正如某些答主所说，这两个概念通常和固定收益产品（通常为债券）的估值联系在一起！下面，我就详细说一下这两个概念的区别与联系！
首先是YTM（英文全称为yield to maturity），翻译出汉语为汉语为到期收益率，其含义是一个债券在不发生信用风险（严格来说这里应为违约风险，因为信用风险不只包含违约风险）的情况下，债券的持有者将债券持有到期，可以获得的一个回报率！这么说，可能有点抽象！我们举个例子来说明一下，假设一个债券的市场价格为102元，期限为三年，半年付息一次，息票率为4%（年化），那么这个面值为100的债券的YTM的收益率是多少呢？答案是1.6472%（以半年计）。采用金融计算器的按键顺序如下：
而discount rate的使用范围就比YTM广多了，可以说，很多金融产品就是依靠discount rate估计得出来的！discount rate，翻译成汉语就是折现率的意思，一搬用在金融产品的估值中！我们还是举一个例子来说明一下：一张债券，面值为100，期限为3年，半年付息一次，息票率为4%（年化），现在的市场利率为3.2944%（年化）。问一下这张债券的合理价格是多少？聪明的小伙伴，相必已经知道答案了！那就是它的价值为102元！采用金融计算器计算过程与结果如下：
在这个例子中，市场利率3.2944%其实就是discount rate！当然了，在实际的估值过程中，discount rate就不是这么简单了。它有可能是spot rate或forward rate！
现在，我们来说一下这两个之间的区别与联系！
先说区别：
说完了区别，我们再来说一下联系：
从上面的两个例子中，我们就可以看出，这两个的数值在某些情况下是有可能相等的！在假定利率的期限结构是水平的情况下，如果债券的内在价值等于其在市场上的交易价格，那么，YTM就与discount rate在数值上相等！
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YTM=market Discount rate/ price you pay for the money you lend: Interest rate, or market dsicount rate, is Yield to Maturity (YTM)
Value and YTM, if we know one, we can calculate another:
This is kind of why, market value/YTM does not matter to a bond investor, as individual investor usually rely on coupon as a source of profit, and they can not trade as bond trader, and to watch the bond market value as frequently.
If market discount rate is 8%, lower than 10%. it would sell at a preimum of 134.2, why? above it's par value. When bond yields decreases, the present value of its payments, its market value, increases. (lower discount rate means lower risk and safer investment; so HY almost always has cheaper market value than IG)
If calculating a semi-annual bond, we change the PMT to 50, rather than 100 for the annual payment. Remember to also divide YTM by 2, and increase N from 10 t0 20.
Conversely, need to double YTM to get full year YTM
The value of a zero-coupon bond is simply the present value of the maturity payment.
With a discount rate of 3% per period, a 5-period zero-coupon bond with a par value of $1,000 has a value of:
We can summarize the relationships between price and yield as follows:
1. At a point in time,a decrease(increase) in a bond's YTM will increase(decrease) its price.
2. If a bond's coupon rate is greater than its YTM, its price will be at a premium to par value. If a bond's coupon rate is less than its YTM, its price will be at a discount to par value.
3. The percentage decrease in value when the YTM increases by a given amount is smaller than the increase in value when the YTM decreases by the same amount (the price-yield relationship is convex).
4. Other things equal, the price of a bond with a lower coupon rate is more sensitive to a change in yield than is the price of a bond with a higher coupon rate.
5. Other things equal, the price of a bond with a longer maturity is more sensitive to a change in yield than is the price of a bond with a shorter maturity.
Relationship Price V.S. Maturity - constant-yield price trajectory
Prior to maturity,a bond can be selling at a significant discount or premium to par value. However, regardless of its required yield, the price will converge to par value as maturity approaches.
The number of bond coupon payments per year is referred to as the periodicity of a bond.A bond with a periodicity of 2 will have its yield to maturity quoted on a semiannual bond basis. For a given coupon rate, the greater the periodicity, the more compounding periods, and the greater the annual yield.
Adjusting periodicity for comparability
It may be necessary to adjust the quoted yield on a bond to make it comparable with the yield on a bond with a different periodicity.This is illustrated in the following example.
4% on a semiannual bond basis is an effective yield of 2% per 6-month period.
YTM是静态的，买入债券交易价格决定你的YTM，对未来现金流进行折现，刚好等于交易价格的利率，即持有到期利率；Discount Rate是折现率，你可选择任何你认为合适的利率，例如10年国债收益率，作为折现率。
可以说是一样，也可以说是完全不同的东西。
YTM是债券中特有的持有到期收益率，所有的现金流都用同一个折现率来折现的话，那么这个就是YTM；
discount rate就是折现率，可以是YTM，可以是spot rste。
ytm是债券没有违约情况下的irr（内涵收益率），是基于未来各期现金流入和当前债券价格（也就是买这个债的成本）倒算的。
discount rate是折现率，是个很复杂的值，一般是无风险收益率加各种风险溢价，是用来将未来各期现金流入折现成当前价值（pv）
ytm是你买债的收益率，discount rate是主体发债的成本
没啥区别，本质是一个东西
债券的YTM类似于 多期DISCOUNT的一个平均值
一个剩余期限为5年的债券，已知当前价格，可以求ytm。而discount rate是为了求当前价格而存在的，还是以这个剩余期限为5年期的债券为例，假如每半年付息一次，不同期限的现金流的discount rate可以不同。ytm只有一个，而且ytm的假设更强，比如再投资收益率也是它。具体见教材。
YTM就是使得购入债券未来现金流折现值等于购入价的一个Discount rate，不知道这么说能不能帮你理解他们的关系
标签：ytm,discount,rate
