I am struggeling with the question, for example lets take a swap with rate of 3.2 for one year and 3.6 for 2 years and Discount Factor 0.96899 for the first year and 0.93158 for the second year.

Under the assumption that cash holidings are feasible the Dicount Factor stays the same for the 3rth year if the swap rate is unknown. However this leads me to the quesion:

Why is the discount function non increasing if pure cash holdings are feasible?

I appreciate your answer!


The essence of discounting is that now is less risky than later. So a contract to deliver £1 in 1 year is more risky than one to deliver £1 tomorrow, (the counterparty could suffer a credit event) so it is worth less.

Discount factors multiply; if I know that £1 at 1y is worth £0.98 today, and £1 at 2y is worth £0.98 at 1y (i.e. equal rates for both periods), then that £1 at 2y is worth £1 x 0.98 x 0.98 = £0.9604 today.

Increasing discount factors, then, are not impossible, they just imply negative interest rates. I guess the 'pure cash holdings' assumption is that you can always at worst deposit cash at 0% risk-free, so you wouldn't invest in anything with a negative rates; i.e. negative rates wouldn't exist.

But in reality negative rates are quite possible, and actually the case in some markets at present. They just indicate that interest rates are low enough and costs of carry high enough that you are charged for the assurance of keeping your money safe, rather than being paid interest to use the money.


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