Question

In: Finance

Using a binomial tree, what is the price of a $40 strike 6-month put op- tion,...

Using a binomial tree, what is the price of a $40 strike 6-month put op-
tion, using 3-month intervals as the time period? Assume the following
data: S = 37:90; r = 0:05; = 32:1%
(a) 3.52
(b) 3.66
(c) 3.84
(d) 3.91

Solutions

Expert Solution

D is right answer

value given in question

Strike price = K = $40

current price =S0= $37.90

price at down node = Sd = $32.1

here we have to use binomial tree so we need value of u and value of d

value of d = Sd/S0 =$32.1/ $37.9 = 0.847

value of u = 1/d = 1/0.847 =1.1806

now find the probability of up (P) = [(1+r) t- d )] / (u - d) = [(1+(0.05*0.5)) - 0.847)] / (1.1806 - 0.847 ) = [(1.0250 - 0.847)] / (1.1806 - 0.847 ) = 0.5335

where r = risk free rate and t is maturity time of option

probability of down (Q) = 1 - P = 1 -0.5335=0.4665

Su = share value at up node = S0 * u = $37.5 * 1.1806 = $44.272

Suu = value at up and up node Su * 1.1806 = $44.272 * 1.1806 = $52.268

Sud = Value st up and down node = Su* d = $44.272 * 0.847 = $37.5

Sdd = value at down and down = Sd * 0.847 = $32.1 * 0.847 = $27.1887

Puu = put value at up up node = Max(0, X - Suu) = Max (0, $40 - $52.268 ) = 0

Pud = put value at up and down node =Max(0, X - Sud) = Max (0, $40 - $37.5) = $2.5

Pdd = value of put option at down and down node = Max(0, X - Suu) = Max (0, $40 -$27.1887) = $12.8113

Pu = put value at up node = [(Puu * P) + (Pud*Q)] / 1+rt=[(0 * 0.5335) + ($2.5 * 0.4655)] / 1+(0.05*0.25)= $1.1493

Pd = put value at up node = [(Pud * P) + (Pdd*Q)] / 1+rt=[($2.5 * 0.5335) + ($12.8113 * 0.4655)] / 1+(0.05*0.25)= $7.2073

P0 = current value of put = [(Puu * P) + (Pud*Q)] / 1+rt=[($1.1493* 0.535) + ($7.2073 * 0.4655)] / 1+(0.05*0.25)= $3.92

where p = probability of up

Q= probability of down

t = interval between node

hence option d is right


Related Solutions

The price of a stock is $40. The price of a one-year put with strike price...
The price of a stock is $40. The price of a one-year put with strike price $30 is $0.70 and a call with the same time to maturity and a strike of $50 costs $0.50. Both options are European. (a) An investor buys one share, shorts one call and buys one put. Draw and comment upon the payoff of this portfolio at maturity as a function of the underlying price. (b) How would your answer to (a) change if the...
A call with a strike price of $60 costs $6. A put with the same strike...
A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4. For each of the intervals defined by the strike price, show the profit functions associated with forming a straddle (long position), and its graphical representation. For what range of stock prices would the straddle lead to a loss?
A 2-step binomial tree is used to value an American put option with strike 104, given...
A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?...
Problem 3 – Naked Put A put with the strike price of $40 was sold short...
Problem 3 – Naked Put A put with the strike price of $40 was sold short at $4.20 when the price of the underlying stock was $38.00 per share. Draw the gain/loss chart for the naked put.
You buy a put with a strike price of $40. Current price is $37.82, has a...
You buy a put with a strike price of $40. Current price is $37.82, has a u of 1.21 and a d of .82. The risk free rate is 1% per period. Use a time period binomial model. if price goes down, what is your holding period return?
Calculate three step Binomial tree call option price please. Stock price = 124.2862, Strike price =...
Calculate three step Binomial tree call option price please. Stock price = 124.2862, Strike price = 120, Volatility = 20%, Interest rate= 0.15%, Days to expiration = 247 days / 365 days Thank you so much
1.The price of a three-month European put option on a stock with a strike price of...
1.The price of a three-month European put option on a stock with a strike price of $60 is $5. There is a $1.0067 dividend expected in one month. The current stock price is $58 and the continuously compounded risk-free rate (all maturities) is 8%. What is the price of a three-month European call option on the same stock with a strike price of $60? Select one: a. $5.19 b. $1.81 c. $2.79 d. $3.19 2.For the above question, if the...
Price a put option with a one-step binomial tree. Suppose So=50, X=40, 1+r=1.06. The u factor...
Price a put option with a one-step binomial tree. Suppose So=50, X=40, 1+r=1.06. The u factor is 1.4 and the d factor is 0.6. Show the steps. (12 points)
Given the following: Call Option: Strike Price = $60, expiration costs $6 Put Option: Strike Price...
Given the following: Call Option: Strike Price = $60, expiration costs $6 Put Option: Strike Price = $60, expiration costs $4 In excel, show the profit from a straddle for this. What range of stock prices would lead to a loss for this? Including a graph would be helpful.
Calculate the value of an 8-month European put option on a currency with a strike price...
Calculate the value of an 8-month European put option on a currency with a strike price of 0.60. The current exchange rate is 0.62, the volatility of the exchange rate is 14%, the domestic and foreign risk-free interest rates are 3% and 5% respectively.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT