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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%.
(a) Use the fundamental theorem to find 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.
(b) Comment briefly 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?
(c) 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.
Illinois Tool Company (ITC) fixed operating costs are $1,260,000 and its variable cost ratio (i.e. variable costs as a fraction of sales) is 0.70. The firm has $3,000,000 in bonds outstanding at an interest rate of 8 percent.
Hafers, an electrical supply company, sold $3,200 of equipment to Jim Coates Wiring, Inc. Coates signed a promissory note May 12 with 3.75% interest. What proceeds will Hafers receive.
During the year, Belyk Paving Co. had sales of $2,385,000. Cost of goods sold, administrative and selling expenses, and depreciation expense were $1,440,000, $436,500, and $491,500, respectively.
Assuming the sale price for each Christmas tree stays the same in 2014; calculate the contribution margin per Christmas tree for 2014. Show all workings.
Your parents are giving you $310 a month for 5 years while you are in college. At a 8 percent discount rate, what are these payments worth to you when you first start college
The Black-Scholes formula by change of numeraire Let St be the price at time t of a stock that pays no dividends. - Draw the payout functions for the two options.
Jarvie loves to bike. In fact, he has always turned down better paying jobs to work in bicycle shops where he gets an employee discount. At Jarvie's current shop, Bad Dog Cycles, each employee is allowed to purchase
Bangor Company makes products C and D. Information for overhead costs and for the two products appears below. The company makes 50,000 units of product C each year and 20,000 units of product D.
Sony Corp. packed a shipment of videocassette tapes into a 40-foot ocean container for transport to England. Sony put the tapes into 1,320 cardboard cartons, then strapped the cartons onto fifty two wooden pallets.
The real risk-free rate is 3%, and inflation is expected to be 2% for the next 2 years. A 2-year Treasury security yields 7.5%. What is the maturity risk premium for the 2-year security
Which of the following uncertainties should a well-written sales contract contain provisions for?
Solve the problem of minimizing 3x1 + 4x2 subject to 2x1 + 3x2 ≥ 10 and x1, x2 ∈ {0, 1, 2, 3} using branch and relax without bounds propagation.
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