Question 4 -A stock price is currently worth $20. It is known that at the end of a 6month period it is expected to go up by 8% or down by 5%. The risk-freeinterest rate is 4% per annum with continuous compounding. Use a two-steptree to calculate the value of a 1-year American exotic option whose payoffispayoff max (S+ ST - S²; 0).State in which node the option is early exercised.

Step 1 - Up Node (Su) - Continued (C(Su)):Risk-Neutral Valuation: We assume the expected return on…

Answered: Question 4 - A stock price is currently…

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 4MC

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3. A stock has a 15 percent change of moving either up or down per period and is currently priced at $25. Using a one period binomial model, and assuming that the risk-free rate is 10 percent, complete the following. a. Determine the possible stock prices at the end of the first period. b. Calculate the intrinsic values at expiration of an at-the-money European call option. c. Find the value of the option today. d. Construct a hedge by combining a position in stock with a position in the call. Show that the return on the hedge is the risk-free rate regardless of the outcome, assuming that the call sells for the value you obtained in c. e. Determine the rate of return from a riskless hedge if the call is selling for $3.50 when the hedge is initiated.
aa.3 Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $50.00, = 0.20, r = 0.06 and the dividend yield = 3.5%. What is the lowest strike price where early exercise would occur with an American put option?
Consider a 3-month European call option on a non-dividend-paying stock. The current stock price is $20, the risk-free rate is 6% per annum, and the strike price is $20. Assume a risk-neutral world. You calculate the following values using the Black-Scholes-Merton model: d1 = 0.2000 N(d1) = 0.5793 d2 = 0.1000 N(d2) = 0.5398 a) What is the probability that the call option will be exercised? b) What is the expected stock price at the option’s expiration in 3 months? Assume that all values of the stock price less than $20 are counted as zero. c) What is the expected payoff on the option at expiration (in 3 months)? d) Calculate the PV of the expected payoff from part c).
6. A stock price is currently at $20 and has a volatility of 20% p.a. The risk-free rate is 4% p.a. with continuous compounding. Use a three-step binomial tree model with step size 1 year to compute the arbitrage-free price of an American put option written on that stock with strike price K $20 and maturity T = 3 years.
3. Consider a non-dividend paying stock whose initial stock price is 62 and has a log- volatility of σ = 0.20. The interest rate r = 10%, compounded monthly. Consider a 5-month option with a strike price of 60 in which after exactly 3 months the purchaser may declare this option a (European) call or put option. Assume u = 1.05943 and d = = 0.94390 (a) Compute the values of the binomial lattice for 5 1 month period. 0 1 2 3 4 5 62 (b) Compute the appropriate risk-free rate. (c) Find the risk-neutral probability p of going up? (d) Find the values of call option and put option along this lattice: 0 5.85 1 2 3 4 5 call option 0 1 2 3 4 5 1.40 put option
User A European call option with a strike price of 105 will expire in two years. The current stock price is $ 100. The value of u = 1.3 and the value of d = 0.8. The annual interest rate (based on continuous compounding)is 10%. Using a three-period binomial model （a）Determine the risk-neutral probability values at each end node (Hint: draw a tree) Please draw a binomial tree！！！ Can you give me the steps （b）Find the expected value of the call in two years. （c）Find the current price of the call option.
The current price of a non-dividend paying stock is $30. Use a two -step tree to value a European call 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 8% per annum with continuous compounding. What is the option price when the volatility is 20%? (Hint: Calculate u and d using the CRR approach.) A. $1.48 B. $1.08 C. $1.68 D. $1.28
Suppose that the price of a stock today is at $25. For a strike price of K = $24 a 3-month European call option on that stock is quoted with a price of $2, and a 3-month European put option on the same stock is quoted at $1.5 Assume that the risk-free rate is 10% 3. per annum. (a) Does the put-call parity hold?
Suppose that Stock XYZ is currently trading at $50 and does not pay any dividends. Using a binomial tree with two periods, we would like to price a European call option with a strike of $50 and a maturity of six months. Assume that annual continuously compounded interest rate is 1% and the volatility of the stock is 30% per year. What is the value of q? 0.5565 0.4709 0.5000 0.3401 0.5000. You selected this answer.
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What is the price of an American CALL option that is expected to pay a dividend of $2 in three months with the following parameters? s0 = $40d = $2 in 3 monthsk = $43 r = 10%sigma = 20%T = 0.5 years (required precision 0.01 +/- 0.01)

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