Take the 2-minute tour ×
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

Assume a money market has interest rate process $R(t)$. In Shreve's Stochastic Calculus for Finance II, formula (5.2.17) on page 215 defines the discounted process as $$ D(t) = e^{-\int_0^t R(s) ds}. $$

Why is $D(t)$ called "discounted" process?

Does it mean that any value at time t times $D(t)$ will give its present value at time $0$?

share|improve this question
    
Note that this question is really barely on topic: I guess you're not a professional quant are you? Anyway, a quick answer was enough, but please look at the faq in the future. –  SRKX Mar 27 '13 at 13:09
    
@SRKX: I have taken a course for the first four chapters of the book by Shreve, and I am learning the rest of the book now. –  Ethan Mar 27 '13 at 13:17
    
I get that. But the question is trivial; you even guessed the answer inside. So I guess you can see why I say that if you were a professional quant, you wouldn't have asked it. You can accept the answer if you're OK with it. –  SRKX Mar 27 '13 at 13:23
add comment

1 Answer

up vote 5 down vote accepted

Indeed, $D(t)$ is the discount factor used to compute the present value of a cash flow at time $t$:

$$PV = D(t) \cdot CF_t$$

It is more convenient to write it that way when you assume stochastic interest rate because you don't have to write the integral all the time.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.