Had a free hour, so I made a very basic statistical model for the conspiracy theorists out there. It makes a lot of shaky assumptions (as I only had an hour) but I thought I would share the bottom line, which I believe to be accurate within an order of magnitude - the RMA + crop insurers saved approximately $2 billion based on the October rally from $3.21 to $3.76 (and final harvest price of $3.49 vs Oct 1 price of $3.21).

I have no idea how much cash it would take to cause the rally ($20m, $200m, $2bn $20bn) which is why I am posting here, but if it is relatively small, then there would be a large incentive for folks on the other side of the insurance market to see what they can do to increase prices. Anyone know what sort of $$ it would take based on volume seen last month?

I put my code below in case anyone wants to play around with the model assumptions (it is written in R, which is free to use).

#Assume you have a sample of 100000 acres with a mean yield of 174 and sd of 17
#would choose a better distribution if I had more time
yields.2014 = rnorm(100000, mean=174, sd=17)

#Assume those acres have an average TA APH of 160 and sd of 16
yields.average = rnorm(100000, mean=160, sd = 16)

#Assume those acres are insured based on farmdocdaily's analysis
#http://farmdocdaily.illinois.edu/2014/07/will-crop-insurance-make-payments-2014.html
#with 90% GRIP HR assigned to 80% RP and 85% GRIP HR assigned to 75% RP
insured = c(rep(.65,1000),rep(.7, 3000),rep(.75,12000), rep(.8,33000), rep(.85,35000), rep(0,16000))

#Feb prices
feb.price = 4.62
oct1.price = 3.21
harvest.price = 3.49

#Get distributions of guarantees and outcomes
guarantees = yields.average*insured*feb.price
outcomes.oct1price = yields.2014*oct1.price
outcomes.harvestprice = yields.2014*harvest.price

#Get payout distributions
diffs.oct1price = guarantees-outcomes.oct1price
diffs.harvestprice = guarantees-outcomes.harvestprice

#Fix 'negative' payouts
diffs.oct1price <- sapply(diffs.oct1price,function(x){max(0,x)})
diffs.harvestprice <- sapply(diffs.harvestprice,function(x){max(0,x)})

#scale this to 91.6 million planted acres to get final answer
sum(diffs.oct1price-diffs.harvestprice)*(91600000/100000)