Problem 5.3. A stock that does not pay dividend is trading at $100. The stock price will increase by 10% or decrease by 10% in one year. After that, the stock price will increase or decrease by 20% in the second year. The risk-free interest rate is 5% per annum with continuous compounding. Value a two-year American put option with strike price of $102. Note that risk-neutral probabilities or replicating portfolios may differ across two periods. You must also check for early exercise.

Recently, verizon wireless ran a pricing trial in order to estimate the elasticity of demand for its services. the manager selected three states that were representative of its entire service area and increased prices by 5 percent to customers in those areas. one week later, the number of customers enrolled in verizon's cellular plans declined 4 percent in those states, while enrollments in states where prices were not increased remained flat. the manager used this information to estimate the own-price elasticity of demand and, based on her findings, immediately increased prices in all market areas by 5 percent in an attempt to boost the company's 2016 annual revenues. one year later, the manager was perplexed because verizon's 2016 annual revenues were 10 percent lower than those in 2015"the price increase apparently led to a reduction in the company's revenues. did the manager make an error? yes - the one-week measures show demand is inelastic, so a price increase will decrease revenues. yes - the one-week measures show demand is elastic, so a price increase will reduce revenues. yes - cell phone elasticity is likely much larger in the long-run than the short-run. no - the cell phone market must have changed between 2011 and 2012 for this price increase to lower revenues.

The green revolution is a scientific breakthrough that improved seeds for basic crops. how did the green revolution impact the supply of basic crops such as wheat and corn? the supply of wheat and corn increased. there was no impact on the supply of basic crops. the supply of basic crops did not change, but the quantity supplied of basic crops increased. the supply of wheat and corn decreased.

Rachel died in 2014 and her executor is finalizing her estate tax return. the executor has determined that rachel’s adjusted gross estate is $10,120,000 and that her estate is entitled to a charitable deduction in the amount of $500,000. using 2014 rates, calculate the estate tax liability for rachel’s estate.