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- Question 4 - A stock price is currently worth $20. It is known that at the end of a 6 month period it is expected to go up by 8% or down by 5%. The risk-free interest rate is 4% per annum with continuous compounding. Use a two-step tree to calculate the value of a 1-year American exotic option whose payoff is payoff max (S+ ST - S²; 0). State in which node the option is early exercised.Question 5: A call option on a stock that expires in a year has a strike price of $99. The current stock price is $100 and the one-year risk free interest rate is 10%. The price of this call is $6. a) Is arbitrage possible? What is the arbitrage position? b) do you het this minimum? Find the minimum arbitrage profit for this strategy. WhenQuestion 3 - (2 Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.
- Question 1 Help = 1. Find the expected profit for a holder of a European call option with K = 94 to be exercised in six months if the stock price at maturity is ST (90, 96, 98) with probabilities p = (1, 1, 1), given that the option is bought for Co= 10 financed by a loan at the interest rate of 10% (per annum).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?Question 5 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. What is the price of the option if it is a European call? b. What is the price of the option if it is a European put? c. Verify that put-call parity holds. a.
- Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%.Question 5 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 call? b. What is the price of the option if it is a European put? c. Verify that put-call parity holds. ●3.2 Find the current price of a one-year, R110-strike American put option on a non- dividend-paying stock whose current price is S(0) = 100. Assume that the continuously compounded interest rate equals r = 0.06. Use a two-period Binomial tree with u = 1.23, and d = 0.86 to calculate the price VP(0) of the put option.
- Question Assume the Black-Scholes framework. For a non-dividend paying stock, you are given: i. The stock's continuously compounded expected rate of return is 7%. ii. The continuously compounded risk-free interest rate is 3%. iii. The stock' s volatility is 25%. iv. The price of an at-the-money 1-year European call option on the stock is 13.05. Calculate the stock' s current price. Possible Answers A Less than 110 B At least 110 but less than 120 c At least 120 but less than 130 D At least 130 but less than 140 E At least 140 iQuestion 3 We are using a two-step binomial tree to price a 6-month European put option with a strike price of $60. The current stock price is $50, the risk-free rate is 3% for all maturities. At each step, the price can increase or decrease by 20%. The continuously compounded dividend yield is 3%. What is the option price today? $9.7 $12.8 $13.9 $10.1Problem 4 Consider a stock with current price $60. You are given: • Dividends of $1 each will be paid every three months; the next dividend will be paid in 2 months. • σ = 0.3. ⚫ The continuously compounded risk-free interest rate is 4%. Use the Black-Scholes methodology to price a nine-month at-the-money European put option on the stock.