Low Present Value

Wednesday, Sept. 25^th, 2013

This was a frustrating afternoon. An idea which I had been thinking about for months back to the days when living in Mission Apartment didn’t work! I tried several DSGE setups and there were always problems. Then I found the main reason is either there is no clearing for a market or the issue I want to ask becomes trivial if I assign a new exogenous condition. I wrote an email to tell older Joe, my colleague and coworker in Japan, that I got stuck in the bottleneck.

On the Fallen Arm

Xenoblade Chronicles is a critically acclaimed game. I haven’t had a chance to play it, but I have enjoyed its music on Youtube very much. Sunday night I was listening to a song call “On the Fallen Arm.” The music is simple and touching, like sea rolling toward the cliff, the flushing water sparkling in daylight.

A Trip with Low Returns

-->March 8^th

       

      If it were not the EEA annual conference was held in Boston, I couldn't participate in it. I flew to Boston one day prior to the conference day. As usual, I kept awake for the early flight departing at 9am. I was tired while arriving the hotel by subway.

      Boston Park Plaza is a well-known historical hotel located in the old Boston area. However, its service was quite disappointing. I booked a room with a king size bed one month ago, but the hotel gave me a room with double twin beds. The one-night cost $185 didn't include a breakfast and the Internet connection. No refrigerator in the room. What bothered me the most was I have to call room service for a razor and a toothbrush or they are not available.

Infinite Horizon, Infinite Trouble

     To generalize the idea that capital outflow is beneficial to a capital-abundant country, I extended the two-country, two-period model to a two-country, infinite-horizon model. I’d like to discuss the evolution of current accounts and compare consumption paths between open and closed regimes.

      The key factor in the model is the interest rates which depend on the marginal productivity of capital. A capital-abundant country will enjoy higher interest revenue if it exports parts of its capital to a labor-abundant country. So my first hypothesis is that the country’s consumption will decrease for sure in the initial period when the capital restriction is removed and will increase in the future. My second hypothesis is quite bold: the capital-abundant country is always capital abundant. In order to focus on the effect of capital movement on interest rate and welfare, I assume two countries are the identical except the initial capital stocks.

      When I began modeling, I found myself get into big trouble. The calculation is a mess. It took hours and hours to rearrange the equations and hours and hours to correct the wrong rearrangement.  The most significant contribution is that I found one hypothesis is related to the other under some strong conditions. But overall the final result is ambiguous and unsatisfactory, like it was in the two-period model. 

     

A comment to myself: ambitious, incompetent though. 

Pricing Longevity Bonds Makes Live Shorter

The final exam required us to price longevity bonds and incorporated long-run risks into pricing. It is said no paper does this very successfully so far.  One of the biggest problems is that there are many uncertainties should be considered.
To simplify the analysis and make the pricing tractable, I consider only two uncertain sources: interest rates and life expectancy. Since the coupon payment will not be realized until a period of time after the holder purchases the bonds, it is no doubt we need a stochastic discount factor to calculate its price today. This is the same for the mortality rate which is expected to be declined with time. Mimicking the idea of forward rate, I create something called forward mortality rate. Then assume both of them follow Ito process.
Assigning an arbitrary life length, T, I can calculate the present value of coupon for each period starting from the day of realization to T. The price of longevity bonds is just the sum of present values.
Of course it is impossible to get the closed-form present value or price unless we know the exact form of Ito process and T.
The take-home exam is as hard as hell, but it's indeed a good practice for modeling.