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Risk Neutral Valuation of a Derivative

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A stock is currently $25. It is known that at the end of 2 months it will be either $23 or $27. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a 2-month derivative that will be either 529 (if the stock price is 23) or 729 (if the stock price is 27)? Use no-arbitrage arguments. Consider a portfolio of:

+delta : shares
-1: derivative

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Solution Summary

The solution values a derivative using Risk Neutral Valuation.

Solution Preview

See the attached Excel file for a proper presentation of this solution.

Portfolio has

+delta : shares

-1: derivative

Therefore

At time t=0

Value of portfolio at time t=0 is $25 delta -f

where f is the value of derivative

At time ...

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