Pricing ZCBs
A risk-free ZCB promises to pay $1000 in one year. Its price is $800 Interest rate at which you can borrow/lend in the market is 10% per year What is the fair value of the ZCB? What drives the price to the fair value? Arbitrage : If you have two ways of generating the same payoff for sure, they must have the same price If not? Buy low sell high
What drives prices to fair value? Arbitrage
What are the two ways you have to get $1000 in one year? .Buy the ZCB, pay$ Lend$ in the marketplace Lending is like buying a riskfree asset: you pay cash now and get cash later Borrowing is like short selling a riskfree asset: you get cash now and pay cash later So the two ways are: . Buy for$ . Buy for $ What will you do? Buy low sell high What will everyone do? When will they stop doing what they're doing? What if the ZCB cost $980?
Once again
"Fair value" tells you what it would cost to buy an asset's cashflows in the market :Two ways to get those CFs: : Buy asset, cost is price : Invest in market at risk free rate, cost is fair value If the two costs are different, arbitrage will drive them together The arbitrage argument only works when the "two ways" are guaranteed to have the same cashflows
Risky CFs
What is the fair value of a risky cash flow?
I am trying to sell you an asset now for $9fl, whose payoff in one year is uncertain. Its expected payoff is $10fl. There are other assets in the market with "similar" risk tisame "kind" and same "level"ff which have expected returns of 1fl%.
Fair value
If you wanted to get $10fl tiexpectedff with this level of risk in one year, what are your two options? You know that for the same amount of risk, you would need to invest to make an expected amount of $10fl in one year. How did you find that val