1. You inherit a package of call options on a stock currently selling for $53 (all of the call options expire in exactly one year). In a year, the stock could sell for anywhere between $40 and $80. The package consists of 1 call with a exercise price at $50, 1 written call with an exercise price of $55, one written call with an exercise price of $60 and one call with an exercise price of $65. Just to be clear, you have two calls and two written calls.
a. What is the payoff structure for this portfolio of options? A graph would be an appropriate way to answer this part of the question.
b. What can be known about the sum of the prices of the $50 and $65 calls relative to the sum of the prices of the $55 and $60 call? That is, is C50+C65 greater than, equal to or less than C55+C60? How do you know?

2. You observe that a stock is currently selling for $100. Somehow you know that the two possible values for the stock at time T are $80 and $130. You also observe that (1+r)T = 1.1. You don't know the probabilities of the two states of the world occurring. Using the two-state approach, determine the value of a T period call option with an exercise price of $110.

Answers and explanations to 2 questions on derivatives- the first one on payoff structure for a combination of call options, the other on Binomial tree.

A European Call Option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6-mo.
a) Calculate u, d, and p for a two-step tree
b) Value the option using a two-step tree.

The share value of Drummond, Griffin and McNabb, a New Orleans publishing house, is currently trading at $100.00 but is expected, 90 days from today, to have risen to $150.00 or to have declined to $50.00, depending on critical reviews of its new biography of Ezra Pound. Assuming the riskless interest rate over the next 90 days

Consider a European call option on a non-dividend-paying stock where the stock price is $60, the strike price is $60, the risk-free rate is 6% per annum, the volatility is 30% per annum, and the time to expiration is six months.
Q1: Calculate u, d, and p for a two-step tree. Hint: if the expiration is six months and there ar

An American put option to sell a swiss franc for dollars has a strike price of $0.80 and a time to maturity of one year. The volatility of the swiss franc is 10%, the dollar interest rate is 6%, the swiss franc interest rate is 3%, and the current exchange rate is 0.81. Use a tree with three time steps to value the option. Estim

1) Consider a stock currently selling for $80. It can go up or down by 15% per period. The risk-free rate is 6%. Use a one period binomial model. You want to price a European call option with exercise price of $84.
a. Determine the two possible stock prices at expiration.
b. Construct two portfolios with equivalent payoffs. On

A binomialtree of height O, Bo is a one node tree. A binomialtree of height k, Bk is formed by attaching a binomialtree, Bk-1 to the root of another binomialtree another binomialtree Bk-1. Prove that a binomialtree Bk has 2to the power k nodes.

Calculate of the price of a call option by binomialtree models and compare the results with the theoretical Black-Scholes formula.
Parameters:
Strike price = $120;
Expiration time = 1 year;
Annual interest rate = 0.05;
Stock volatility = 0.35.
For the initial stock price, S0 = 100.45
Requirements:
1. Find the price

I'm trying to answer the questions about the two period binomialtree pasted here. Thanks for your help!!
Pricing options on binomialtree: Consider a two-period binomial example where the underlying asset's price movements are modeled over the next two months, each period corresponding to one month. The current level of the

The current price of a stock is $20. In 1 year, the price will be either $26 or $16. The annual risk-free rate is 5%. Find the price of a call option on the stock that has a strike price of $21 and that expires in 1 year.