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Derivatives, call option, Binomial tree

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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.

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Solution Summary

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.

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Interest rate derivative management

A fund wishes to sell (write) European calls on 2-year, 4.5% coupon Treasury notes. The notes currently sell for $98.90. The one-year forward rate (r0) is 4.65 percent. The assumed one-year forward rate one year from now (r1,L) is 5.0 percent. The standard deviation is 10 percent. Fill in the seven boxes of the following binomial tree. ASSUME EACH STATE HAS A PROBABILITY OF 50% AND INTEREST IS PAID ANNUALLY. Please show the work needed to complete this problem. So, I am able to learn from it and repeat it.

Textbook used: Investment Analysis Portfolio Management, 8th edition, Reilly and Brown

Reading Assignment: attached "Interest Rate Derivatives" Document
Reading Assignment: attached "Pricing Interest Rate Derivatives" Document

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