Consider a stock with a price of $50 that is expected to increase by 6% or decrease by 8% each month over the next two months. Having a risk-free rate at 3% per year with continuous compounding, calculate the value of a two-month Anmerican put option with a strike price of $55.
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You Consider a stock with a price of $50 that is expected to increase by 6% or decrease by 8% each month over the next two months. Having a risk-free rate at 3% per year with continuous compounding, calculate the value of a two-month Anmerican put option with a strike price of $55.
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- Suppose Carol's stock price is currently $20. If the standard deviation of the continuously compounded returns (σ) on a stock is 60 percent per year. The monthly risk-free rate is 1 percent. Using one-step binomial tree, what is the current value of a six-month call option with an exercise price of $15?Suppose Carol's stock price is currently $20. If the standard deviation of the continuously compounded returns (σ) on a stock is 60 percent per year. The annual risk-free rate is 12%, compounded every 6 months. A. Using one-step binomial tree, what is the current value of a six-month call option with an exercise price of $25?B. Using two-step binomial tree, what is the current value of a one-year put option with an exercise price of $25?TreeOlivia's stock price is $180 and could halve or double in each six-month period. The interest rate is 12% a year. What is the value of a six-month call option on TreeOlivia with an exercise price of $120? What is the option delta for the six-month call with an exercise of $120? The payoffs of the six-month call option can be replicated by buying shares of stock and borrowing. What amount should be invested in stock and what amount must be borrowed? Assume the exercise price is $120. What is the value of the one-year call option on TreeOlivia with an exercise of $150? (Hint: use the two-step binominal tree) What is the value of the one-year put option on TreeOlivia with an exercise of $150?
- The current price of a non-dividend paying stock is $100. Every three months, it is expected to go up or down by 9% or 5%, respectively. The risk-free rate is 4% per year with continuous compounding. Compute the price of a European call option with strike price $98 and maturity six months written on the stock.A stock is currently selling for $55 per share. A call option with an exercise price of $65 sells for $3.85 and expires in six months. If the risk-free rate of interest is 3.5 percent per year, compounded continuously, what is the price of a put option with the same exercise price?The common stock of the C.A.L.L. Corporation has been trading in a narrow range around $50per share for months, and you believe it is going to stay in that range for the next 3 months. Theprice of a 3-month put option with an exercise price of $50 is $4.a. If the risk-free interest rate is 10% per year, what must be the price of a 3-month call optionon C.A.L.L. stock at an exercise price of $50 if it is at the money? (The stock pays nodividends.)b. What would be a simple options strategy using a put and a call to exploit your convictionabout the stock price’s future movement? What is the most money you can make on thisposition? How far can the stock price move in either direction before you lose money?c. How can you create a position involving a put, a call, and riskless lending that would havethe same payoff structure as the stock at expiration? What is the net cost of establishing thatposition now?
- XYZ Corp. will pay a $2 per share dividend in two months. Its stock price currently is $60 per share. A call option on XYZ has an exercise price of $55 and 3-month time to expiration. The risk-free interest rate is .5% per month, and the stock’s volatility (standard deviation) = 7% per month. Find the Black-Scholes value of the option. (Hint: Try defining one “period” as a month, rather than as a year, and think about the net-of-dividend value of each share.)Suppose the stock price is 40 and we need to price a call option with a strike of 50 maturing in 4 months. The stock is not expected to pay dividends. The continuously-compounded riskfree rate is 3%/year, the mean return on the stock is 7%/year, and the standard deviation of the stock return is 40%/year.The price of a stock is currently $20. Over each of the next two three-month periods, the stock can go up by 10% or down by 10%. The risk free interest rate is 12% per annum with continuous compounding. (a) What is the current value of a six-month European put option with a strike price of $22? (b) What is the current value of a six-month American put option with a strike price of $22?
- The current price of a stock is $20, and at the end of one year its price will be either $22 or $18. The annual risk-free rate is 2.0% (use daily compounding with 365 days/year), based on daily compounding. A 1-year call option on the stock, with an exercise price of $19, is available. Based on the binominal model, what is the option's value?(Please Show Work)Suppose the stock price is 43 and we need to price a call option with a strike of 45 maturing in 4 months. The stock is not expected to pay dividends. The continuously-compounded riskfree rate is 3%/year, the mean return on the stock is 7%/year, and the standard deviation of the stock return is 40%/year. Use excel.You Consider a stock with a price of $50 that is expected to increase by 6% or decrease by 8% each month over the next two months. Having a risk-free rate at 3% per year with continuous compounding, calculate the value of a two-month European put option with a strike price of $55. Repeat your calculations for a two-month American put option with a strike price of $55. Show clearly all your calculations and results with the use of the relevant equations and graphs. Discuss your investment decision in each case separately.