The futures price of a .com non-dividend stock is $90. The volatility is 20% and the risk-free rate (all maturities) is 5% per year with continuous compounding. Use a three-step tree to value:

I.

An eighteen-month European PUT option with strike price $98. Required to design a three-step tree and include the prices of the stock and the value of the option on every node.

II. a)

b) c) d)

e)

IV.

Under the risk neutral valuation: Explaintheriskneutralvaluationpricingofderivativesprinciple. What is the percentage up movement? Required the calculation. What is the percentage down movement? Required the calculation. Whatistheprobabilityofanupmovementinarisk-neutralworld?Required the calculation. What is the probability of a down movement in a risk-neutral world? Required the calculation.

Applying Put-Call parity, find the price for European CALL with same strike, maturity and underlying asset. Required the calculation.

If the premium for a CALL option is $13, is there any arbitrageur opportunity? Explain the strategy and find the profit.