Question: PLEASE USE R CODE TO SOLVE pricing an arithmetic mean Asian call option for a stock modeled by a geometric Brownian motion with an initial

PLEASE USE R CODE TO SOLVE

pricing an arithmetic mean Asian call option for a stock modeled by a geometric Brownian motion with an initial price of $100, a volatility of 40%, and zero interest rate. Let the expiry time be 12 weeks in the future (consider 52weeks a year), and let the monitoring frequency be weekly. The strike price is $110

a) Estimate the arithmetic mean Asian call option price using simple Monte Carlo method. What is the 99% confidence interval? b) Estimate the arithmetic mean Asian call option price using the discounted payoff of the geometric mean Asian call option as the control variate. [Hint: The exact price for a geometric mean Asian option is given in Lecture note 6.]. What is the 99% confidence interval? c) Estimate the arithmetic mean Asian call option price using the discounted payoff of the European call option as the control variate. What is the 99% confidence interval? d) Which method gives the narrowest confidence interval [i.e., smallest estimation error]? Can you explain why?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Finance Questions!

advanced financial engineering. please help!!! urgent Problem 2 (Application of Monte Carlo simulation in pricing financial derivatives) Background information about Black-Scholes Model Black-Scholes...

R question Here is a question and the answer. Please use R to write the code for the formula to obtain the given answer. Thank you. . (40 points) Consider the case where an asset price, S(t), with...

Data: An Asian option is a type of exotic option. Unlike a vanilla European option where the price of the option is dependent upon the price of the underlying asset at expiry, an Asian option pay-off...

Please solve the question in Python Jupyter notebook and show all the codes. Task 2: MC Simulation & European Option Pricing In lab session 4 (lab04) we covered how to simulate an arithmetic and a...

Question 6 10 pts N(x) 0.50 0.60 0.69 0.77 0.84 0.89 0.93 1.75 2.00 0.96 0.98 6. For this problem please reference the above table for N(), the cumulative distribution function (CDF) of the standard...

MONTECARLO SIMULATION (USING EXCEL?): Please I would like help to know what to do. I have the excel spreadsheet with 100 rows and 252 columns for the random normal variables. I need some intuition on...

Assume the stock price S(t) paying a continuous dividend yield q follows the following geometric Brownian motion: dSt = (r - 9) Stdt + o(St,t)StdWt, where r is the risk free interest rate and W is a...

I need help answering question 13 and 17 in this homework set. Thank you that is all I need currently. HOMEWORK SET 4 Derivatives 1. What is a lower bound for the price of a 4 months call option on a...

1 = (a) Consider the following IID N(0,1) random variables X; that come from a pseudo-random number generator: i 2 3 4 X; -1.3011 0.9032 -0.0339 1.3695 Use these random numbers to construct the...

please put the answers to the questions in order :) Question 2 - Monte Carlo Simulation to Value Exotic Contracts (10 Marks) Considering an underlying stock that follows Geometric Brownian Motion; dS...

Find the number of ways a run of seven cards in order of the same suit can be drawn from a standard 52-card deck of cards a. How many ways can the suit be chosen? b. How many ways can the seven cards...

1. Write the Six name of Natural Resources? 2. Which Project needs EIA? n

Can you take into account the following to highlight how Fund II will have strong co-invest flow potentially Similar to Fund I, Fund II will target investments that require $100 million to $700...

The par value of a bond is: Multiple Choice the stated interest rate on the bond. the face value of the bond. the price of the bond being traded. the yield to maturity.

LO22.3 Relate the rationale for farm subsidies and the economics and politics of price supports (price floors).

1. Suppose that there are only three types of fruit sold in the United States. Annual sales are 1 million tons of blueberries, 5 million tons of strawberries, and 10 million tons of bananas. Suppose...

12. Use economic analysis to explain why the optimal amount of product safety may be less than the amount that would totally eliminate the risk of accidents and deaths. Use automobiles as an example....