Value of a call option is given by C >= max{0,So-K}
Considering that strike price K will be used in future, this needs to be discounted for time T at risk free rate Rf
Hence C >= max{0,So-K*e^(Rf*T)} …...………..(1)
Value of zero coupon bond with face value 1 = e^(Rf*T) = B(T)
Substituting this in eq 1:
C>= max{0,So-KB(T)}
Consider a European call option on a non-dividend-paying stock. The strike price is K, the time...
Consider a European call option on a non-dividend-paying stock. The strike price is K, the time to expiration is T, and the price of one unit of a zero-coupon bond (with face value one) maturing at T is B(T). Denote the price of the call by C. Show that C > max{0, So – KB(T)}, where So is the current stock price.
The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. What is the price of a one-year European put option on the stock with a strike price of $50? $2.09 $7.52 $3.58 $9.91
A European call option on a non-dividend payment stock with a strike price of$18 and an expiration date in one year costs $3. The stock price is $20 and the risk free rate is 10% per annum. Can you design an arbitrage scheme to exploit this situation?
Question 7: Consider a European call option and a European put option on a non dividend-paying stock. The price of the stock is $100 and the strike price of both the call and the put is $103, set to expire in 1 year. Given that the price of the European call option is $10.57 and the risk-free rate is 5%, what is the price of the European put option via put-call parity? Question 8: Suppose a trader buys a call...
A six-month European call option on a non-dividend-paying stock is currently selling for $6. The stock price is$64, the strike price is S60. The risk-free interest rate is 12% per annum for all maturities. what opportunities are there for an arbitrageur? (2 points) 1. a. What should be the minimum price of the call option? Does an arbitrage opportunity exist? b. How would you form an arbitrage? What is the arbitrage profit at Time 0? Complete the following table. c....
Question 3 - 20 Points 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...
Consider a European call and a European put on a non-dividend-paying stock. Both the call and the put will expire in one year and have the same strike prices of $120. The stock currently sells for $115. The risk-free rate is 5% per annum. The price of the call is $7 and the price of the put is $5. Is there an arbitrage? If so, show an arbitrage strategy. (To show the arbitrage, present the table listing actions and resulting...
Consider a European put option on a non-dividend-paying stock. The current stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum and the time to maturity is 6 months. a. Use the Black-Scholes model to calculate the put price. b. Calculate the corresponding call option using the put-call parity relation. Use the Option Calculator Spreadsheet to verify your result.
(b) A 6-month European call option on a non-dividend paying stock is cur- rently selling for $3. The stock price is $50, the strike price is $55, and the risk-free interest rate is 6% per annum continuously compounded. The price for 6-months European put option with same strike, underlying and maturity is 82. What opportunities are there for an arbitrageur? Describe the strategy and compute the gain.
Problem 12.25. Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months a. Calculate u, d, and p for a two step tree b. Value the option using a two step tree. c. Verify that DerivaGem gives the same answer d. Use DerivaGem to value the option with 5,...