# Why interest rate has positive relationship with option value

### Relationship between bond prices and interest rates (video) | Khan Academy When the interest rate rises by 1%, call value will increase by the Here is an example from an options calculator showing a positive rho for. Rho is the measure of an option's sensitivity to interest rate changes. take into consideration an options price based on its “hedged value”, the idea that an investor uses long or Rho is positive for purchased calls as higher interest rates increase call premiums. It has to do with the cost of carrying the position over time. Why do bonds lose value when interest rates rise? To explain the relationship between bond prices and bond yields, let's Because new bonds are now being issued with a % coupon, your bond, which has a % coupon, is not worth as much as it was U.S. Treasury securities are one such option.

So how much could you sell this bond for? I'm not being precise with the math. I really just want to give you the gist of it. So now, I would pay more than par. Or, you would say that this bond is trading at a premium, a premium to par. So at least in the gut sense, when interest rates went up, people expect more from the bond.

This bond isn't giving more, so the price will go down. Likewise, if interest rates go down, this bond is getting more than what people's expectations are, so people are willing to pay more for that bond. Now let's actually do it with an actual, let's actually do the math to figure out the actual price that someone, a rational person would be willing to pay for a bond given what happens to interest rates.

And to do this, I'm going to do what's called a zero-coupon bond. I'm going to show you zero-coupon bond. Actually, the math is much simpler on this because you don't have to do it for all of the different coupons. You just have to look at the final payment. There is no coupon.

## RHO: How Do Interest Rates Affect Our Option Premiums?

So if I were to draw a payout diagram, it would just look like this. This is one year. This is two years. Now let's say on day one, interest rates for a company like company A, this is company A's bonds, so this is starting off, so day one, day one.

### Why would a value of a call go up when risk-free rate goes up? | AnalystForum

The way to think about it is let's P in this I'm going to do a little bit of math now, but hopefully it won't be too bad. Let's say P is the price that someone is willing to pay for a bond.

Let me just be very clear here. If you do the math here, you get P times 1. So what is this number right here? Let's get a calculator out. Let's get the calculator out. If we have 1, divided by 1. Now, what happens if the interest rate goes up, let's say, the very next day?

And I'm not going to be very specific. I'm going to assume it's always two years out. It's one day less, but that's not going to change the math dramatically. Let's say it's the very next second that interest rates were to go up.

Let's say second one, so it doesn't affect our math in any dramatic way. Let's say interest rates go up. So now all of a sudden, so interest, people expect more.

We'll use the same formula. We bring out the calculator. For money might look like this. Those first few dollars someone has a very low opportunity cost of lending it out, so, their willing to lend it out at a very low interest rate. Then every incremental dollar after that theirs higher opportunity cost, and people will lend it out at a higher and higher rate. Then you have a market equilibrium interest rate. Let me copy and paste this. Then we could think about what happens in different scenarios. Now we have 2 scenarios that we can work on, and then let me just do 1 more. Let's think of a couple.

Let's say that the central bank of our country, in the United States, that would be the Federal Reserve, the central bank prints more money. Then decides to lend out that money. It is disturbed when central banks print money. The way that it enters into circulation in most countries is that the central bank then goes and essentially lends that money. The way it's done in the US Fed, most part they go out and buy government securities which is essentially lending money to the Federal Government.

They do that because that's considered to be the safest investment. They go out there and they lend money. If this is our original supply curve. If this is our original supply curve, but now your Federal Central Bank is printing more money and lending it out. What is going to happen over here? Your supply curve is going to shift to the right at any given price, at any given interest rate.

• RHO: Why Interest Rates Effect Our Option Premiums
• Why would a value of a call go up when risk-free rate goes up?
• Relationship between bond prices and interest rates

Your going to have a larger quantity of money being available. It might look something like Assuming that's the only change that happens you see its effect.

Your new equilibrium price of money, the rent on money, or the interest rate on money is now lower. That's why when the Federal Reserves say I want to lower interest rates, they do so by printing money. They print that money, and they lend it out in the market. That essentially has the effect of lowering interest rates. Let's think about another situation. Let's say this is the Fed prints and lends money. Their lending the money by buying government bonds. When you buy a government bond, your essentially lending that money to the Federal Government. I've done other videos on that where we go into a little bit more detail on that.

Let's think of another situation. Let's think about consumer savings go down. One interesting thing about savings, savings and investment are two opposite sides of the same coin.

When you save money You have the whole financial system right over here. This is the finincial system. That money goes out and is lent to other people. For the most part, hopefully, that money when it's lent is used to invest in someway. If consumer savings goes down that means the supply of money will be shifted to the left. At any given price and any given interest rate their be less money available. In this situation our supply curve is shifting to the left. That would increase interest rates.

ACCA P4 Interest rate options (part 1)

Then you could even make an argument that if consumers savings is going down consumers are going to borrow less as well. You could argue that maybe demand would go up as well.