Question

In: Finance

For a three-period binomial model for modeling the price of a stock, you are given: The...

For a three-period binomial model for modeling the price of a stock, you are given:

  1. The current price of the stock is 125.
  2. The length of each period is one year.
  3. u = 1.2, where u is one plus the rate of capital gain on the stock if the price goes up.
  4. d = 0.8, where d is one plus the rate of capital loss on the stock if the price goes down.
  5. The continuously compounded risk-free interest rate is 6%.
  6. The price of a three-year $90-strike European put option is $0.89.

Calculate the price of a three-year $100-strike European put option.

  1. 1.23

  2. 1.49

  3. 1.78

  4. 2.01

  5. 2.48

Please provide full explanation

Solutions

Expert Solution

I have solved the question below:

Price of put option is 2.019.

Option 4 is correct.

Please let me know in case you have any queries, I would be happy in assisting you.


Related Solutions

You construct a one-period binomial tree to model the price movements of a stock. You are...
You construct a one-period binomial tree to model the price movements of a stock. You are given: The length of one period is 6 months. The current price of the stock is 100. The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%. Suppose: u denotes one plus the rate of gain on the stock if the stock price goes up. d denotes one plus the rate of loss on the stock if...
The current spot price for a stock is $100, using a binomial model, in every period...
The current spot price for a stock is $100, using a binomial model, in every period it has been determined that the probability for this stock to go up is 70%, in this case the stock will increase in value a 12 %. If the stock goes down, the value will decrease 13%. For a call option with strike price of $186  and after 12 periods:             1) Calculate the values of the factor "u" and "d".             2) Show a diagram with...
Consider a two-period binomial model in which a stock trades currently at $44. The stock price...
Consider a two-period binomial model in which a stock trades currently at $44. The stock price can go up 6% or down 6% each period. The risk free rate is 2% per period. A) Calculate the price of a call option expiring in two periods with an exercise price of $45. B) Calculate the price of a put option expiring in two periods with an exercise price of $45.
Consider a two-period binomial model in which a stock trades currently at $44. The stock price...
Consider a two-period binomial model in which a stock trades currently at $44. The stock price can go up 6% or down 6% each period. The risk free rate is 2% per period. A) Calculate the price of a call option expiring in two periods with an exercise price of $45. B) Calculate the price of a put option expiring in two periods with an exercise price of $45. C) Based on your answer in A), calculate the number of...
Consider a two-period binomial model in which a stock currently trades at a price of K65....
Consider a two-period binomial model in which a stock currently trades at a price of K65. The stock price can go up 20 percent or down 17 percent each period. The risk-free rate is 5 percent. (i)         Calculate the price of a put option expiring in two periods with an exercise price of K60. (ii)        Calculate the price of a call option expiring in two periods with an exercise price of K70.
In a one-period binomial model with h= 1, the current price of a non-dividend paying stock...
In a one-period binomial model with h= 1, the current price of a non-dividend paying stock is 50, u= 1.2, d= 0.8, and the continuous interest rate is 2%. Consider a call option on the stock with strike K= 50. What position in the stock (i.e. long or short and how many) is there in a replicating portfolio of this call option?
Consider a 2-period binomial model. the annual interest rate is 9%. the initial stock price is...
Consider a 2-period binomial model. the annual interest rate is 9%. the initial stock price is $50. In each period the stock price either goes up by 15% or down by 10%. a. Price a European call option on the stock with exercise price $60 b. Price a European put option on the stock with exercise price $60
Consider a two-period binomial model for the stock price with both periods of length one year....
Consider a two-period binomial model for the stock price with both periods of length one year. Let the initial stock price be S0 = 100. Let the up and down factors be u = 1.25 and d = 0.75, respectively and the interest rate be r = 0.05 per annum. If we are allowed to choose between call and put option after one year, depending on the up and down states (head and tail respectively), which option do you choose...
Consider a two-period binomial setting. The current stock price is $48.6 in each period, the stock...
Consider a two-period binomial setting. The current stock price is $48.6 in each period, the stock may increase by 1.2 or decrease by 0.84. One plus the risk-free, rf is 1.02. The risk-free rate applies to each period within the two-period setting. What is the initial value of a call option with a strike price of $49?
In Financial Derivatives Consider the two-period, Binomial Options Pricing Model. The current stock price S= $105...
In Financial Derivatives Consider the two-period, Binomial Options Pricing Model. The current stock price S= $105 and the risk-free rate r = 3% per period (simple rate). Each period, the stock price can go either up by 10 percent or down by 10 percent. A European call option (on a non-dividend paying stock) with expiration at the end of two periods (n=2), has a strike price K = $100. The risk-neutral probability of an “up” move is q = (R-D)/(U-D),...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT