Consider an European put option. Suppose Exercise price=$60. Expiration date=50 (and we assume 360 days of conversion). If risk-free rate is 5%, and the underlying stock price is $100, what is the lower boundary for this European put option?
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- 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. Required: (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 avoid arbitrage?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?Consider a 2-year EUROPEAN PUT with a strike price of $65 on a stock whose current stock price is $60. Suppose that there are two time steps, and in each time step the stock price either moves up by 20% or moves down by 20%. Also suppose that risk-free rate is 5% per annum with continuous compounding . What is the value of the European put option?
- Use the following data to estimate the value of a European put option with X = $120. The current stock price now is SO = $100. The two possibilities for ST are $150 and $80. If the risk-free rate is 10%, estimate the value of the put option now. a. P0 = $0 b. P0 = $40 c. P0 = $20.78 d. P0 = $22.86You are considering a European put option and a European call option on ABC Ltd and have available the following information. The put option with an exercise price of $15 and time to maturity of 60 days is priced at $2.00. The call option with the same exercise price and time to maturity is priced at $3.00. The underlying asset price is $15. The risk-free rate is 2% per 60 days. Could an arbitrage profit be earned? If so, how much the arbitrage profit is? Show your works (Hint: use discrete put-call parity equation and consider two scenarios for stock price at maturity of the options: $10 or $20).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?
- 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).Consider a European call option and a European put option that have the same underlying stock, the same strike price K = 40, and the same expiration date 6 months from now. The current stock price is $45. a) Suppose the annualized risk-free rate r = 2%, what is the difference between the call premium and the put premium implied by no-arbitrage? b) Suppose the annualized risk-free borrowing rate = 4%, and the annualized risk-free lending rate = 2%. Find the maximum and minimum difference between the call premium and the put premium, i.e., C − P such that there is no arbitrage opportunities.Use Two-State Binomial Option (European) Pricing Model. Suppose you bought a stock today for $38.00. The stock price can either go up by a factor of 1.30 or down by a factor of 0.70 with equal probability in 0.50 years (or 180 days). Suppose the annual risk-free rate is 3.50% and the option exercise price is 35.00. How much should be the Call Option Value that expires in 0.50 years (or 180 days)?Enter your answer in the following format: 1.23Hint: The answer is between 6.74 and 9.38
- You are given the following information. S=50, X=50, simple annual risk-free interest rate is 5%, standard deviation of monthly stock returns is 10%. What is the value of a one-year European call option using the three-period Binomial model?Consider a two year put options with strike Price sh. 52 on a stick whose current price is sh.50. suppose there is 2 times steps and each step is one year and in each times steps the price move up or down by 20%. Suppose the risk Free rate is 5% . Calculate value of put assuming; A) Europeans options B) American optionsThe current stock price of MRF is ₹ 81000. A European call option on the stock with exercise price of ₹ 75000 will expire in 40days. The annual continuously compounded risk-free interest rate is 10%, standard deviation of the continuously compounded rate of return is 60% p.a. Calculate the value of the Call option. Find the value of the Put option using Put-Call Parity Rule.