Question

Suppose that you have a stock in the one-period binomial model with fixed u, d,and r...

Suppose that you have a stock in the one-period binomial model with fixed u, d,and r suchthat 0< d <1 + r < u. Suppose that there are positive numbers p1and q1such that p1,q1<1, p1+q1= 1, and (1 +r)S0=p1S1(H) +q1S1(T). Show that p1= ̃p and q1= ̃q

.Hint: You know that the risk-neutral probabilities satisfy these equations as well.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In the one-period binomial model, let d be the down factor and let r be the...
In the one-period binomial model, let d be the down factor and let r be the risk-free rate. What will be the arbitrage opportunity if d > 1 + r?
You have a stock in the one-period binomial model such that S0 = 4,S1(H) = 8,S1(T)...
You have a stock in the one-period binomial model such that S0 = 4,S1(H) = 8,S1(T) = 2, and r = 1.5. Show how to extract arbitrage by explicitly defining a portfolio (X, ∆) such that X0 < 0 while X1 ≥ 0.
Suppose that, in each period of a two-period stock price model, the cost of a security...
Suppose that, in each period of a two-period stock price model, 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 $80 and that the interest rate r is 0. a). Compute the risk neutral probabilities p (price moves up) and q = 1−p (price moves down) for this model. b). Sketch a diagram of this two period stock...
Problem: For a two-period binomial model, you are given: (i) Each period is one year. h=1...
Problem: For a two-period binomial model, you are given: (i) Each period is one year. h=1 (ii) The current price for a non-dividend-paying stock is 100. S(0)=100 (iii) when stock price goes up u=1.25, (iv) when stock price down d=0.80, (v) The continuously compounded risk-free interest rate is 7%. r=0.07 Calculate the price of an American call option on the stock with strike price of 100. K=100, was there early exercise?
Consider a one step binomial model. The initial stock price is S0 = $80. There is...
Consider a one step binomial model. The initial stock price is S0 = $80. There is a 60% chance the stock price will rise to $90, and a 40% chance it will fall to $75. The risk-free interest rate is 5%. • Identify u and d • What would the option prices be if the probabilities changed to 70% chance the stock price rises and 30% chance it falls?
Suppose that stock price moves up by 5% (u=1.05) and d=1/u. The current stock price is...
Suppose that stock price moves up by 5% (u=1.05) and d=1/u. The current stock price is $50. Dividend is zero. Compute the current value of a European call option with the strike price of $51 in 3 months using both replicating portfolio valuation method and the risk neutral valuation method. The risk free rate is APR 5% with continuous compounding (or, 5% per annum)1.  Draw the dynamics of stock price and option price using the one step binomial tree. 2. Draw...
1. Consider a stock which trades for $50 (S0 = 50). Consider also a European call...
1. Consider a stock which trades for $50 (S0 = 50). Consider also a European call option with an exercise price of $50 which expires in one year. The risk free rate is 5% cc. Suppose that you calculate the risk-neutral probability of an upward move to be 0.5064.    What is the fair price of the option, based on a two-period binomial model?   Choose the closest answer. A)5.28 B)5.84 C)6.45 D)13.05 2. Consider a stock which trades for $50 (S0...
a. Price a call option using the two-period binomial model assuming the following data. S=120,X=80,u=0.2, d=-.2,and...
a. Price a call option using the two-period binomial model assuming the following data. S=120,X=80,u=0.2, d=-.2,and r=0.10 per period b. What is the hedge ratio for this call option? c. If the call option were priced at $55, what would an arbitrageur do? Discuss an exact strategy?
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
3) Price a put option with a one-step binomial tree. Suppose So=50, X=40, 1+r=1.06. The u...
3) 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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT