QUESTION 1 A one-month European put option on a non-dividend-paying stock is currently selling for $1.5. The stock price is $37, the strike price is $43, and the risk-free interest rate is 5% per annum. What is the minimum arbitrage profit you can make in today's value? (Keep to 2 decimal places)
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- Question 1 • Springtime Insurance Brokers Ltd. (SIBL) stock is currently selling for $42. A put option on the stock with a value of $3 has an exercise price of $40 and 6 months until expiration. To prevent arbitrage opportunities, what should be the value of a call option with the same strike price and expiration date? Assume that the options are European and that the effective annual risk-free rate is 6%.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).Question Two (a) A six-month European Call option on a non-dividend paying Stock Index has a strike price of $4900. The index price is $5000, the risk-free rate is 5% per annum, and the value of u and d are 1.06 and 0.94, respectively. Use a two-step binomial tree to calculate the option price.
- 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. ●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 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 $10.1
- Question 10. The prices of European call and put options on a non-dividend paying stock with an expiration date in 12 months and a strike price of $120 are $20 and $5, respectively. The current stock price is $130. What is the implied risk-free rate?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 20%, and the constant current stock price is 50, the lognormal volatility of the stock is a = continuously compounded interest rate is r 10% (b) Repeat part (a) for a European put with strike 60 and maturity 18 months from nowA one-month European call option on a non-dividend-paying stock is currently selling for $1. The stock price is $47, the strike price is $50, and the risk-free rate is 6% per annum (continuously compounded). What is the time value of a one-month European put on the same stock with the same strike price? A. $3.00 B. $3.75 C. $0.75 D. $0.00
- What is the price of a one-month European call option given the following information: the exercise price is $19, the current share price is $19, and the risk-free interest rate is 1% per month. Furthermore, the share price is expected to be either $25 or $15 at the end of the month. The company does not pay dividends. Assume a risk-neutral world. Group of answer choices $3.11 $1.91 $2.49 $3.32 None of the above answers is correct.Aa.1 The current price of stock XYZ is 100. In one year, the stock price will either be 120 or 80. The annually compounded risk-free interest rate is 10%. i. Calculate the no-arbitrage price of an at-the-money European put option on XYZ expiring in one year. ii. Suppose that an equivalent call option on XYZ is also trading in the market at a price of 10. Determine if there is a mis-pricing. If there is a mis-pricing, demonstrate how you would take advantage of the arbitrage opportunity.Question 4. A stock that pays no dividends has price today of 100. In one year’s time the stock is worth 110 with probability 0.75 and 85 with probability 0.25. The one-year annually compounded interest rate is 5%. a) Calculate the forward price of the stock for a forward contract with maturity one year. b) Calculate the price of a one-year European put option with strike 100. c) Suppose you observe that the put option in part (b) has a market price of 4. Determine an arbitrage portfolio and calculate how much profit is generated at time T = 1 by this portfolio.