Problem 1. Assume that the interest rate is 5%, contimuously compounded annually, and considercall and put options of both American and European style expiring in 6 months onnon-dividend paying stock. For each of the following scenarios, check if you can findan arbitrage opportunity and, if you can, describe it:(i) The strike price of a European put option is $3 and the option is traded at $4.(ii) The shares are traded at $3 and the American call option is traded at $3.20.

Arbitrage is a trading strategy capitalizing on price differences between related financial…

Answered: roblem 1. Assume that the interest rate…

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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When the non-dividend paying stock price is $20, the strike price is $20, the risk-free rate is 6%, the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European call option on the stock Group of answer choices 0.95 1.05 0.36 1.17
Consider an American put option (K=$100) expiring in one year on a stock trading for $84. The return volatility on the stock is 27.3% and the riskless rate is 5%. Find the price of the option using a Binomial Model with two steps. (Respond with two decimal places, such as "-12.34") 26.59 Correct Answer: 18.28
1. For each of the following cases, calculate (i) the cashflow paid or received today on entering the position, (ii) the gross payoff at expiry, and (iii) the net payoff from your option trading All options are European style and cover 100 shares in the underlying asset. a) You enter a long call option with a strike price of $6 and premium of $2.30. At expiry, the share price is $7.80. b) You enter a long call option with a strike price of $9 and premium of $0.80. At expiry, the share price is $7.90. c) You enter a short call option with an exercise price of $5 and premium of $0.70. The share price at expiry is $5.40. d) You enter a short call option with an exercise price of $5 and premium of $0.70. The share price at expiry is $4.90. e) You buy a long - put option with a strike price of $10 for a premium of $ 1.20. At expiry, the share price is $8.50. f) You write (i. e., short) a put option with strike price $7 for a premium of $0.60. At expiry, the share price is $5.
Consider a stock in two periods (two years). The stock price goes up by 30% or down by 10%in each period. Current stock price is $100. There is a European put option on the stock withexercise price $110 and time to maturity of two years. The interest rate in each period is 6%. Inthe template, Date 0 denotes today, Date 1 denotes the end of year 1 and Date 2 denotes the endof year 2. Use the two-period binomial tree model and discrete discounting to find the put optionprice on Date 0.
(a) The table below gives information about European options with a maturity date of 6 months. Type Of option Strike Price Call 65 Call 58 Put 65 Premium 5 8 4 (i) Devise the payoff profile of the hedging strategy from the above for an investor betting on an increase in the stock price and calculate the payoff if the stock price increases to $66 after 6 months. (8 marks) (ii) Suppose that another investor expects a big stock price movement but is not sure of the direction. She however bets that the downward movement is more likely. Devise the corresponding trading strategy and calculate the payoff if the stock price is $55 after 6 months. (8 marks) (b) By analysing the pay off profiles of a protective put strategy and a straddle, discuss in what ways these strategies shield the investor from potential losses.
Problem 1. Assume that the interest rate is 5%, continuously compounded annually, and consider call and put options of both American and European style expiring in 6 months on non-dividend paying stock. For each of the following scenarios, check if you can find an arbitrage opportunity and, if you can, describe it: (i) The strike price of a European put option is $3 and the option is traded at $4. (ii) The shares are traded at $3 and the American call option is traded at $3.20.
The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 896, and u = 1.1 and d = 0.9. O $2.24 $2.44 $2.64 $2.84

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