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1. Binomial tree: change of numeraire
Consider a one-step, two-state world where a stock has current price 100. After one year the stock is worth 110 with probability 0.8, and 90 with probability 0.2. One-year annually compounded interest rates are 5%.
Use the fundamental theorem to ?nd the risk-neutral probability (of the stock being worth 110) with respect to the numeraires:(i)the money market account; (ii) the ZCB with maturity 1; and (iii) the stock.
Comment brie?y on your answers to (a) (i) and (ii). In particular, can the riskneutral probabilities with respect to the ZCB and money market account ever differ?
By assuming no-arbitrage (thus CK(m,1)/Nm is a martingale for the appropriate numeraire and risk-neutral probability pair), price a one-year 105-strike call using the risk-neutral probabilities from(a)(i),(ii)and(iii). Verify the answers are the same.
Here is Simple Bank's balance sheet (with associated interest rates):
Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected.
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An investor in the USA bought a one-year Singapore security valued at 200,000 Singapore dollars. The US dollar equivalent was $100,000. The Singapore security earned 15 percent during the year
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Need the project's expected NPV and standard deviation of NPV.
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