...Chapter 12 & 20 Chapter 21 The Black-Scholes Formula and Option Greeks Adapted from Black & Scholes (1973), The Pricing of Options and Corporate Liabilities, The Journal of Political Economy, Vol. 81, No. 3., pp. 637-654. 2 Black-Scholes Assumptions • Assumptions about stock return distribution Continuously compounded returns on the stock are normally distributed and there is no jumps in the stock price The volatility is a known constant Future dividends are known, either as discrete dollar amount or as a fixed dividend yield • Assumptions about the economic environment The risk-free rate is a known constant There are no transaction costs or taxes It is possible to short-sell costlessly and to borrow at the risk-free rate 3 Black-Scholes Assumptions • The original paper by Black and Scholes begins by assuming that the price of the underlying asset follows a process like the following dS (t ) ( )dt dZ (t ) S (t ) where (20. 1) S(t) is the stock price dS(t) is the instantaneous change in the stock price is the continuously compounded expected return on the stock δ is the dividend yield on the stock is the continuously compounded standard deviation (volatility) Z(t) is the standard Brownian motion dZ(t) is the change in Z(t) over a short period of time 4 Black-Scholes Assumptions • There are 2 important implications of equation (20.1) Suppose the stock price now is S(0). If the stock...
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...persuade my audience that IF they choose to support a children’s charity, to support St Jude Children’s Research Hospital. Central Idea: Many charities are deserving of support, but St Jude is truly special. Everything they do for these children makes their lives and their family’s lives just a little bit easier. Pattern of Organization: Problem-Solution Introduction: Attention: How many of you here think that one day, you will choose to support a charity, whether through donating your money or volunteering your time? Reveal Topic: There are hundreds of deserving charities across the nation, but a really special one is St Jude Children’s Research Hospital. Credibility: If you remember from my introductory speech, I’m a member of Delta Delta Delta and our sorority nationally supports St Jude as our philanthropy. I have toured this hospital and have seen first-hand how incredible St Jude really is. Relate to the Audience: As college students, we don’t all necessarily have the means to donate to a charity like this, but there are many little things that you can do that will help more than you think. For example, the last Monday in September, Chili’s, who also is a huge contributor to St Jude, donates 100% of that days profit nationwide to the hospital. It’s as easy as going out to lunch or dinner. Preview: Today I’m going to share with you some information on pediatric cancer, what St Jude is and how they are setting the standard for children’s research hospitals ...
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...The land of Louisiana has been created over thousands of years. Through the Mississippi River, sediment has made its way down to the gulf to build up and create the land we stand upon today. However, when more people settled, they had to find a way to stop the spring floods of the river. For over 280 years, the New Orleanians struggled with this issue. When the river was swollen, the fear of the town being submerged was ubiquitous. The Mississippi river changes course because of a distributary that has a shorter route to the gulf. Sometimes, the meanders in the river become very looped turns due to the land getting eroded between the turn. Soon enough, the turn is cut off and becomes what is called an oxbow lake. In 10,000 years, the Mississippi...
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...1. The Arbitrage Theorem: -‐>Derivatives cannot be priced by discounting tech, cause underlying moves and risk changes -‐>arbitrage pricing: Replicating portfolio: should equal cost of instr. è Prices are represented by vector ������! (������) ������! ������! = … ; N=Assets ������ = … ;K=states ������! (������) ������! ������!! … ������!! ������ = … … … ; payoff Matrix (row=assets) ������!! … ������!" S=Asset prices; arbitrage free only if Q are positive If we want q as column: D_inv*S; if not: D_tran_inv Example: 1 asset rf=10% and 1 stock=150 or 100 1) Use state prices ∆������ = ������ ∆������ where ������ = ������ 0,1 Mean of Δz=0; Variance of Δz=Δt ������������ = ������������������������ + ������������������������ è Also geometric Brownian Motion Ito’s lemma: ������������ ������������ 1 ! ! ������ ! ������ ������������ ������������ = + ������������ + ������ ������ ������������ + ������������������ ������������ ������������ 2 ������������ ! ������������ Where G(S,t) is a function of S (process); term to the left in brakets is expected change...
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...Shihab General Information: 1. Address: The ALS Association St. Louis Regional Chapter 2258 Weldon Parkway St. Louis, MO 63146 Phone Number: 314-432-7257, 888-873-8539 Email: info@alsastl.org Web site: www.alsa-stl.org 2. Number of Employees/Volunteers: Officer: 5 Board of Director: 13 Director Emeritus: 9 (decreased) Advisory Directors: 3 3. Mission Statement: “Leading the fight to treat and cure ALS through global research and nationwide advocacy while also empowering people with Lou Gehrig’s Disease and their families to live fuller lives by providing them with compassionate care and support.” 4. Latest Impact Statement / Latest Main Accomplishments “The ALS Association and The American Academy of Neurology are awarding the 2015 Sheila Essey Award to Adriano Chio, M.D., F.A.A.N. (The University of Turin, Italy) and Robert P. Bowser, Ph.D. (Barrow Neurological Institute in Phoenix, Arizona). The award prize $50000 is given to continue ALS research.” Contact/2014 Financial Challenge: Kathi Henson, Board vice chair, Phone: 314-432-7257 According to the form 990, the ALS Association St. Louis Regional Chapter’s revenue is decreasing from the previous year. In 2012 contribution and gift was $1,518,636 but in 2013 it decrease to 1,429,073. This is a big threated issue for the ALS Association St. Louis Regional Chapter. Identify Donor Demographics: From the ALS Association St. Louis Regional Chapter’s official website we can find the past fundraisers...
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...indenture calling for issuer to periodically repurchase some proportion of outstanding bonds before maturity *Serial bond – does not require sinking fund, sell bonds w/ staggered maturity dates. (more expensive, bond of each maturity dater are different bonds) *Bullet – debt instrument where entire FV is paid at once on maturity date. Non callable, cannot be redeemed earlier, low rate of interest straight v. option embedded bonds s- o- a bond that gives the holder of issuer a right to perform action at some point in future 11 interest rate sensitivity – reverse relationship between price and yield. Y^Pfall ^ytm=smaller price change IRR less than proportional to bond maturity Low coupon more sensitive than high LT more sensitive than ST Duration – measure of the effective maturity of a bond (time it takes to recoup initial investment or price) Macaulays duration – weighted avg of times until each pmt made by bond Modified duration = macaulays / 1+y (measures interest rate sensitivity of bond) Higher duration = higher sensitivity Convexity – duration of a bond changes as interest rate changes Portfolio mgmt. – mgmt. of one or more port Active – strategy where manager makes specific investments with goal of outperforming benchmark(swap, horizon analysis) Passive – opposite of active – follow benchmark, manager attempt to beat mkt w/ various investing strategies (CF matching, immunization) Contingent - 15/16 American – can exercise anytime between inception...
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...leadership qualities evidently among the following leaders Harvey Najim Harvey Najim is the executive chairman of Sirius Computer Solutions, Inc., the company he founded in 1980 under the name Star Data Systems. In 1997, Mr. Najim renamed his company Sirius, after the brightest star in the night sky. Since then he has been working not only to make Sirius the nation's top IBM solution provider, but also to use his success to build a brighter future for less-privileged members of the San Antonio community. Nido Quebein Nido Qubein is a businessman, motivational speaker, and President of High Point University since 2005. He received his Associate's Degree in Business from Mount Olive College, where he was a member of (Delta Pi Delta) fraternity. He earned his Bachelor's Degree in Human Relations from High Point University in 1970, and his Master of Science in Business Education degree from the University of North Carolina at Greensboro Bryan School of Business & Economics in 1973; in 2009, he was awarded an Honorary Doctor of Letters in Humanity degree from the University of North Carolina at Greensboro. Qubein is the Founder and Chairman Emeritus of the National Speakers Association Foundation. He has served as Chairman of the Great Harvest Bread Company since 2001 and on the Board of Directors of BB&T since 1990 and La-Z-Boy Corporationsince 2006. In 1999, Qubein was honored with the Distinguished Alumni Award from the University of North Carolina at Greensboro Bryan...
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...Affairs This portion of the paper will include key information about Delta Air Lines, Inc. (Delta): (a) history; (b) culture; (c) important leaders over the years; (d) current products and service offerings: (e) target markets; and (f) methods of product and service delivery. History This section describes the history of Delta. The company was founded in Macon, Georgia, in 1924, as the world’s first crop-dusting service, Huff-Daland Dusters. The company moved to Monroe, Louisiana, in 1925. In 1928, field manager C. E. Woolman and two partners purchased the service and renamed it Delta Air Service after the Mississippi Delta region it served. Delta was the first international mail and passenger route on the west coast of South America. Delta operated its first passenger flights over route stretching from Dallas, Texas to Jackson, Mississippi, via Shreveport and Monroe, Louisiana. Also, Delta was awarded a US Postal Service contract in 1934 to fly from Fort Worth to Charleston via Atlanta (Hoover’s, 2011). In 1941, Delta relocated to Atlanta. Woolman became the president in 1945 and he managed the company until his death in 1966 (Delta, 2011). Delta offered its first night service in 1935, using the Stinson Model A; the first Delta aircraft with two pilots. Douglas DC-2 and DC-3 service was introduced and the introduction of flight attendants, called “stewardesses,” added to flight crews. Delta contributed to the war effort by modifying 1,000 plus aircraft, over-hauling...
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...call parity –replicate by moving everything else in the other side sell most expensive buy least expensive Slide 5 Bull spread/bear spread using calls and puts, e.g. max profit in bull/bear spread Box spread- payoff difference between strike prices = price today pv of difference of strike price Calendar spread(not specific question) Strip-strap whats strategy in place, profit expectation Ch. 12 Use contrstuct binomial trees Derivative with payoff = st2 – 750 <-pays this amount in maturity T=0.5 years Rf= 5% continuously compounded So=30 Volatility=20% delta(t)=.25 /36.64 30 -<33.16 27.15 \24.56 U=e^sigmasqrt(deltaT)=e.2sqrt(.25)=1.10517 d=e^-sigmasqrt(deltaT)=1/u=0.90484 Upper bound 30*1.10517=33.16 33.16*1.10517=36.64 Lower bound 30*.90484=27.15 27.15*.90484=24.56 p=(e^rdelta*t)-d/u-d=.5378 1-p=.4622 Payoff St^2-750= 36.64^2-750=592.5 30^2-750= 150 24.56^2-750=-146.81 Calculate value of derivative thru nodes B: ([.5378)(592.5)+.4622(150)) e^-.05(.25) C=.5378(150)+.4622(-146.81)e^-.05(.25) A=(.5378(B) + .4622(B) )e^-.05(.25) Payoff 33 = put 36.64 strike price payoff =0 30 strike price payoff = 3 24.56 strike price payoff=8.94 ------------------------------------------------- Black scholes formula ch13. How we can use options to use portfolio insurance e.g. put options Couple formulas 1) determines number of contracts you have to pay, a function of beta ...
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...CHAPTER 7: ADVANCED OPTION STRATEGIES END-OF-CHAPTER QUESTIONS AND PROBLEMS 1. (Bull Spread) Buy one put with exercise price X1 and sell one put with exercise price X2. The profit equation is ( = Max(0, X1 – ST) – P1 – Max(0, X2 – ST) + P2 If ST < X1 < X2 ( = X1 – ST – P1 – X2 + ST + P2 = X1 – X2 – (P1 – P2) Recall from Chapter 3 that the difference between exercise prices is less than the difference between premiums. Since X1 < X2 and P1 < P2, the above profit is negative. If X1 < ST < X2 ( = – P1 – X2 + ST + P2 This figure increases dollar for dollar with ST. The breakeven is found by setting the profit to zero, – P1 – X2 + ST* + P2 = 0 and solving for ST* ST* = X2 + (P1 – P2) If X1 < X2 ( ST ( = – P1 + P2 Since P2 > P1, this figure is positive. The minimum profit occurs in the first profit range, ST < X1 < X2 and equals X1 – X2 – (P1 – P2). The maximum profit occurs in the third profit range, X1 < X2 < ST and equals – P1 + P2. 2. (Straddle) A straddle is a strategy based on the expectation that the market will have high volatility. If, however, everyone else in the market believes that the market will have high volatility, then the prices of the call and put will reflect the higher volatility, which will result in breakeven points further away from the current stock price. A straddle is most likely to be successful when the investor believes that the market will be more volatile...
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...use of these trademarks is licensed from McDonald’s Corporation. MONOPOLY, ®, ™ & © 2013 Hasbro. All Rights Reserved. © 2013 Wal-Mart Canada Corp. EA, EA SPORTS and the EA SPORTS logo are trademarks of Electronic Arts Inc. Snapfish is a registered trademark of Hewlett-Packard Development Company, L.P. All Rights Reserved. Interac, the Interac logo and Interac Flash are trade-marks of Interac Inc. Used under license. FIAT is a registered trademark of Fiat Group Marketing & Corporate Communication S.p.A., used under licence by Chrysler Canada Inc. Beaches® Resorts – The Luxury Included® Family Vacation. Beaches® is a registered trademark of Sandals Resorts International. All rights reserved. Delta Vacations is managed, operated and marketed by MLT Vacations, a wholly owned subsidiary of Delta Air Lines. NON-FOOD PRIZES† For all non-food Prizes, obtain the necessary Game Stamp(s).† See the Official Rules for details.† To redeem: 1) Call the telephone number provided on Game Stamp...
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...integration problem ∞ 0 f (t)e−st dt, succinctly denoted L(f (t)) in science and engineering literature. The L–notation recognizes that integration always proceeds over t = 0 to t = ∞ and that the integral involves an integrator e−st dt instead of the usual dt. These minor differences distinguish Laplace integrals from the ordinary integrals found on the inside covers of calculus texts. 7.1 Introduction to the Laplace Method The foundation of Laplace theory is Lerch’s cancellation law ∞ −st dt 0 y(t)e = ∞ −st dt 0 f (t)e (1) L(y(t) = L(f (t)) implies or implies y(t) = f (t), y(t) = f (t). In differential equation applications, y(t) is the sought-after unknown while f (t) is an explicit expression taken from integral tables. Below, we illustrate Laplace’s method by solving the initial value problem y = −1, y(0) = 0. The method obtains a relation L(y(t)) = L(−t), whence Lerch’s cancellation law implies the solution is y(t) = −t. The Laplace method is advertised as a table lookup method, in which the solution y(t) to a differential equation is found by looking up the answer in a special integral table. 7.1 Introduction to the Laplace Method 247 Laplace Integral. The integral is called the Laplace N integral of the function g(t). It is defined by limN →∞ 0 g(t)e−st dt and depends on variable s. The ideas will be illustrated for g(t) = 1, g(t) = t and g(t) = t2 , producing the integral formulas in Table 1. ∞ −st dt...
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...Financial Derivatives Revision Sheet Futures: * agreements to buy or sell an asset at a future time or date * traded on exchange * standardised * choose to close out before delivery * Daily settlement * Margins * Range of delivery dates * Virtually no credit risk Forwards: * agreement to buy or sell an asset at a future time or date * private agreement between two traders (clients or financial institutions) * Not standardised * Settled at end of contract * Delivery of final cash settlement usually takes place * Usually one specified delivery date * Some credit risk Closing out: entering into the opposite trading strategy to the original Hedging using futures: the objective is to take a position that neutralises risk as far as possible. Knows it will lose with an x decrease in price= take a short hedge. It will loss on an x increase= take a long hedge. Arguments for and against Hedging: * Shareholders * Competitors * Can Lead to a worse outcome Basis = spot price of an asset- Futures price of contract used Calculating Minimum Variance Hedge Ratio: * Optimal hedge ratio is when ρ=1 and σs=σf as hedge=1 * Hedge Ratio= ρσsσF * Rolling the Hedge Forward: Sometimes expiration is greater than delivery dates of the future contracts that can be used. The hedger must then roll the hedge forward by closing out one future contract and taking the same position in a futures contract with a later...
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...The History of the Blues * In my Assignment I will be mostly taking about the ways that the blues has influenced culture. So what did the blues influence…? Everything. The blues influenced nearly every genre of music that came after it. Jazz in all of its various styles and flavors. From just a basic 12bars you get everything that you need in order to play great music. It’s not like without the blues we would not have any current music actually it’s a lot like that. The influence of blues can even be seen in the classical music of the later Romantic period as well as in various aspects of Contemporary classical music. Literally every style of music that’s come out in the past eighty or more years has once or a few times borrowed something from the blues. To think the whole world would of changed if there was not the blues, or slavery for that matter. To think we would not even have big band music or loud electric guitars, or a guy going yo yo into a microphone. * When you think of the blues, you think about misfortune, betrayal and regret. You lose your job, you get the blues. Your mate falls out of love with you, you get the blues. Your dog dies, you get the blues. * While blues lyrics often deal with personal adversity, the music itself goes far beyond self-pity. The blues is also about overcoming hard luck, saying what you feel, ridding yourself of frustration, letting your hair down, and simply having fun. The best blues is visceral, cathartic, and starkly...
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...I find it to be insulting. I am not apart of a fraternity, I am not hazing pledges, I am not causing people to die and neither is my chapter locally or globally. Specific people at certain colleges contribute to cause an overall negative connotation with the organization. This idea is more prevalent now because of the easily accessible content mobily, “Fraternities and sororities are often negatively regarded due to the media’s tendency to dramatize the social aspects of Greek-letter organizations.” I am apart of the Delta Delta Delta Phi chapter here at the University of Iowa. My chapter and fellow chapter across the nation contribute to our philanthropy which is for St. Jude Children’s Research Hospital. In July 2014, Tri Delta made the largest single fundraising commitment by a St. Jude partner in the hospital's history–pledging $60 million in 10 years. In 2018 we have already raised more than half of the goal in only 4 years with $45 million dollars. Tri Delta is not the only sorority that is positively giving back and making a change in the world. These Combined efforts of the student organized greek life, loyal alumea, and extensive networks of friends and families are not represented in the headlines. Media seems to focus on only the tragedies in the greek life community. The aspects of philanthropy, grades, friendship, and community involvement are overshadowed. Greek life is taking the correct actions by addressing the problems within the organization, but are not illustrating...
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