Answered: Consider Asian options that are based…

Consider Asian options that are based on quarterly stock prices over 2 years and matures two years from now. Calculate the payoff of a 100-strike arithmetic average price call.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Question

A stock has a time-t price of s(t). You are given the following values of S(t)
S(t)
100
107
102
96
94
110
115
120
108
Consider Asian options that are based on quarterly stock prices over 2 years and matures two years from now.
Calculate the payoff of a 100-strike arithmetic average price call.
Possible Answers
A -8
B
t
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
-6.5
O
6.5
E 8

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13. 3. Build a three-step CRR stock price tree using the following information:•maturity: 3 months, i.e. each step is one month•annual volatility of the stock: 0.35•annual, continuously compounded risk-free rate: 1%•stock price today: 50 (b) Calculate the price of an American put option with strike K = 50.
M4
10. Assume the following data: Stock price = $50; Exercise price = $45; Risk-free rate = 6 percent per year; Continuously compounded variance = 0.2; Expiration = three months. Calculate the value of a European call option. (Use the Black-Scholes formula.) Options- $5.92 $7.62 $5 $7.90
Give typing answer with explanation and conclusion J&J stock price is currently trading at $100. Over each of the next two three-month periods it is expected to go up by 8% or down by 7%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of the first 3-month if it is expected to down by 7% European call option with a strike price of $95? Compute the current price if use American call option with a strike price of $95. (draw the tree figure for stock movement).
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The Hang Seng TECH Index (HSTECH) is currently trading at 8,100. The index is anticipated to pay no dividends in the next 8 months. It has an annualized volatility of 30%. The interest rate is 5% per annum with continuous compounding. Consider a 6-month American put option on HSTECH with a strike of 8,200. Construct a 2-period binomial model to answer the following questions. (a) Draw and determine the stock index process at each node. (b) Compute the prices of the American put option at each node. (c) How much is the early exercise premium? (d) Explain why early exercise of an American put option on non-dividend-paying asset may be optimal
When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6% per year with continuous compounding, the volatility is 30% and the time to maturity is 3 months which of the following is the price of a European call option on the stock? 19.7N(0.175)-20N (0.025) 19.7N(0.025)-20N (0.175) 20N(0.175)-19.7N(0.025) O 20N(0.025)-19.7N(0.175)
10. A stock is selling today for $110. The stock has an annual volatility of 64 percent and theannual risk-free rate is 7 percent.a. Calculate the fair price for a 1-year European call option with an exercise price of $95.b. Calculate how much the current stock price would need to change for the purchaser ofthe call option to break even in one year.c. Calculate the fair price for a 1 year European put option with an exercise price of $95.
Year End Index Realized Return 2000 23.6% 2001 24.7% 2002 30.5% 2003 9.0% 2004 -2.0% 2005 -17.3% 2006 -24.3% 2007 32.2% 2008 4.4% 2009 7.4%
A stock price is currently $60. You predict that at the end of 6 months stock price will increase or decrease by 20%. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a 6-month European put option with a strike price of $60?
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