The price of a certain security follows a geometric Brownian motion with drift parameter u = 0.12 and the volatility parameter o = 0.24. If the current price of the security is $40 and if the interest rate is 10%, then the risk-neutral arbitrage free value of the call option, with a strike price of $50 and having three months until expiration is given by O 87 cents O 5 cents 11 cents O 64 cents

The price of a certain security follows a geometric Brownian motion with drift parameter u = 0.12 and the volatility parameter o = 0.24. If the current price of the security is $40 and if the interest rate is 10%, then the risk-neutral arbitrage free value of the call option, with a strike price of $50 and having three months until expiration is given by O 87 cents O 5 cents 11 cents O 64 cents

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter5: Financial Options

Section: Chapter Questions

Problem 4MC

See similar textbooks

Similar questions

1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.
Q.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.
The price of a certain security follows a geometric Brownian motion with drift parameter mu=.05 and volatility parameter sigma =.3. The present price of the security is 95. (a) If the interest rate is 4%, find the no-arbitrage cost of a call option that expires in three months and has exercise price 100. (b) What is the probability that the call option in part (a) is worthless at the time of expiration?
Q roshu Suppose that a futures price is currently $42. A European call option and a European put option on the futures with a strike price of $40 and maturity in two months are both priced at $3 and $2 respectively in the market. The continuously compounded risk-free rate of interest is 5% per annum. Use the put-call parity condition to show that an arbitrage opportunity exists. Explain what position could be set up to exploit it. (Show all relevant calculations to support your argument. For example, your calculations should include what strategy an arbitrageur could follow in order to lock in a risk-free profit from the arbitrage strategy, as well as the arbitrageur’s net profit from the strategy).
Q.3 Determine 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.
Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent. Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent.
Question 3 The quoted futures price corresponds to a forward rate of 8% per annum with quarterly compounding and actual/360. The parameters for Black’s model are therefore: Fk = 0.08, K= 0.08, R= 0.075, σk = 0.15, tk = 0.75 and P(0,tk+1) = e-0.075*1 =0.9577 Use these information to estimate the call price.
Question 3 The quoted futures price corresponds to a forward rate of 8% per annum with quarterly compounding and actual/360. The parameters for Black’s model are therefore: Fk = 0.08, K= 0.08, R= 0.075, σk = 0.15, tk = 0.75 and P(0,tk+1) = e-0.075*1 =0.9577 Use these information to estimate the call price with mathematical formulars.
H2. Using the Black-Scholes model (BSOPM), compute the standard deviation that is implied by the following call option data as: the time to the option's maturity is 0.25 years, the price of the underlying option asset is RM30, the continuously compounded risk-free interest rate is 0.12. the exercise or striking price is RM30, and the cost or premium of the call is RM1.90.
Assume investors are indifferent among security maturities. Today, the annualized 2-year interest rate is 2.20 percent, and the 1-year interest rate is 2 percent. What is the forward rate according to the pure expectations theory? Group of answer choices 2.25% 2.20% 2.00% 2.40%
The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.) If the interest rate is 8%, what is the risk-neutral valuation of the call option?
Problem 1: Hedging market risk using S&P500 index futures Assume you have a portfolio worth currently $5,000,000. Let portfolio beta be ß, = 2. Assume you want to hedge market risk until 3 months from now.' Current value of S&P500 index futures 3 month from now is 3,900.00. You are using mini futures i.e. $50 per point. a) If you want to completely remove market risk without using futures. What would you do? b) If you use S&P500 mini futures, how many futures you would buy to completely hedge your exposure to market risk. c) What would be the value of your new (i.e. hedged) portfolio when S&P500 goes up by 2% 3 months from now? d) What would be the value of your new portfolio when S&P500 declines by 3% 3 months from now. e) What should you do in a) if you want to change the ß of your portfolio approximately to ß = 1? f) What should you do in b) if you want to change the ß of your portfolio approximately to B = 1?