Suppose that the price S(t) of a share is described by the GBM with pa-rameters So, μ, σ, and r is the continuously compounded interest rate. Aderivative on this share provides at time T a payoff R(S(T)) = S(T)1.2.(a) Compute the no-arbitrage price C of this derivative.(b) Derive the formula for the probability that the payoff at time T to theowner of one share will be grater than A. Compute this probability ifT = 1 year, μ = 0.05, σ = 0.14, So = 40, A = 44.

a. Compute the no-arbitrage price C of this derivativeThe no-arbitrage price C of the derivative is…

Answered: Suppose that the price S(t) of a share…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following table represents the prices of copper futures (in USD) from theperiod of time from 14.06.2020 to 06.06.2021, where t is time since 14.06.2020 (measured in weeks) and f(t) is the corresponding price: t f(t) 0 2.6655 1 2.7120 2 2.7800 3 2.9255 4 2.9355 5 2.9220 6 2.9110 7 2.8445 8 2.9070 t f(t) 9 2.9570 10 3.0365 11 3.0810 12 3.0590 13 3.1215 14 2.9785 15 2.9900 16 3.0800 17 3.0720 t f(t) 18 3.1305 19 3.0565 20 3.1635 21 3.1890 22 3.3125 23 3.4210 24 3.5285 25 3.5340 26 3.6370 t f(t) 27 3.5675 28 3.5240 29 3.6800 30 3.6070 31 3.6315 32 3.5565 33 3.6265 34 3.7885 35 4.0775 t f(t) 36 4.0925 37 4.0755 38 4.1400 39 4.1130 40 4.0680 41 3.9905 42 4.0400 43 4.1680 44 4.3360 t f(t) 45 4.4680 46 4.7485 47 4.6545 48 4.4810 49 4.6775 50 4.5290 51 4.5375 Let L(x) be the third Lagrange polynomial for the function f(x) with the nodes X0 = 0, x1 =…
The team meeting will be held in 3 days from the date of the assignment and because of the limitation of time the Chief economist has given you the following guidelines: (a) Is there a trend in total accidents? (b) Is there seasonality in total accidents? (c) Consider the following change in the time series model: y; = P1yt-1 + ut where ut follows a white noise process. What is the condition we need to impose on p1 in order for the series yt to be weakly stationary? Why? (d) Consider the following change in the time series model: y; = Bo + B1x1-1+ B2xt-2 + u where y, is some outcome variable of interest, and x-1 and x-2 are strictly exogenous explanatory variables. How would you test for the presence of serial correlation in the residual uz? (e) Briefly explain how you would carry out econometric analysis of the model in (d) if u, is found to be stationary, but positively serially correlated.
Ay 1
7. (a) If land that can be farmed L is eroding continuously at a rate of 4.5% per year because of changing climatic conditions, how much of this land will be left after 25 years? (b) A piece of art currently worth $2500 is appreciating in value 'V' according to the formula: 2500et0.5 However, assuming continuous discounting, the present value of V is given by: P = Vert = How long should the piece of art by kept to maximise its present value under continuous compounding with: (i) r = 0.05 (ii) r = 0.09
Q2 (a) Azli and Iman are both traveling for Batu Pahat to Melaka on daily basis. The average travelling time for both them is 98.4 minutes with a standard deviation of 7.8 minutes and 110.7 minutes with standard derivation of 29.8 minutes respectively. Assume that the traveling population are approximately normal distributed and random samples of traveling time of Azli and Iman are 36 and 49 respectively. (i) Calculate the probability of Azli's average travelling time to be more than 100 minutes. (ii) Find the probability of Iman's average travelling time to be in between 105 and 115 minutes.
Exercise 3 Ana owns a car worth €50 000 which can get stolen with probability 1%. She can pur- chase coverage of the amount q € [0; 50 000] at premium 7 = €0.05 for each euro covered. Her utility function is u = ln(w), where w is money. Assume she has no other assets. (a) Formulate her maximization problem. (b) How much insurance (q) will she choose to buy? Explain. (c) How much profits does the insurance company earn on insuring Ana?
What is Power and Multiple Rules?
Assume the stock price follows a geometric Brownian motion, where current price S0=50, expected return µ=0.02 and volatility σ=0.80. The risk-free interest rate r=0.05 p.a. Using the Black-Scholes formula, what is the current value c0 of an European call option written on the stock with a strike of K=50 and a maturity of 3 months?
a) A university projects that enrollments are going to decline as the pool of college-aged applicants begins to shrink. They have estimated the number of applications for coming years to behave according to the function a = f(t) = 6,500 – 250t where a equals the number of applications for admission to the university and t equals time in years measured from this current year (t = 0). i. What class of function is this? ii. What is the expected number of applications 5 years from today? 10 years? iii. Do you think this function is accurate as a predictor indefinitely into the future? iv. What kinds of factor would influence the restricted domain on t?
According to the U.S. Customs and Border Protection Agency, the average airport wait time (time from arrival at the airport until the completion of security screening) at Chicago's O'Hare Inter- national airport is 32 minutes for a passenger arriving during the hours 4-5 PM. Assume the wait time is exponentially distributed so that p(t) = ke-kt for 0≤t<∞, where k is the reciprocal of the average wait time. Assume t is measured in minutes. 1. Sketch a labeled plot of the relevant pdf on the interval [0, 90] minutes (while remembering that it is defined for all t≥ 0.) 2. Set up integrals (you can write p(t) for the integrand) for the following probabilities: (a) Waiting longer than 60 minutes. (b) Waiting shorter than 30 minutes. (c) Waiting between 20 and 40 minutes. 3. Evaluate the probability that the waiting time is longer than 60 minutes (part 2(a) above) and convert to a percentage with two decimal places.
A poll commissioned by a politician estimates that t days after he makes a statement degenerating women, the percentage of his constituency ( those who support him at the time he made the statement) that still supports him is given by S(t) = 75(t2 - 3t +25)/t2 + 3t + 25 The election day is 10 days after he made the statement. 1. If the derivative S'(t) may be thought of as an approval rate, derivate the a function for his approval rate. 2. Was the approval rate positive or negative on the date of the election?
The quantity, Q mg, of nicotine in the body t minutes after a cigarette is smoked is given by Q = f (t). (a) Interpret the statements ƒ (20) = 0.36 and ƒ' (20) and -0.002? ƒ (20) = 0.36 means ƒ' (20) = -0.002 means (b) Use the information given in part (a) to estimate ƒ (21) and ƒ (24). Round your answers to three decimal places. ƒ(21) ≈ ƒ (24) ≈ i mg = - 0.002 in terms of nicotine. What are the units of the numbers 20, 0.36, mg A

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