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- A stock price is currently $30. It is known that at the end of one year, it will be either $36 and $24. The exercise price of a one-year European call option is $32. The risk-free interest rate is 5% per annum. a. Construct a binomial tree to show the payoff of the call option at the expiration date. b. Based on the binomial tree model, what is the value of the call option?The following information is given: Time to expiration 1 year. Standard deviation 40% per year. Exercise price $72. Stock price $72. Risk free rate 4% a year. Use the Black–Scholes formula to find the value of the calloption. What is the value of the put option with the same exercise price and time to expiration? What is the value of the call option if time to expiration is 3 years? What is the value of the call option if the standard deviation is 20%? What is the value of the call option if the exercise price is $90? What is the value of the call option if the current stock price is $50? What is the value of the call option if the risk-free rate is 8%?What are the prices of a call option and a put option with the following characteristics? Stock price = $93 Excerise price = $90 Risk - free rate = 4% per year, compounded continuously Maturity = 5 months Standard deviation = 62% per year
- Suppose the stock price is $20 today. In the next six months it will either fall by 50 percent or rise by 50 percent. What is the current value of a call option with an exercise price of $15 and expiration of one year? The six-month risk-free interest rate is 10 percent (periodic rate). Use the two-stage binomial method. $7.86 $2.14 $8.23 $8.93A put option and a call option with an exercise price of $115 and three months to expiration sell for $5.45 and $8.75, respectively. If the risk-free rate is 2.0% per year, compounded continuously, what is the current stock price? $111.13 $121.13 $117.73 $112.40What is the price of an American CALL option that is expected to pay a dividend of $2 in three months with the following parameters? s0 = $40d = $2 in 3 monthsk = $43 r = 10%sigma = 20%T = 0.5 years (required precision 0.01 +/- 0.01)
- Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. What is the value of the option. Provide all necessary calculations.Use the Black-Scholes formula to find the value of the following call option.i. Time to expiration 1 year.ii. Standard deviation 40% per year.iii. Exercise price $50.iv. Stock price $50.v. Interest rate 4% (effective annual yield).Now recalculate the value of this call option, but use the following parameter values.Each change should be considered independently.i. Time to expiration 2 years.ii. Standard deviation 50% per year.iii. Exercise price $60.iv. Stock price $60.v. Interest rate 6%.c. In which case did increasing the value of the input not increase your calculation of option value?Consider a European call option on a stock with current price $100 and volatility 25%. The stock pays a $1 dividend in 1 month. Assume that the strike price is $100 and the time to expiration is 3 months. The risk free rate is 5%. Calculate the price of the the call option.
- Consider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25). The put has a strike price of $100 and expires in 1 year. The risk-free rate is 3% (.03). If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ). What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?Please calculate the price of a put option that matures in 2 months with a strike price of $58. Assume the risk free rate is 3%/month. 50 Month 1 A. 7.29 B.1.07 OC.11.3 OD.O 62.5 45 Month 2 78.125 56.25 40.5A. What is the price of a call option with a strike of $80 and a maturity of 2.5 years? The underlying asset is currently trading at $75. The risk-free rate is 6% and the volatility of the underlying asset is 64% B. What is the price of a put option with an identical strike price? C. Calculate the delta, theta, and vega of the call option. Express theta per month and verga per 1% increase in volatility. D. After 5 months the price has gone up by $10 and the volatility by 10%. Using delta, theta, and vega that you have calculated, what is the total change in value of the option?