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Evolution of short term rates

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In tuckman evolution of short term rates for 3 years ZCB, while computing the today's price we took risk premium into consideration... but when we are computing expected returns he computed p(2,2) as 1000/1.18 instead of 18.4% ....please clarify on that

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @Puneeta because in two years, the bond will have only one year until maturity and its price at maturity (per pulling to par) will be $1,000 (or $100 or 1.0). Under the one-year-per-step, at that point in time, the uncertainty of the interest rate has no impact on the price: the price is the face value discounted at the then-prevailing spot rate (of either 10% or 18%). I think it's helpful also to keep in mind that the risk premium is added to the tree's actual rates only for purposes of increasing the (effective) discount rate: the actual rate tree reflects expectations, then the risk premium concept adds something for purposes of discounting. I have a YouTube video where I try to super simplify this idea, here at Risk Neutral Probabilities https://www.bionicturtle.com/forum/threads/t5-07-risk-neutral-probabilities.22905/