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 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 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 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 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. ●A 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
- 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 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 $10.1Aa.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 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 nowQ.3Determine the risk-neutral value for a European put option (for a FLB (First Local Bank) share) that expires in eight months. The strike price is R500 and the current price is R650. The interest rate is 11%, and the volatility of the security is 0.026.D3 Finance Consider the data on European put option, as described below. stock price today: 5.03 exercise price: 5.00 Maturity: One year risk free interest rate: 0.4822% per annum stock prices may either go up by 57.04% or down by 36.32% between now and the maturity. (i) use a one-period binomial tree approach to value the put option (ii) replicate an investment in the stock by a combination of the put option and risk-free lending.