Wilson's School Maths: economics

Showing posts with label economics. Show all posts

Tuesday, 1 May 2012

Black-Scholes: The maths formula linked to the financial crash

BBC News Magazine recently featured a formula that is apparently related to the financial crash - the Black-Scholes model.

$C(S,t)=N(d_1)~S-N(d_2)~K e^{-r(T-t)}\,$
$d_1=\frac{\ln(\frac{S}{K})+(r+\frac{\sigma^{2}}{2})(T-t)}{\sigma\sqrt{T-t}}$
$d_2=\frac{\ln(\frac{S}{K})+(r-\frac{\sigma^{2}}{2})(T-t)}{\sigma\sqrt{T-t}} = d_{1}-\sigma\sqrt{T-t}.$

$\begin{align} P(S,t) &= Ke^{-r(T-t)}-S+C(S,t)\\ &= N(-d_{2})~K e^{-r(T-t)}-N(-d_{1})~S. \end{align}\,$

See the Wikipedia article for details. A-level students will notice the following:

it's multivariable
it's got exponentials
it's got logarithms
it's hard!

Here is an excerpt from the BBC article:

Black-Scholes was first written down in the early 1970s but its story starts earlier than that, in the Dojima Rice Exchange in 17th Century Japan where futures contracts were written for rice traders. A simple futures contract says that I will agree to buy rice from you in one year's time, at a price that we agree right now.

By the 20th Century the Chicago Board of Trade was providing a marketplace for traders to deal not only in futures but in options contracts. An example of an option is a contract where we agree that I can buy rice from you at any time over the next year, at a price that we agree right now - but I don't have to if I don't want to.

Options allow a trader to have a delicious risk-free portfolio You can imagine why this kind of contract might be useful. If I am running a big chain of hamburger restaurants, but I don't know how much beef I'll need to buy next year, and I am nervous that the price of beef might rise, well - all I need is to buy some options on beef.

But then that leads to a very ticklish problem. How much should I be paying for those beef options? What are they worth? And that's where this world-changing equation, the Black-Scholes formula, can help.

from http://www.bbc.co.uk/news/magazine-17866646

Thursday, 22 March 2012

The Budget 2012

Statisticians and economists have had a field day in interpreting this year's Budget. It is difficult to find an unbiased report on George Osborne's offerings this year, but Channel 4 News Factcheck does a credible job in trying to answer the question, who really are the winners and losers?

Will the wealthiest pay more or less?

The blog nicely sums up how difficult it is to model people's behaviour with respect to tax avoidance: "all academics stress that these numbers are vague and forecasts can easily be wrong."

Saturday, 4 February 2012

European Super Highway of Debt

Wondering just how big the Euro debt crisis is? These frightening infographics show you using lorries packed with €100 notes...

Source: http://demonocracy.info/infographics/eu/debt_piigs/debt_piigs.htm

Monday, 30 January 2012

Stephen Hester's bonus

What else could you buy with a bank chief's bonus? What is Stephen Hester worth - visualised. What is Stephen Hester worth?

Source - http://www.guardian.co.uk/news/datablog/graphic/2012/jan/28/stephen-hester-bonus-graphic

Wednesday, 25 January 2012

Economics - UK recessions compared

The latest GDP figures released today showed that the UK economy shrank by 0.2% in the last quarter of 2011. How does this recession compare to previous ones?

National Institute of Economic and Social Research

National Institute of Economic and Social Research

Source http://www.niesr.ac.uk/

Wednesday, 11 January 2012

Economics - UK exports

Which products does the UK export and where does it export them to?

UK Trade exports graphic

Source - http://www.guardian.co.uk/news/datablog/2010/feb/24/uk-trade-exports-imports

Wilson's School Maths