2. (a) Compute the price of a European call option written on a non-dividend-payingstock. The current stock price is $100 and the volatility of the stock price is 30%.The maturity of the option is in three months and the strike price is $105. Therisk free interest rate with continuous compounding is 3% per annum. You shoulduse a three step (period) binomial model to price the option.(b) The option can be replicated by a portfolio consisting of the stock and a risk-freeasset. What is the replicating portfolio strategy of the call option?(c) Explain how the delta should change, as the stock price increase and check if thisis indeed the case in your tree.

(a) Pricing the European Call Option with a Binomial TreeWe'll use a three-step (period) binomial…

Answered: 2. (a) Compute the price of a European…

International Financial Management

14th Edition

ISBN:9780357130698

Author:Madura

Publisher:Madura

Chapter5: Currency Derivatives

Section: Chapter Questions

Problem 5ST

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Put–Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?
Binomial Model The current price of a stock is 20. In 1 year, the price will be either 26 or 16. The annual risk-free rate is 5%. Find the price of a call option on the stock that has a strike price of 21 and that expires in 1 year. (Hint: Use daily compounding.)
Suppose a 10-year, 10% semiannual coupon bond with a par value of 1,000 is currently selling for 1,135.90, producing a nominal yield to maturity of 8%. However, the bond can be called after 5 years for a price of 1,050. (1) What is the bonds nominal yield to call (YTC)? (2) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why?
Consider a European put and a European call option which are both written on a non-dividend paying stock, have the same strike price K = £80 and expire in T = 2 months. These options are trading for p = £21 and c = £30.80, respectively. The underlying stock price is S0 = £90. The continuously compounded risk-free rate of interest is r = 10% per annum. What is the present value of the arbitrage profit? Please explain your answer and show your workings. In your response, please show all cash flows (both today and at expiration) and explain why this is an arbitrage (i.e. risk-less) profit.
The market price of a one-year European call option is $9.243, written on a stock that is currently selling for $70. The stock is expected to go ex‑dividend in 6 months on a declared dividend of $5. The exercise price of the call is $80 and the current riskless rate of return is 3% per annum. What is the volatility (standard deviation) implied by the market price of this call option and an appropriate option pricing model allowing for dividends? Your answer should be within 2% of the correct solution (i.e., the correct σ ± .02).
Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a) What is the price of the option if it is a European put?
Suppose we have both a European call option and put option with an exercise price of $53 and the underlying stock is currently priced at $50. We are to note also that both options will expiry in six months. Further, market surveys suggest that the price of the stock can either go up by 20% or decrease by 25%. The current risk-free rate of interest is 2% per annum. (a) What is the expected price of the underlying asset at expiry date? (b) What is the value of the call option, using the binomial model? (c) If the put option is selling for $4.80, what should be the price of the call option to avoidarbitrage?
The price of a European call option on a stock with a strike price of $50.9 is $5.6. The stock price is $40.1, the continuously compounded risk-free rate (all maturities) is 5.2% and the time to maturity is one year. A dividend of $0.6 is expected in six months. What is the price of a one-year European put option on the stock with a strike price equal to the call's strike price? Please state the formula and steps, thanks
You observe that a non-dividend paying stock currently trades for ₺150 on Borsa Istanbul. The annual standard deviation of its returns is expected to be 41% per year over the next year and the continuously compounded risk-free rate of interest is flat at 18% per year over all investment horizons. Compute the theoretical price of a European call option with a strike price of ₺200 and five months remaining until expiration written on a single share of this stock using to the Black-Scholes option pricing model
1. Consider an option on a non-dividend paying stock when the stock price is $30, the exercise price is $28, the annual interest rate is 5%, the annual volatility is 25%, and the time to maturity is 6 months. Show the details of your calculations. a) What is the price of the option if it is a European call?
What would be the price of a two-month European put option on a non-dividend-paying stockwhen the stock price is $68.50, the strike price is$70, and the risk-free interest rate is 5% per annum?Assume a volatility of 60% for this stock.
What is the lower bound for the price of a 7-month European call option on a dividend-paying stock when the stock price is $38.3, the strike price is $40, the risk-free interest rate is 1.1% per annum, and the stock is expected to pay a dividend of $2.56 in three months? Report your answer in dollars and cents.

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