Do flight costs to/from the host nation of an Olympics generally increase around the time of the event, compared to normal seasonal changes? Is there any information available as to how much these increases have been in the past?
While I unfortunately haven't been able to find any comprehensive, hard statistics regarding this, and my personal guess would be an increase, I have found no consistent, conclusive evidence to back up that guess. Instead, I have found examples of it going both ways.
Regarding the 2016 Rio Olympics, according to The Telegraph, flight prices from the UK and Austria to Rio increased by 48% and 74% respectively, compared to the year before. However, the flights from Switzerland and Italy dropped by 1% and 18% respectively for the same comparison.
Regarding the 2012 London Olympics CBC News noted that (emphasis mine):
[Flight] prices are largely unchanged from the same dates last year, in part because mega-events like the Olympics can scare off as many visitors as they attract, [Travel Agent Chris March] said.
"It can work both ways. It entices people to go there and be a part of such an amazing event. But also, people are aware that it's a big city and [with] an extra 3 million people on top of that, it's going to be a busy time."
Before the 2008 Beijing olympics, The Independent noted (emphasis mine):
Air fares have also been cut. In February, the cost of return flights to Beijing during the Olympics started at around £1,200 with Air China and £1,500 with British Airways. Emirates is now offering return flights during the Games from as little as £497, Air China from £503 and BA from £972.