MATLAB: An Introduction with Applications
5th Edition
ISBN: 9781118629864
Author: Amos Gilat
Publisher: WILEY
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Chapter 9, Problem 2P
Determine the solution of the equation
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Question 1: Determine and interpret the correlation coefficient between the two variables. In your interpretation, discuss the direction of the relationship (positive, negative, or zero relationship). Also discuss the strength of the relationship.
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Direction of the relationship (positive, negative, or zero relationship):
Strength of the relationship (strong/moderate/weak):
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In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
Chapter 9 Solutions
MATLAB: An Introduction with Applications
Ch. 9 - Prob. 1PCh. 9 - Determine the solution of the equation 2cosx0.5x=1...Ch. 9 - 3. Determine the solution of the equation .
Ch. 9 - 4. Determine the solution of the equation .
Ch. 9 - 5. A box of mass m = 25 kg is being pulled by a...Ch. 9 - 6. A scale is made of two springs, as shown in the...Ch. 9 - An estimate of the minimum velocity required for a...Ch. 9 - 8. The diode in the circuit shown is forward...Ch. 9 - 9. Determine the minimum and the maximum of the...Ch. 9 - A paper cup shaped as a frustum of a cone with...
Ch. 9 - 11. Consider again the block that is being pulled...Ch. 9 - 12. Determine the dimensions (radius r and height...Ch. 9 - 13. Consider the ellipse. Determine the sidesa...Ch. 9 - 14. Planck’s radiation law gives the spectral...Ch. 9 - A 108-in.-long beam AB is attached to the wall...Ch. 9 - 16. Use MATLAB to calculate the following...Ch. 9 - 17. Use MATLAB to calculate the following...Ch. 9 - 18. The speedofarace carduring the first seven...Ch. 9 - 19. The shape of the centroid line of the Gateway...Ch. 9 - The flow rate Q (volume of fluid per second) in a...Ch. 9 - 21. The electric field E due to a charged circular...Ch. 9 - Prob. 22PCh. 9 - The variation of gravitational acceleration g with...Ch. 9 - 24. A cross section of a river with measurements...Ch. 9 - Prob. 25PCh. 9 - Prob. 26PCh. 9 - Prob. 27PCh. 9 - Prob. 28PCh. 9 - Prob. 29PCh. 9 - Prob. 30PCh. 9 - Prob. 31PCh. 9 - Use a MATLAB built-in funtion to numerically...Ch. 9 - The growth of a fish is often modeled by the von...Ch. 9 - A water tank shaped as an ellipsoid (a = 1.5 m, b...Ch. 9 - The sudden outbreak of an insect population can be...Ch. 9 - An airplane uses a parachute and other means of...Ch. 9 - Prob. 37PCh. 9 - An RL circuit includes a voltage source vs, a...Ch. 9 - Prob. 39PCh. 9 - The velocity, v, of an object that falls freely...
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- Problem 4. Margrabe formula and the Greeks (20 pts) In the homework, we determined the Margrabe formula for the price of an option allowing you to swap an x-stock for a y-stock at time T. For stocks with initial values xo, yo, common volatility σ and correlation p, the formula was given by Fo=yo (d+)-x0Þ(d_), where In (±² Ꭲ d+ õ√T and σ = σ√√√2(1 - p). дго (a) We want to determine a "Greek" for ỡ on the option: find a formula for θα (b) Is дго θα positive or negative? (c) We consider a situation in which the correlation p between the two stocks increases: what can you say about the price Fo? (d) Assume that yo< xo and p = 1. What is the price of the option?arrow_forwardWe consider a 4-dimensional stock price model given (under P) by dẴ₁ = µ· Xt dt + йt · ΣdŴt where (W) is an n-dimensional Brownian motion, π = (0.02, 0.01, -0.02, 0.05), 0.2 0 0 0 0.3 0.4 0 0 Σ= -0.1 -4a За 0 0.2 0.4 -0.1 0.2) and a E R. We assume that ☑0 = (1, 1, 1, 1) and that the interest rate on the market is r = 0.02. (a) Give a condition on a that would make stock #3 be the one with largest volatility. (b) Find the diversification coefficient for this portfolio as a function of a. (c) Determine the maximum diversification coefficient d that you could reach by varying the value of a? 2arrow_forwardQuestion 1. Your manager asks you to explain why the Black-Scholes model may be inappro- priate for pricing options in practice. Give one reason that would substantiate this claim? Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager asks you to pick only one of them to invest in based on the model provided. Which one do you choose and why ? Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price at time t of a European put with maturity T and strike price K. Then, the discounted option price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.) Question 4. You are considering pricing an American put option using a Black-Scholes model for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no more than 2 sentences), explain how you would proceed to price it. Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the interest rate…arrow_forward
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