Assume a 1-year, zero coupon bond trading at $95. One year benchmark rate is 3%.
Recovery rate = 60%
So,
(60p+100(1-p))/1.03 = 95
(100-40p)/1.03 = 95
p = 5.38%, this is the risk neutral probability of default
Can someone please explain why they use the risk-free rate here? I understand to calculate the risk neutral probability, you would use a rate without any risk premiums which is the risk free rate, but why do we even calculate a “risk-neutral” probability? What is the point of it here? Thanks!
Although they use the term “risk-neutral probability”, it’s nothing more nor less than a weight.
Specifically, it’s the weight that leads to an arbitrage-free price.
Thanks, but why is the risk free rate used to discount instead of the YTM?
Because arbitrage is risk-free.
It’s the same reason that you use the risk-free rate to determine the forward price for, say, GOOG. You don’t honestly think that GOOG is going to increase in value at the risk-free rate, but the price in the forward contract uses the risk-free rate to avoid the possibility of arbitrage.
Can I buy you a coffee? thanks a lot… your comments are the best
Thanks, but no thanks, cat.
I hate coffee.
You can buy me tea or hot chocolate, though.
Hi @solebreadwinner , may I know how do you arrive at the formula (60p+100(1-p))/1.03 = 95?
May I know what is risk neutral probability of default in simple terms? I have difficulty trying to understand the concept
Would appreciate if any of you can provide an explanation on this @solebreadwinner @S2000magician
Thank you!
Imagine a binomial tree
Down CF= 60*probability of default
Up CF= 100*probability of success
Discount the answer by onne year
No problem - btw studyign for CFA level 3. which city are u located?
Yorba Linda, CA.
And you?
When’s your Level III exam?