Gender Based Violence And Gender Inequality Essay

Introduction In recent years, in the United States, the nation’s view towards Middle Eastern women has been altered due to their involvement in domestic and global terrorism. In addition, news of Middle Eastern women being mistreated by men and societal circumstances because of gender has arisen. In other words, Middle Eastern women are subjected to gender-based violence and gender inequality as a result of their sex. In Anne Meneley’s Tournament of Values: Sociability and Hierarchy in a Yemeni Town, Meneley briefly touches upon gender-based violence and gender inequality, but focuses more on how hierarchy plays a role in the way sociability is developed in Zabid, a Yemeni town. When I read Anne Meneley’s Tournament of Values, I learned that in Zabid, women play a pivotal role in building relations, the economy, domestics, and fashion. Active can be defined as an act of physical engagement. In the contrast, passive can be defined as not taking part on what is happening or wha t occurs to others. Yemeni women do not always play passively; they also partake in the active role. A Deeper Look at Anne Meneley’s Tournament of Values In â€Å"Economy and the Bayt,† a sub-chapter in â€Å"The Bayt: Family and Household,† Meneley explained how the role of women has changed in the Zabidi household. Back then, it was unacceptable for a woman to take care of a man. However, that belief no longer exists because education is now deemed important. Having a woman help in the house can help meet theShow MoreRelatedGender Inequality : A Critical Issue That Affects Women s Rights1662 Words   |  7 PagesGender Inequality Research Paper Gender inequality is a critical issue that affects more women than their male counterparts all around the world. Gender inequality is a form of legal discrimination towards women’s rights. In order to progress and grow as a community and society, gender equality needs to be acknowledged. According to LISTVERSE, the top ten â€Å"extreme† examples of gender inequality towards women that exists around the world today, specifically in the Middle East and North Africa, areRead MoreGender Inequality : A Critical Issue That Affects Women s Rights1665 Words   |  7 Pages Nguyen P.AD-201-D Professor Williamson 11/10/15 Gender Inequality Research Paper Gender inequality is a critical issue that affects more women than their male counterparts all around the world. Gender inequality is a form of legal discrimination towards women’s rights. In order to progress and grow as a community and society, gender equality needs to be acknowledged. According to LISTVERSE, the top ten â€Å"extreme† examples of gender inequality towards women that exists around the world today, specificallyRead MoreIn His Account of the Sociological Imagination, C. Wright Mills (1959) Distinguishes Between ‘Private Troubles’ and ‘Public Issues’. Discuss in Relation to Domestic Violence.746 Words   |  3 PagesDomestic violence (at a glance) is considered to be a private matter; it is something that occurs between couples in the privacy of their homes and affects the individuals involved personally (Knoblock, 2008). But if we look closer, domestic violence is largely driven by social forces and structures (Furze, Savy, Br ym, Lie, 2008). Ideologies and social norms about men and women such as patriarchy and gender inequalities contribute greatly to the occurrence of domestic violence in society. Hence CRead MoreGender And Gender Violence1482 Words   |  6 PagesGender-based violence is the unequal power relationships between men and women. It includes rape, sexual assault and harassment, domestic abuse, and stalking. Gender violence reflects the idea that violence is often used to uphold structural gender inequalities. 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The scope of gender inequality has changed drastically over the years, but there is stillRead MoreWar And Peace, By Nancy Scheper Hughes And Philippe846 Words   |  4 Pagesnormalization of violence in everyday life. Violence, as defined by the World Health Organization is the intentional use of physical force or power, threatened or actual, against one self, another person, or against a group or community that may result in various harms ranging from psychological harm and deprivation to injury and death. From an anthropological perspective, all dimensions of violence are shaped by cultural and social structures, ideas and ideologies. In their publication titled Violence in WarRead MoreGender Inequality And Gender Equality1673 Words   |  7 Pages Gender inequality Women are one-half of the world population they deserve equal opportunity as men because at the end gender equality is part of humanity progress. Many women around the world are treated less favoured than men not only in countries that have traditional gender role but even in societies that believe in equal right for both male and female. Gender inequality means unequal treatment or perceptions of individuals based on their gender. It results from differences in socially constructedRead MoreGender-Based Violence. Gender-Based Violence Is Only One1438 Words   |  6 PagesGender-Based Violence Gender-based violence is only one of the many inequality problems that women face within our society. In the midst of this problem something that becomes more infuriating is the fact that it most often happens at the hands of friends, loved ones, and family members who find a way to justify the abuse and/or put the blame back on the victim. Gender-based violence against women is commonly seen as both a consequence and a cause of gender inequality (Walby, Towers, Francis, 2014

Christian Life And The Teachings Of The Bible - 1243 Words

I have been participating in the Korean language class on Monday and Wednesday from August 10 to now. Last Sunday, I participated in the 1st annual golden harvest 5k marathon. First, I’d like to discuss the spiritual concepts/values from text that relate to personal beliefs. I am a Christian since birth. So all I’d like to talk about is Christian life and the teachings of the bible. Throughout my whole life, I have learned about spiritual things and what kind of spiritual things are in my ego. The spiritual values that I always have is love, hope, and trust. Love is an element that Christians value and have in their Christian mind and the bible says to love each other. I am doing my best to understand this word throughout my whole life and it is the reason why I chose my major Nursing. The dictionary meaning of love is an intense feeling of deep affection or feel a deep romantic or sexual attachment to someone. The bible states that Christian love is selfless and a gi ving love. I realized something when I went to Africa for doing some volunteer work. I felt what it meant to be selfless and what it was to give love through volunteering and now I keep this in mind through my life too. The second value is hope. All of religion is based on hope, just like forgiveness, and going to heaven and waiting for God to give them something that they want. But in the bible it says, â€Å"set your hope fully on the grace that will be brought to you at the revelation of Jesus Christ†(PeterShow MoreRelatedChristianity And The Holy Trinity955 Words   |  4 Pagesof the Bible are the answers for all the problems men face.† (Quotes About Christianity) This quote is from Ronald Regan, and I think it is a good representation of Christianity. Christianity is centered on the teachings and life of Jesus of Nazareth which is found in the Bible. Along with the teachings of Jesus, Christians believe in the Old Testament, that has biblical records that date back to 1500 B.C.E.. Some of these beliefs include the Holy Trinity, salvation, afterlife, and the Bible. TheRead MoreBible as the Inspired Word of God Essay1103 Words   |  5 PagesBible as the Inspired Word of God The Bible is the work of various authors, who lived in different continents and wrote in different eras. Furthermore, much of the text does not claim to have been dictated by God and is not always God speaking to people. In parts it consists of people speaking to God, as in the Psalms, and people speaking to people, as in the New Testament letters written by Paul. In light of this, some maintain that it is not possible to treat theRead MoreIslam And Christianity : Christianity And Islam1684 Words   |  7 PagesChristianity and Islam, both, follow by a sacred book of their God’s word although the Bible is also written by many other authors . They both also have a designated place of worship. Christians gather in a church although the bible does not specifically talk about attending church. Muslims, on the other hand, gather at a mosque that the Qur’an says they should attend as often as possible. Christians follow the bible to guide their way towards Jesus Christ. It is made up of sixty-six different booksRead MoreEssay about The Role Of Women In Christianity522 Words   |  3 PagesThe Role Of Women In Christianity Many people also think that the Christian Church is sexist and does not treat men and women equally. Paul said that: Women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the Law says. If they want to enquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church. 1 Corinthians 14:34-35 Now I want you to realise thatRead More Ethical Teachings in Christianity and Islam Essay1054 Words   |  5 PagesThere are several ethical teachings in Christianity and Islam that instruct Christians and Muslims on how they should act in everyday life. 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It doesn’t matter how many classes I take in Christian theology or history I always seem to learn something new and interesting. I will be discussing just three topics about Christianity that I had previously not known before starting this course. So far threeRead Mo reThe Teachings About Abortion and the Sanctity of Life that are Found in the Bible1048 Words   |  5 PagesThe Teachings About Abortion and the Sanctity of Life that are Found in the Bible An abortion is the premature expulsion of a foetus from the womb, which may be induced or natural, in which case it is usually called a miscarriage. Abortion was legalised in 1967 and before then around 200,000 backstreet illegal abortions took place each year. For Christians, the topic of abortion is a problem as it raises many difficult issues. As it is an issue that concerns lifeRead MoreMessenger Of Christianity, Jesus Of Nazareth1412 Words   |  6 PagesImmanuel, which means, God with us † (Teen Study Bible NIV, Mat.1.23). The name Immanuel, also refers to the leader of the Christian society, Jesus Christ. The word â€Å"Jesus means God is salvation, and the word Christ, or Messiah, means the anointed, that is, the one anointed of God, who came to guide the people walking in darkness† (Arabic Bible). This Christian man, Jesus, is the central deity to the monumental religion of Christianity. He lived a life modeling faith, courage, selflessness, and love

Tea Snob free essay sample

Thewinter of 2001 reared its mild, rain-drenched head in late October. For me winteris less about an exact day on the calendar and more about the state of mind thataccompanies it. Each season invokes in me a new attitude. Spring has beenhistorically a time of languor and laziness as the school year comes to a close;summer, a time of musical enrichment and self-searching; fall a season of death,as the days get shorter and trees turn to naked frames of their former selves. Myinner reaction to winter has always been based on seclusion for a few reasons:the reduced daylight and the inclement weather that keeps me indoors; the forcedgaiety and commercialization of Christmas that leaves me feelingmorose. My mother always kept a private stock of hot chocolate for ourreturn from sledding, and little by little I began to resent the young Swiss girl for telling me that what I was drinking was chocolate. We will write a custom essay sample on Tea Snob or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page When Ivoiced my grievances one snowy afternoon, my mother offered an alternative:Well, fine then, have some tea. She said it with exaggeratedhospitality, and I, calling her bluff but not in any way intending to drink it,agreed to a cup of generic orange pekoe. I followed the instructions:Brew one tea bag in one cup of boiling water. Steep five minutes, more forflavor. It smelled good. It probably tasted good, too. Still, there was aconcern that if I took part in this cup of tea, I would become every Britishnoble who ever turned his nose up at a half-burned crumpet. I took a sip andlooked around, making sure that any witnesses would know I was justexperimenting. My first reaction was cautious; I didnt take a follow-up sipuntil I was sure that the aftertaste of the first was pleasing. It was verypleasing, and before I knew it I was gulping it, disregarding temperature anddregs. When the cup was empty, I brewed a second, then a third and afourth. My guilty pleasure became an obsession, and soon I was doingeverything in my power to get my tea fix. I would accompany my mother to thestore on the premise that I was there to help, but instead I would set up camp inthe cereal/tea aisle. With each visit, I would sneak a new box into the cart.After two months I had nearly three dozen boxes of tea bags and five bags ofloose tea. I had already begun to appreciate the subtle flavor of the green teas,and I fell in love with the thin yet satisfying allure of the Indian Assam loosetea, and adored the sweet aftertaste of the lemon varieties. With thisnewfound love of tea came a sobering realization I had become the tea snob Ihad feared in the first place. The transformation was slow, but noticeable. Istarted to turn up my nose at restaurants Lipton and Tetley teas, and insteadwould bring my own Green Ceylon, imported from Japan. Dont youhave any imports? Even a Spanish Regale would suffice. My pleas wereanswered with an eye roll or a look of total confusion. Sometimes both. Coffee or tea, sir? the attendant would ask. No,thanks, pal, I dont like coffee, and thats not real tea. I didnt evenrealize how I was acting, all I knew was that I found comfort in the actual andfigurative warmth tea provided. When summer rolled around, I found that mysnobbiness was not seasonal. When my family started to buy iced tea, I took it asa personal insult and brewed my own batches of regular and sun tea. As myexperience in brewing grew, my family members drank my teas, and commented on myprogress. I still refuse to drink canned iced tea, even when it is the onlybeverage available. When my average hot and cold tea intake was up toabout six cups a day, my mother warned me that too much tea could result inkidney stones. When I learned more about kidney stones and the pain involved, Icurbed my tea habit sharply to one glass a day, iced or hot. This has taught meto relish and value the tea I allot myself. I still savor even the dregs when Iindulge in a cup of loose Formosa Oolong, and with my daily intake reduced, Iappreciate each swallow. Now when winter approaches, I no longer despairin the quickening dark, nor the forced jolliness of the holiday season. When Ifind myself feeling glum with the colder months and all they represent, I drownmy troubles in one warm cup of water at a time, steeping a bag of OrientalMandarin Orchard for five minutes, or more for flavor.

Solutions to end of Chapter Problems Part Essay Example

Solutions to end of Chapter Problems Part Paper Fin 4910/6990 Further Questions Problem 7. 19 (a) Company A has been offered the rates shown in Table 73. It can borrow for three years at 6. 45%. What floating rate can it swap this fixed rate into? (b) Company B has been offered the rates shown in Table It can borrow for S years at LABOR plus 75 basis points. What fixed rate can it swap this floating rate into? (a) Company A can pay LABOR and receive 6. 21% for three years. It can therefore exchange a loan at 6. 45% into a loan at LABOR plus 0. 24% or LABOR plus 24 basis points (b) Company B can receive LABOR and pay 6. 51% for five years. It can Hereford exchange a loan at LABOR plus 0. 75% for a loan at 7. 26%. Problem 7. 21. The one-year LABOR rate is With annual compounding. A bank trades swaps where a fixed rate of interest is exchanged for 12-month LABOR with payments being exchanged annually. Two. And three-year swap rates (expressed with annual compounding) are 11% and 12% per annum. Estimate the two- and three year LABOR zero rates. The u-year swap rate implies that a two-year LABOR bond with a coupon of 11% sells for par. If is the two-year zero rate so that The three-year swap rate implies that a three-year LABOR bond with a coupon of 12% sells for par. We will write a custom essay sample on Solutions to end of Chapter Problems Part specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Solutions to end of Chapter Problems Part specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Solutions to end of Chapter Problems Part specifically for you FOR ONLY $16.38 $13.9/page Hire Writer If is the three-year zero rate so that The and three-year rates are therefore 11. 05% and 12. 17% with annual compounding. Problem 7. 22_ Company A, a British manufacturer, wishes to borrow U. S. Dollars at a fixed rate of interest. Company B, a US multinational, Wishes to borrow sterling at a fixed rate of interest. They have been quoted the following rates per annum (adjusted for differential tax effects): Sterling LIST Dollars Company A 11. 0% Company B 10. 6% 6. 2% Design a swap that will net a bank, acting as intermediary, 10 basis points per annum and that Will produce a gain Of IS basis points per annum for each Of the no companies. The spread between the interest rates offered to A and B is 0. 4% (or 40 basis points) on sterling loans and 0. 8% (or 80 basis points) on U. S. Dollar loans. The total benefit to all parties from the swap is therefore It is therefore possible to design a swap which will earn 10 basis points for the bank while making each of A and B 15 basis points better off than they would be by going directly to financial markets. One possible swap is shown in Figure SO. 5. Company A borrows at an detective rate of 6. 85% per annum in U. S. Dollars. Company B borrows at an effective rate of 10. 45% per annum in sterling. The ann. earns a ID-basis-point spread. The way in which currency swaps such as this operate is as follows. Principal amounts in dollars and sterling that are roughly equivalent are chosen. These principal amounts flow in the opposite direction to the arrows at the time the swap is initiated. Interest payments then flow in the same direction as the arrows during the life of the swap and the principal amounts flow in the same direction as the arrows at the end Of the life of the swap. Note that the bank is exposed to some exchange rate risk in the swap. It earns 65 basis points in US. Dollars and pays AS basis points in sterling. This exchange rate risk could be hedged using forward contracts. Figure 57. 5 One Possible Swap for Problem 7. 22 Problem 7. 23. Lender the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and receive three-month LABOR in return on a notional principal to $100 million with payments being exchanged every three months. The swap has a remaining life of 14 months. The average of the bid and offer fixed rates currently being swapped tort three-month LABOR is 12% per annum for all maturities. The three-month LABOR rate one month ago was II per annum. All rates are compounded quarterly. What is the value of the swap? The swap can be regarded as a long position in a floating-rate bond combined with a short position in a fixed-rate bond. The correct discount rate is 12% per annum with quarterly compounding or 1 182% per annum with continuous compounding. Immediately after the next payment the floating-rate bond will be worth $100 million. The next floating payment ($ million) is The value of the floating-rate bond is therefore The value of the fixed-rate bond is The value Of the swap is therefore As an alternative approach we can value the swap as a series of forward rate agreements. The calculated value is which is in agreement with the answer obtained using the first approach. Problem 7. 24. Suppose that the term structure of interest rates is flat in the United States and Australia. The USED interest rate is 7% per annum and the LAID rate is 9% per annum_ The current value of the SAID is C,62 SAID, In a swap agreement, a financial institution pays 8% per annum in LAID and receives per annum in LESS. The principals in the two currencies are $12 million SAID and 20 million ADD. Payments are exchanged every year, with one exchange having just taken place. The Swap will last two more years. What is the value of the Swap to the financial institution? Assume all interest rates are continuously compounded. The financial institution is long a dollar bond and short a LESS bond. The value of the dollar bond (in millions Of dollars) is The value of the ADD bond (in millions of LAID) is The value of the swap (in millions of dollars) is therefore or -$795,000. As an alternative we can value the swap as a series of forward foreign exchange contracts. The one-year forward exchange rate is . The non-year tankard exchange rate is . The value of the swap in millions of dollars is therefore which is in agreement with the first calculation, problem 7,25_ Company X is based in the United Kingdom and would like to borrow $50 million at a fixed rate of interest for five years in funds. Because the company is not well known in the United States, this has proved to be impossible. However, the company has been quoted per annum on fixed-rate five-year sterling funds, Company Y is based in the United States and would like to borrow the equivalent of $50 million in sterling funds for five years at a fixed rate of interest It has been unable to get a quote but has been offered US. Dollar funds at 10. % per annum. Vive-year government bonds currently yield 9. 5% per annum in the Lignite States and 10. 5% in the united Kingdom. Suggest an appropriate currency swap that Will net the financial intermediary 0. 5% per annum. There is a 1% differential bet. en the yield on sterling and dollar 5-year bonds. The financial intermediary could use this differential when designing a swap. For example, it could (a) allow company X to borrow dollars at 1% per annum less than the rate offered on sterling funds, that is, at 11% per annum and (b) allow company Y to borrow sterling at 1% per annum more than the rate offered on alular funds, that is, at 11% per annum. However, as shown in Figure SO. , the financial intermediary would not then earn a positive spread. Figure 57. 6 First attempt at designing swap for Problem 7. 25 To make C. S% per annum, the financial intermediary could add 0 25% per annum, to the rates paid by each of X and Y. This means that X pays 11. 25% per annum, for dollars and Y pays I I _ per annum, for sterling and leads to the swap shown in Figure SO. 7. The financial intermediary would be exposed to some foreign exchange risk in this swap. This could be hedged using forward contracts. Figure SO. Final swap for Problem 7. 5 Problem 9. 23. The price of a stock is $40. The price of a one-year European put option on the stock with a strike price to $30 is quoted as $7 and the price to a one-year European call option on the stock with a strike price of is quoted as Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options, Draw a diagram illustrating how the investors profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options? Figure SO. Wows the way in which the investors profit varies with the stock price in the first case. For stock prices less than $30 there is a loss of $1,200. As the stock price increases from $30 to $50 the profit increases from -51,200 to $800. Above $50 the profit is $800. Students may express surprise that a call which is $10 out Of the money is less expensive than a put Which is SIS out Of the money. This could be because of dividends or the acrophobia phenomenon discussed in Chapter leg. Figure So. 8 shows the way in Which the profit varies with stock price in the second case. In this case the profit pattern has a zigzag heap. The problem illustrates how many different patterns can be obtained by including calls, puts, and the underlying asset in a portfolio. Figure SO. 7 Figure 59. 8 Profit in first case considered Problem g_23 Profit for the second case considered Problem 9. 23 Problem 9. 25. Use Derivable to calculate the value of an American put option on a undivided paying stock when the stock price is $30, the strike price is $32, the risk-free rate is 5%, the volatility is 30%, and the time to maturity is IS years. (Choose Binomial American for the option type and 50 time steps. A. What is he options intrinsic value? B. What is the options time value? C. What would a time value Of zero indicate? What is the value Of an option With zero time value? D. Using a trial and error approach calculate how low the stock price would have to be for the time value Of the option to be zero. Derivable shows that the value of the option is 4. 57. The options intrinsic value is . The options time value is therefore . A time value of zero would indicate that it is optimal to exercise the option immediately. In this case the value of the option would equal its intrinsic value. When the stock price is 20, Derivable ivies the value of the option as 12, which is its intrinsic value. When the stock price is 25, Derivable gives the value of the options as 7. 54, indicating that the time value is still positive Keeping the number to time steps equal to 50, trial and error indicates the time value disappears when the stock price is reduced to 21. 6 or lower. (With 500 time steps this estimate of how low the stock price must become is reduced to 21. 3. ) Problem 9,26_ On July 20, 2004 Microsoft surprised the market by announcing a $3 dividend. The ex-dividend date was November 1 7, 2004 and the payment date was December 2, 2004. Its stock price at the time was about $28. It also changed the terms Of its employee stock options so that each exercise price was adjusted downward to Pre-dividend Exercise Price The number Of shares covered by each stock option outstanding was adjusted upward to Number of Shares Pre-dividend Closing Price means the Official NASDAQ closing price Of a share Of Microsoft common stock on the last trading day before the ex-civilized date. Evaluate this adjustment. Compare it with the system used by exchanges to adjust for extraordinary dividends (see Business Snapshot 9. 1). Suppose that the closing stock price is SIB and an employee has 1000 options with a strike price of $24. Microsofts adjustment involves changing the strike price to and changing the number of options to The system used by exchanges would involve keeping the number of options the same and reducing the strike price why 53 to $21, The Microsoft adjustment is more complicated than that used by the exchange because it requires a knowledge to the Microsoft stock price immediately before the stock goes ex-dividend. However, arguably it is a better adjustment than the one used by the exchange. Before the adjustment he employee has the right to pay 524,000 for Microsoft stock that is worth $28,000. After the adjustment the employee also has the option to pay $24,000 for Microsoft stock worth 528,000 Under the adjustment rule used by exchanges the employee would have the right to buy stock worth $25,000 for $21 ,OHO. If the volatility of Microsoft remains the same this is a less valuable option. One complication here is that Microsoft volatility does not remain the same. It can be expected to go up because some cash (a zero risk asset) has been transferred to shareholders. The employees therefore have the same basic option as before UT the volatility Of Microsoft can be expected to increase. The employees are slightly better off because the value of an option increases with volatility. Problem 10. 22. A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19, and a $1 dividend is expected in one month. Identify the arbitrage opportunity open to a trader. Fifth call is worth $3, put-call parity shows that the put should be worth This is greater than $3. The put is therefore undervalued relative to the call. The correct arbitrage strategy is to buy the put, buy the stock, and short the call. This costs $ leg, If the stock price in three months is greater than $20, the call is exercised. If it is less than $20, the put is exercised. In either case the arbitrageur sells the stock for 520 and collects the $1 dividend in one month. The present value of the gain to the arbitrageur is Problem 10. 6. Consider an option on a stock when the stock price is $41, the strike price is $40, the risk-free rate is 6%, the volatility is 35%, and the time to maturity is I year. Assume that a dividend of $0. 50 is expected after six months. . Use Derivable to value the option assuming it is a European call. B. Use Derivable to value the option assuming it is a European put. C. Verify that put-call parity holds. D. Explore using Derivable what happens to the price of the options as the time to maturity becomes very large. For this purpose assume there are no dividends. Explain the results you get. Derivable shows that the price of the call option is 6. 9686 and the price of the put option is 41244 In this case Also As the time to maturity becomes very large and there are no dividends, the price of the call option approaches the stock price of 41. For example, when T = 100 it is 40,94_) This is because the call option can be regarded as a position in the stock where the price does not have to be paid for a very long time. The present value of what has to be paid is close to Zero As the time to maturity becomes very large the price of the European put option becomes close to zero. For example, when T 100 it is 014_) This is because the present value of the expected payoff from the put option tends to zero as the time to maturity increases. Problem 10. 27 Consider a put option on a Nan-dividend-paying stock When the stock price is 40, the strike price is $42, the risk-free rate of interest is 2%, the volatility is 25% per inurn, and the time to maturity is 3 months. Use Drainage to determine: a. The price of the option if it is European (use Black-Schools: European) b. The price Of the option if it is American (Else Binomial: American With 100 tree steps) c. Point B in Figure 10. 7 (a) 9. 06 (b) $3. 08 (c) 535. 4 (using trial and error to determine when the European option price equals its intrinsic value). Problem 12. 16. A stock price is currently It is known that at the end of six months it will be either $60 or $42. The risk-free rate of interest with continuous compounding is per annum_ Calculate the value of a six-month European call option on the stock with an exercise price of $48. Verity that no-arbitrage arguments and risk- neutral valuation arguments give the same answers. At the end Of six months the value Of the option Will be either $12 (if the stock price is $60) or SO (if the stock price is $42). Consider a portfolio consisting of: The value of the portfolio is either or in six months. If the value of the portfolio is certain to be 28. For this value of the portfolio is therefore reckless. The current value of the portfolio is: here is the value of the option. Since the portfolio must earn the risk-free rate of interest The value of the option is therefore $6. 96, This can also be calculated using risk-neutral valuation. Suppose that is the probability of an upward stock price movement in a risk-neutral world. We must have The expected value of the option in a risk-neutral world is: This has a present value Of Hence the above answer is consistent With risk-neutral valuation. Problem 12. 17. A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk This is greater than the value Of the European option because it is optimal to exercise early at node C. Figure SIS. S Tree to evaluate European and American put options in Problem 12. 17. At each node, upper number is the stock price, the next number is the European put price, and the final number is the American put price Problem 12. 19. A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or reduce by 10%. The risk-tree interest ate is use a two-step tree to calculate the value of a derivative that pays off where is the stock price in four months? If the derivative is American-style, should it be exercised early? This type of option is known as a power option. A tree describing the behavior of the stock price is shown in Figure SIS_6. The risk-neutral probability of an up move, , is given by The value Of the European option is 5. 394. This can also be calculated by working back through the tree as shown in Figure SIS. 6. The second number at each node is the value Of the European option. Early exercise at node C would give 9. 0 which is less than 13. 2449. The option should therefore not be exercised early if it is American.