We consider an investment in a European call option. The investment horizon is [0,7]. The option...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
We consider an investment in a European call option. The investment horizon is [0,7]. The option will mature at T > 7 with strike price K and it is written on a nondividendpaying stock whose price follows a geometric Brownian motion: dS₁ = μSedt + o SidW₁ = rStdt+oSidWt, t> 0, where {W,:t> 0} and {W₁ : t≥ 0} are standard Brownian motions under the physical proba bility measure P and riskneutral probability measure Q respectively. From the two dynamics above, we have that, W₁ = W₁+"="t₁ t≥ 0. We are interested in the return and risk of this option position at the end of investment horizon. The rate of return R, can be calculated as follows: R where Co and C, are the option prices at time 0 and 7 respectively. For the following questions, we set the parameters as = 0.05, r =0.02, = 0.3, So K = 200, T = 0.5 and T = 1.0. Cre Co et Co 100, 1. Estimate the expected return EP[R] with standard Monte Carlo simulation. 2. Propose and implement an importance sampling estimator that improves your estimator in (1). 3. Based on (2), propose and implement a pathwise estimator and a likelihood ratio estimator for the sensitivity of expected return w.r.t. So, i.e., DE[Rr] aso We consider an investment in a European call option. The investment horizon is [0,7]. The option will mature at T > 7 with strike price K and it is written on a nondividendpaying stock whose price follows a geometric Brownian motion: dS₁ = μSedt + o SidW₁ = rStdt+oSidWt, t> 0, where {W,:t> 0} and {W₁ : t≥ 0} are standard Brownian motions under the physical proba bility measure P and riskneutral probability measure Q respectively. From the two dynamics above, we have that, W₁ = W₁+"="t₁ t≥ 0. We are interested in the return and risk of this option position at the end of investment horizon. The rate of return R, can be calculated as follows: R where Co and C, are the option prices at time 0 and 7 respectively. For the following questions, we set the parameters as = 0.05, r =0.02, = 0.3, So K = 200, T = 0.5 and T = 1.0. Cre Co et Co 100, 1. Estimate the expected return EP[R] with standard Monte Carlo simulation. 2. Propose and implement an importance sampling estimator that improves your estimator in (1). 3. Based on (2), propose and implement a pathwise estimator and a likelihood ratio estimator for the sensitivity of expected return w.r.t. So, i.e., DE[Rr] aso
Expert Answer:
Answer rating: 100% (QA)
1 To estimate the expected return ER using standard Monte Carlo simulation we can generate a large n... View the full answer
Related Book For
Posted Date:
Students also viewed these finance questions

3. The sketch shows an exploded drawing of a pump driven by a 1.5kW, 1800rpm motor integrally attached to a 4:1 ratio gear reducer. Reducer shaft C is connected directly to pump shaft C' through a...

Find the lengths of the curves. The cardioid r = 1 + cos

What are the four rules for effective bootstrapping? How could you apply these rules to a business that you have started or hope to start one day? (LO 5: Explain how bootstrapping can help a small...

In Exercises, find the indefinite integral and check the result by differentiation. X 1x dx

Maximum work is done in compressing air when the compression is: (a) Isothermal compression (b) Adiabatic compression (c) Polytropic compression (d) None of these

An accountant with the Atlanta Olympic Games was charged with embezzling over $60,000 to purchase a MercedesBenz and to invest in a certificate of deposit. Police alleged that he created fictitious...

direction and 0 Find magnitude, resultant for the system of forces 20 kN 25 kN location of of the 60 30 A B shown in figure. 3 m D 3 m C 45 18 kN 12 kN

Each of the following compounds is characterized by a 1H NMR spectrum that consists of two peaks, both singlets, having the chemical shifts indicated. Identify each compound. (a) C6H8; 2.7 ppm (4H)...

At the end of the year, Shamrock Co. has pretax financial income of $538,000. Included in the $538,000 is $65,000 interest income on municipal bonds, $24,000 fine for dumping hazardous waste, and...

Describe your perfect work environment to your classmates. What type of office / location ? How many people would work with you? What would your hours be ?

If the total positive charge is Q = 1.62x106 C, what is the magnitude of the electric field caused by this charge at point P, a distance d = 1.53 m from the charge? Enter your answer numerically in...

People who make good substantive comments and cultivate a healthy group climate tend to have: a . legitimate power. b . reward power. c . earned power. d . referent power.

An AC signal (Vo,f) = (28.3V, 50Hz) is connected across a 100 mH inductor. 1. Calculate the current (rms) in the circuit 2. What is the power dissipated in the inductor? V 28.3V 50Hz L V, 100mH

A company's current stock price is $65.40and it is likely to pay a $2.25 dividend next year. If analysts estimate the company will have a constant 11.25% growth rate, what is its expected return?...

gauss Jorden Methde Solve this with 3 X + X + 5x3 = 9 2 SX,+ 6X2+3Xg : 15 3x + 2x + 5x3 + 5x3 = 25

The Ferris wheel in the figure has a radius of 68 feet. The clearance between the wheel and the ground is 14 feet. The rectangular coordinate system shown has its origin on the ground directly below...

You use the following information to construct a oneperiod binomial forward tree for modeling the price movements of a nondividendpaying stock. (The tree is sometimes called a forward tree.) (i)...

For a fixed strike price K 1 , determine the value of the payment trigger that maximizes the payoff of a European gap option.

Assume the BlackScholes framework. The current price of a nondividendpaying stock is $60 and the continuously compounded riskfree interest rate is 5%. Your boss has asked you to quote a price for...

A 1.0cmdiameter sphere is charged to a potential of \(3400 \mathrm{~V}\). How much charge is on the sphere?

a. What is the electric potential at points A, B, and C in Figure P21.16? b. What is the potential energy of an electron at each of these points? c. What are the potential differences \(\Delta...

a. What is the potential difference between the terminals of an ordinary AA or AAA battery? (If you're not sure, find one and look at the label.) b. An AA battery is connected to a parallelplate...
Study smarter with the SolutionInn App