Of course, if you are allergic to bee venom, you should steer clear of any bees, swarming or otherwise. Its fairly easy for an experienced beekeeper to collect a swarm and move it to a more appropriate location. Its important to collect the swarm before the bees choose a new home and start producing honeycomb. Once they find a place to live and go to work making honeycomb, they will defend their colony and moving them will be a bigger challenge. Sources Honey Bee Swarms, University of Arkansas Cooperative Extension Service website.Honey Bee Swarms and Their Control, Texas AM Agrilife Extension website.Swarms, University of California Davis website.Swarm Control for Managed Beehives, University of Florida IFAS Extension website.

Discipline And Punish The Birth Of The Prison - 1105 Words

French scholar Michel Foucault, in chapter 20 of Discipline and Punish: The Birth of the Prison, titled ‘Panopticism’ discusses his position on the panopticon ability to be a form of surveillance. The following piece will summarize chapter 20 of Foucault’s work, and discuss the creation of panopticism as a figure of societies transition into disciplinary forms of surveillance. Additionally, providing contemporary examples with the creation of Closed-Circuit Television (CCTV), and employ monitoring programs. Foucault’s work is built off the design of Jeremy Bentham’s ‘panopticon’, referring to it as the perfect or architectural figure of power in modern society (1979: 4). This design, encompasses a tower at the center from which is†¦show more content†¦Whether it be, in the penal system, where inmates are plotting an escape, creation of future crime plans, or in education, where schoolchildren are monitored for cheating, loudness, excessive chatter, or just day dreaming (Fludernik 2017: 6). Though, no one may be monitoring the subject at the time of a possible deviance, the possibility of it both eliminates the thought of doing so and maximizes the efficiency of the institution (Wood 2017). Closed-Circuit Television (CCTV), uses video camera technology in predominately urban areas to transmit and watch over specified locations to a monitoring station (Liu and Chen 2011: 1075). The principles of Bentham’s work the ‘panopticon’, are visible in the design and operation of CCTV, with the main premise being, to discourage people from wrong doing through the threat of constant surveillance. The cameras become internalized, as individuals become frightened of the possibility that someone at that moment is watching them, thus they self police themselves. Foucault’s, argument that disciplinary power can be extended to every aspect of society, and not only the penal system is evident through the use of CCTV. Similarly, to the ‘panopticon’, whose primary intended usage was installment as a prison, CCTV’s was to fight crime, being initially installed in September of 1968 in Olean, New York (Zhang 2015:7). Receiving constant support fr om policy creators andShow MoreRelatedDiscipline And Punish : The Birth Of The Prison1345 Words   |  6 PagesMichel Foucault- Discipline and Punish: The Birth of the Prison Michel Foucault is a very famous French intellectual who practiced the knowledge of sociology. Foucault analyzed how knowledge related to social structures, in particular the concept of punishment within the penal system. His theory through, Discipline and Punish: The Birth of the Prison, is a detailed outline of the disciplinary society; in which organizes populations, their relations to power formations, and the corresponding conceptionsRead MoreEssay on Foucaults Discipline and Punish: The birth of the prison2301 Words   |  10 Pagesdisciplinary society can be used to understand the body in the society, I would like to begin this essay by returning to Foucault’s book – Discipline and Punish: The birth of the prison. This book deals with the disciplinary institutions and practices that emerged in the eighteenth and nineteenth centuries. While discipline and punish is concerned with the birth of the prison in modern Europe, it has far wider implications for the everyday lives of ordinary citizens. 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Foucault explains, in Discipline and Punish that ‘this book is intended as a correlative history of the modern soul and of a new power to judge’ (Foucault, 1977) and opensRead MoreMichael Foucaults Panopticism879 Words   |  4 PagesSociety: Comparison to the Panopticon According to Wikepedia, a panopticon is a type of prison where the observer is able to watch the prisoners without the prisoner knowing when they are being watched. The concept of the design is to allow an observer to observe (-opticon) all (pan-) prisoners thereby conveying what one architect has called the sentiment of an invisible omnisciece. The panopticon was invented by English philosopher Jeremy Bentham in 1785. Bentham himself described the Panopticon

Standardized Testing The Best Tool For Evaluating Student...

In 2200 B.C. Chinese, civil servants were assessed using some of the earliest forms of standardized testing. Men would be tested on everything from archery to rites and ceremonies. The archery test would consist of shooting three arrows into a target and would be graded based on how many landed. Three arrows would equate to an excellent grade, two was good and one was passable. Standardized tests have evolved since the 2200s. Today, standardized testing is used as the main form of assessment for students in the American school system. Children as young as four years old are required to take standardized tests when entering school. Is standardized testing the best tool for assessing student development and teacher competency? There are some that would argue that standardized testing has its place, but there is an overwhelming majority that would disagree. From California to New York, there is evidence against high stakes standardized testing. Students and teachers alike buckle under t he weight of these tests. Who could blame them when the tests determine, not only who is eligible to graduate high school but also which schools will receive the funding they need? Standardized tests may have had their place in the American school system fifty years ago, but today they are outdated, unreliable, and should be abolished as the main form of assessment in the public-school system. Standardized tests are unreliable in many ways. Poor and minority students, for instance, often scoreShow MoreRelatedEvaluation Of A Clinical Evaluation Essay2196 Words   |  9 PagesWith the continuous changes in healthcare, evaluation of students’ clinical knowledge and skills relies on the need for continuous evaluation. Evaluation is the process of using data to make judgements about students’ individual performance. 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Mr. Theisenamarachi Marshall. What Was The Worst Decision

Mr. Theisen Amarachi Marshall What was the worst decision Herbert Hoover made that negatively affected the Great Depression? Language and Literature May 4, 2017 Stocks. I read about them every day in the car to my dad because he buys the Wall Street Journal. The newspaper has some interesting topics and it’s not a chore to indulge in as sometimes other newspapers are. Currently, the DOW Jones, a huge stock, is almost 21,047 points. That s very close to the current all time high. Eighty - five years ago, it was nothing like this. In the month of June in 1932, the DOW Jones stock fell to an all time low of 770.26 points. This was part of the aftermath of the Great Depression. Herbert Hoover, the president during the the†¦show more content†¦An investor would contribute a small percentage of the amount of money they would need to buy a stock. A stockbroker or a bank would loan a balance on almost no guarantee they would get their money as needed. This posed a problem. Later, when companies needed it the most, the companies realize that people were still not paying off loans as quickly as needed. The banks and stock brokers start ed to lose large sums of money. They were desperately needing more and more money from people who didn’t have what they needed to begin with. The dismal cycle lead to the stock market crash of 1929. From May 1929 to May 1933 Herbert Hoover served one term as the 31st president of the United States. Hoover was a member of the Republican political party. In his election, he won against Al Smith with 444 of the electoral college votes. A few months into his presidency, the Stock Market Crash occurred. Naturally, the United States as a whole started to look to the president and the government agencies for direction. There were many ideas that Hoover had that didn’t provide relief to the civilians during the Great Depression, they actually worsened the crisis. At some points, he rejected bills that would remedy some of the country s problems, because he believed that the government should not play a huge part in the bettering of the country. This belief was called laissez- faire. (Herbert Hoover) When the stock market crashed, many people were affected. Anyone who had money in the

Absolute Advantage Versus Comparative Advantage - Free Solution

Question: Describe about the Absolute Advantage Versus Comparative Advantage? Answer: On a Valentines Day greeting cards and roses become necessary commodities. The demand for both the goods rises followed by the rise in price. The price of roses always increases more than the price of cards because of price elasticities. The supply elasticity of greetings card on Valentines Day is more elastic than the supply of roses. This is because manufacturers of greetings card can easily increase its production and stock up greetings card. Thus, the supply of cards is relatively elastic. But roses are perishable and are costly enough to increase its supply just for the Valentines Day. This is why the supply is relatively inelastic. (Png et al., 2008) The government imposes a price ceiling of $11 per dozen roses. Price ceiling is the maximum price that the seller can sell to the buyers. The price ceiling provides gains for buyers but some loss is involved for the sellers. (Objectives for Chapter 8 Price Floors and Ceilings, 2015) The gap between the demand and supply causes a shortage of roses. If monitored properly, then this law can be effective to maintain a reasonable price. 2: In consumer behavior what appears to be an irrational behavior to the outsider may be a rational behavior to the individual himself. In this case, the student who was engaging himself in drinking, a day before his exams may seem to be an irrational individual. The irrational behavior arises when an individual has inadequate reason to act, suffering from emotional distress or cognitive deficiency or when individuals interest differs from their expectation, when situation is out of control or one may be fearful, nervous or full of stress. Here the student might be nervous or stressful about his exam the next day and hence he is depicting an irrational behavior by intoxication. The professor might find this rational as some belief that relieving stress is important for exams. (Ariely, 2011) The student can behave rationally by exercising certain stress free techniques to release his nervousness. This could be done by eating well, sleeping well, preparing well for the exam, if possible exercise too be stress free. All these can relieve stress and make the student behave rationally. The profit maximizing condition is given by: Where MR= Marginal Revenue and MC= Marginal Cost. Total Revenue, TR= P(Q)*Q TR= [240 0.10*Q]*Q TR= 240*Q 0.10*Q2 Now: MR= 240 - 0.2*Q Now from the maximizing condition 240 0.2*Q = 30 240 30 = 0.2*Q Q*= 1050 The 1050 wave runners will St. Martin Rentals rent per day. Profit maximizing price (in $) is: P(Q)= 240 0.10*Q* P(Q)= 240 0.10* 1050 P(Q)= 135 Daily revenue (in $): TR= P(Q)*Q TR= 240*Q*- 0.10*(Q*)2 TR= 240*1050 0.10*(1050)2 TR= 141750 The daily cost (in $) is given by: TC= 30*Q* + 80000 TC= 30*1050 + 80000 TC= 111500 Profit (in $) is obtained by: = TR TC = 141750 111500 = 30250 3: Hot Chocolate Snow cones Anna 6 16 Elsa 16 20 It is clear from the above table that Elsa has absolute advantage in producing both cups of hot chocolate and snow cones in an hour. The opportunity cost of producing 1 cup of hot chocolate per hour is 2.66 for Anna. The opportunity of producing 1 cup of hot chocolate per hour is 1.25 for Elsa. The opportunity cost of producing 1 snow cone per hour is 0.375 for Anna. The opportunity cost of producing 1 snow cone per hour is 0.8 for Elsa. Since the opportunity cost of producing 1 cup of hot chocolate for Elsa (1.25) is lower than that of Anna (2.66), Elsa has comparative advantage in producing hot chocolate per hour. And since the opportunity cost for producing 1 snow cone per hour for Anna (0.375) is lower than that of Elsa (0.8), Anna has comparative advantage in producing snow cones per hour. (Absolute Advantage Versus Comparative Advantage, 2015) Hot chocolate Snow cones Anna 15 8 Elsa 32 20 Clearly Elsa has absolute advantage in producing hot chocolate and snow cones. The opportunity cost of producing 1 snow cone per 3 hour is 1.85 for Anna The opportunity cost of producing 1 snow cone per 3 hour is 1.6 for Elsa. Since opportunity cost for Elsa is lower than that of Anna, Elsa has comparative advantage in producing snow cones. The opportunity cost of producing 1 cup of hot chocolate per 3 hour is 0.53 for Anna. The opportunity cost of producing 1 cup of hot chocolate per 3 hour is 0.625 for Elsa. Since opportunity cost for Anna is lower than that of Elsa, Anna has comparative advantage in producing hot chocolate. Anna specializes in hot chocolate and will sell it to Elsa. On the other hand Elsa specializes in snow cones and will sell it to Anna. In this way they will develop trading relationship be better off. 4: Purchasing a Tig Welder would involve an opportunity cost of the spending $90,000 immediately. There will be a loss of annual interest rate on $90,000 which is 0.05*90,000 = $4500. If $90,000 was lent out then $4500 would have been gained. But purchasing this welder would save only $700 in labor costs per year forever which can save a lot of money in the long run. Hence, this investment can be made. By purchasing a three-dimensional printer, $6500 will be incremented in the revenue per year. But by lending $80,000, an interest of (0.05*80,000) $4000 would have been obtained. This interest rate of return is much lower than the incremental revenue. Thus this investment must be made. By lending out $25000, a return of (1.05*25000) $26250 will be earned. But by organizing this six-sigma training, there will be a one time savings of $26000. Hence, it is not advisable to make this investment. By spending $5000, an interest of $250 is lost and by spending $12000 for the next year, $600 is lost. If $17000 were lent out for two years then there would have been a gain of $18700 which is higher than the return from the completion of the six sigma training of $16000 for one time. Thus, this investment must not be made. 5: A fall in the cost of screen manufacturing by 15%, increases the supply. As producers are now able to sell more quantities of good at the same price. The cost reduction also leads to increase in profit. (net, 2015) Uncertainty regarding the nutritional value of drinking carbonated soda reduces the demand for the same at the existing price. The exchange rate of Canadian dollar in terms of US dollar has increased which implies that Depreciation of Canadian dollar had taken place which implies Canada will now import less and export more. Thus a situation of excess supply arises. (CMS Forex, 2015) The popularity gained by the one inexpensive beef brisket had led to increased demand. This increased demand has resulted in increase in price of beef brisket based on The Wall Street Journal. (CAMPOY and KOPPEL, 2015) References Absolute Advantage Versus Comparative Advantage. (2015).Boundless. [online] Available at: https://www.boundless.com/economics/textbooks/boundless-economics-textbook/international-trade-31/introduction-to-international-trade-124/absolute-advantage-versus-comparative-advantage-493-12589/ [Accessed 22 Feb. 2015]. Ariely, D. (2011).Predictably irrational. [Kennett Square, Pa.]: Soundview Executive Book Summaries. CAMPOY, A. and KOPPEL, N. (2015). Brisket Was Cheap and Delicious; Now Its Expensive and You Have to Wait in Line.The Wall Street Journal. [online] Available at: https://www.wsj.com/articles/brisket-was-cheap-and-delicious-now-its-expensive-and-you-have-to-wait-in-line-1423180291 [Accessed 22 Feb. 2015]. CMS Forex, (2015).Supply and Demand in Currency Trading. [online] Available at: https://www.cmsfx.com/en/forex-education/online-forex-course/chapter-2-fundamental-factors/exchange-rates-supply-and-demand/supply-and-demand/ [Accessed 22 Feb. 2015]. Objectives for Chapter 8 Price Floors and Ceilings. (2015). 1st ed. [ebook] Available at: https://www2.palomar.edu/users/llee/101Chapter08.pdf [Accessed 22 Feb. 2015]. Png, I., Lehman, D., Cheng, J. and Png, I. (2008).Study guide to accompany Managerial economics, third edition, by Ivan Png and Dale Lehman. Malden, MA: Blackwell, Pub. Tutor2u.net, (2015).Tutor2u - Market Supply. [online] Available at: https://tutor2u.net/economics/content/topics/demandsupply/supply.htm [Accessed 22 Feb. 2015].

Explain Why It Is Impossible to Derive An Analytic Essay Example For Students

Explain Why It Is Impossible to Derive An Analytic Essay al Formula For Valuing AmericanPuts. Explain why it has proved impossible to derive an analytical formula for valuingAmerican Puts, and outline the main techniques that are used to produceapproximate valuations for such securitiesInvesting in stock options is a way used by investors to hedge against risk. Itis simply because all the investors could lose if the option is not exercisedbefore the expiration rate is just the option price (that is the premium) thathe or she has paid earlier. Call options give the investor the right to buy theunderlying stock at the exercise price, X; while the put options give theinvestor the right to sell the underlying security at X. However only Americaoptions can be exercised at any time during the life of the option if the holdersees fit while European options can only be exercised at the expiration rate,and this is the reason why American put options are normally valued higher thanEuropean options. Nonetheless it has been proved by academics that it isimpossible to derive an analytical formula for valuing American put options andthe reason why will be discussed in this paper as well as some main suggestedtechniques that are used to value them. According to Hull, exercising an American put option on a non-dividend-payingstock early if it is sufficiently deeply in the money can be an optimal practice. For example, suppose that the strike price of an American option is $20 and thestock price is virtually zero. By exercising early at this point of time, aninvestor makes an immediate gain of $20. On the contrary, if the investor waits,he might not be able to get as much as $20 gain since negative stock prices areimpossible. Therefore it implies that if the share price was zero, the putwould have reached its highest possible value so the investor should exercisethe option early at this point of time. Additionally, in general, the early exerices of a put option becomes moreattractive as S, the stock price, decreases; as r, the risk-free interest rate,increases; and as , the volatility, decreases. Since the value of a put isalways positive as the worst can happen to it is that it expires worthless sothis can be expressed as where X is the strike price Therefore for an American putwith price P, , must always hold since the investor can execute immediateexercise any time prior to the expiry date. As shown in Figure 1,Here provided that r 0, exercising an American put immediately always seems tobe optimal when the stock price is sufficiently low which means that the valueof the option is X S. The graph representing the value of the put thereforemerges into the puts intrinsic value, X S, for a sufficiently small value ofS which is shown as point A in the graph. When volatility and time toexpiration increase, the value of the put moves in the direction indicated bythe arrows. In other words, according to Cox and Rubinstein, there must always be somecritical value, S`(z), for every time instant z between time t and time T, atwhich the investor will exercise the put option if that critical value, S(z),falls to or below this value (this is when the investor thinks it is the optimaldecision to follow). More importantly, this critical value, S`(z) will dependon the time left to expiry which therefore also implies that S`(z) is actually afunction of the time to expiry. This function is referred to, according toWalker, as the Optimum Exercise Boundary (OEB). .u8fb39267f2737d903ed0255e8e278e4f , .u8fb39267f2737d903ed0255e8e278e4f .postImageUrl , .u8fb39267f2737d903ed0255e8e278e4f .centered-text-area { min-height: 80px; position: relative; } .u8fb39267f2737d903ed0255e8e278e4f , .u8fb39267f2737d903ed0255e8e278e4f:hover , .u8fb39267f2737d903ed0255e8e278e4f:visited , .u8fb39267f2737d903ed0255e8e278e4f:active { border:0!important; } .u8fb39267f2737d903ed0255e8e278e4f .clearfix:after { content: ""; display: table; clear: both; } .u8fb39267f2737d903ed0255e8e278e4f { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u8fb39267f2737d903ed0255e8e278e4f:active , .u8fb39267f2737d903ed0255e8e278e4f:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u8fb39267f2737d903ed0255e8e278e4f .centered-text-area { width: 100%; position: relative ; } .u8fb39267f2737d903ed0255e8e278e4f .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u8fb39267f2737d903ed0255e8e278e4f .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u8fb39267f2737d903ed0255e8e278e4f .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u8fb39267f2737d903ed0255e8e278e4f:hover .ctaButton { background-color: #34495E!important; } .u8fb39267f2737d903ed0255e8e278e4f .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u8fb39267f2737d903ed0255e8e278e4f .u8fb39267f2737d903ed0255e8e278e4f-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u8fb39267f2737d903ed0255e8e278e4f:after { content: ""; display: block; clear: both; } READ: George Orwell Research EssayHowever in order to be able to value an American put option, we need to solvefor the put valuation foundation and then optimum exercise boundary at the sametime. Yet up to now, no one has managed to produce an analytical solution tothis problem so we have to depend on numerical solutions and some techniqueswhich are considered to be good enough for all practical purposes. (Walker,1996)There are basically three main techniques in use for American put optionvaluations, which are known as the Binomial Trees, Finite Difference Methods,and the Analytical Approximations in Option Pricing. These three techniqueswill be discussed in turns as follows. Cox et al claim that a more realistic model for option valuation is one thatassumes stock price movements are composed of a large number of small binomialmovements, which is the so-called Binomial Trees (Hull, p343, 3rd Ed). Binomial trees assume that in each short interval of time, , over the life ofthe option a stock price either moves up from its initial value of S to , ormoves down to . In general, ; 1 and ; 1. The probability of an up movementwill be denoted by thus, the probability for a down movement is . The basicmodel of this simple binomial tree is shown in Figure 2. Furthermore, the risk-neutral valuation principle is also in use when using a binomial tree, whichstates that any security dependent on a stock price can be valued on theassumption that the world is risk neutral. Therefore the risk-free interest rateis the expected return from all traded securities and future cash flows can bevalued by discounting their expected values at the risk-free interest rate. Theparameters p, u, and d must give correct values for the mean and variance ofstock price changes during a time interval of length . By using the binomial tree, options are evaluated by starting at the end of thetree (that is time T) and working backward. The value of the option is known attime T. As a risk-neutral world is being assumed, the value at each node at timeT can be calculated as the expected value at time T discounted at rate r for atime period . Similarly the value at each node at time T can be calculated asthe expected value at time T discounted for a time period at rate r, and so on. When we are dealing with American options, it is necessary to check at eachnode to see if early exercise is optimal rather than holding the option for alonger while. Therefore by working the binomial backward through all the nodes,the value of the option at time zero is obtained. For example, consider a five-month American put option on a non-dividend-payingstock when the stock price is $50, the strike price is $50, the risk-freeinterest rate is 10% per annum, and the volatility is 40% per annum. With ourusual notation, this means that S = 50, X = 50, r = 0.10, = 0.40, and T = 0.4167. Suppose that we break the life of the option into five intervals of length onemonth (= 0.0833 year) for the purposes of constructing a binomial tree. Then =0.0833 and using the formulas,The top value in the tree diagram above shows the stock price at the node whilethe lower one shows the value of the option at the node. The probability of anup movement is always 0.5076; the probability of a down movement is always0.4924. Here the stock price at the jth node (j = 0, 1, , i) at time is calculated as. Also the option prices at the penultimate nodes are calculated from theoption prices at the first final nodes. First we assume no exercise of theoption at the nodes. This means that the option price is calculated as thepresent value of expected option price in time . For example at node E theoption price is calculated as while at node A it is calculated asThen it is possible to check if early exercise of the option isworthwhile. At node E, the option has a value of zero as both the stock priceand strike price are $50. Thus it is best to wait and the correct value at nodeE is $2.66. Yet the option should be exercised at node A if it is reachedbecause the option would be worth $50.00 $39.69 or $10.31, which is obviouslyhigher than $9.90. Options in earlier nodes are calculated in a similar way. .u48a6e2f413b325582bef2fadab37c777 , .u48a6e2f413b325582bef2fadab37c777 .postImageUrl , .u48a6e2f413b325582bef2fadab37c777 .centered-text-area { min-height: 80px; position: relative; } .u48a6e2f413b325582bef2fadab37c777 , .u48a6e2f413b325582bef2fadab37c777:hover , .u48a6e2f413b325582bef2fadab37c777:visited , .u48a6e2f413b325582bef2fadab37c777:active { border:0!important; } .u48a6e2f413b325582bef2fadab37c777 .clearfix:after { content: ""; display: table; clear: both; } .u48a6e2f413b325582bef2fadab37c777 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .u48a6e2f413b325582bef2fadab37c777:active , .u48a6e2f413b325582bef2fadab37c777:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .u48a6e2f413b325582bef2fadab37c777 .centered-text-area { width: 100%; position: relative ; } .u48a6e2f413b325582bef2fadab37c777 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .u48a6e2f413b325582bef2fadab37c777 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .u48a6e2f413b325582bef2fadab37c777 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .u48a6e2f413b325582bef2fadab37c777:hover .ctaButton { background-color: #34495E!important; } .u48a6e2f413b325582bef2fadab37c777 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .u48a6e2f413b325582bef2fadab37c777 .u48a6e2f413b325582bef2fadab37c777-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .u48a6e2f413b325582bef2fadab37c777:after { content: ""; display: block; clear: both; } READ: Contrast Of Romeo And Juliet An West Side Story EssayAs we keep on calculating backward, we find the value of the option at theinitial node to be $4.48, which is the numerical estimate for the optionscurrent value. However in practice, a smaller value of would be used by whichthe true value of the option would be $4.29. (Hull, p347, 3rd Ed)The second technique that is commonly used is the so-called Finite DifferenceMethods. These methods value a derivative by solving the differential equationthat the derivative satisfies. The differential equation is converted into aset of difference equations and the difference equations are solved repeatedly. For instance, in order to value an American put option on a non-dividend-payingstock by using this method, the differential equation that the option mustsatisfy isThe Finite Difference Methods are similar to tree approaches inthat the computations work back from the end of the life of the derivative tothe beginning. There are two different methods involved; one is called theExplicit Finite Difference Method and the other is the Implicit FiniteDifference Method. The former is functionally the same as using a trinomialtree. The latter is more complicated but has the advantage that the user doesnot have to take any special precautions to ensure convergence. The maindrawback of these methods is they cannot easily be used in situations where thepay-off from a derivative depends on the past history of the underlying variable. Finally there is also an alternative to the numerical procedures which is knownas a number of analytic approximations to the valuation of American options. The best known of these is a quadratic approximation approach proposed byMacMillan and then extended by Barone-Adesi and Whalley. This method involvesestimating the difference, v, between the European option price and the Americanoption price since v must satisfy the differential equation for both. They thenshow that when an approximation is made, the differential equation can be solvedusing standard methods. The techniques mentioned in this paper are those commonly used in practise. Although they are not perfect, they are still considered good enough forpractical purposes. So far no one has managed to create a direct analyticalvaluation method for valuing American put options. Category: Business