What is the price effect and yeild effects of a call and put option?

Well for a call option, the higher price of the underlying asset is relative to the strike price, the more valuable the call option becomes. For a put option, the higher the price of the underlying asset relative to the strike price is, the less valuable the put option becomes.

And for yield effects, I am not sure. I need to check my notes later on.

here are the things I’ve gathered but still need some clarification on:

the lower the coupon = the lower the price and interest rate sensitivity - ?

the shorter the term = the lower the price and interest rate sensitivity

the lower the initial yeild = the greater the price vol

callable bonds trade at higher prices (what about changes their relation to changes yeilds? also what happens with putable bonds?)

Always think about duration/interest rate sensitivity in relation to the highest duration instrument, a Zero-Coupon Bond. This bond has no coupons and thus is very interest rate sensitive b/c all of the outstanding cash flows are at the very end, with nothing paid in the meantime.

You are correct on shorter term = lower duration or interest rate sensitivity, but this has no direct effect by itself on price - you would need to look at its coupon too. Less time remaining on the bond means it’s getting closer to par $100 whether it’s moving up or down depends on if it was trading at a premium or discount

Yield = coupon/price. Coupon is fixed. So the price changes as people trade the bond around.

If price goes up then that whole fraction goes down, so the yield goes down. We want to buy at higher yields and lower prices, so that the price will go up and the yield will go down eventually.

Callables trade at higher YIELDS (higher coupons), not necessarily prices, in order to compensate investors for the call risk.

Let me know any other questions.

Thank you. What about putable bonds?

putable bonds trade at lower yeilds, right? and that doesn’t necessarily correspond to lower prices? (same question with callables)

lower coupons = higher higher duration?

lastly, can you explain why higher coupons means less duration? if you have higher coupons you have lower interest rate risk and can we also say less price risk?

Thanks!

Yeah putables would trade at lower yields since the put option is valuable to you the bond investor.

the price of the bond matters but those can trade around depending on the bond. But in general, a callable bond is usually issued with a higher coupon to entice investors to buy it & compensate them for the call option. And its price will be at a premium, above par, let’s say $120. Let’s say the coupon is $4 semiannually or $8 annually or 8% annually. So the coupon is 8% and the yield or “YTM” will be 6.7% upon issuance. So since the coupon rate is greater than the yield, it trades at a premium.

yes, lower coupons = higher duration in general

Again, Always think about duration/interest rate sensitivity in relation to the highest duration instrument, a Zero-Coupon Bond. This bond has no coupons and thus is very interest rate sensitive b/c all of the outstanding cash flows are at the very end, with nothing paid in the meantime.

Let me know if that explanation isn’t doing it for you.

Yes, lower interest rate risk would mean that the bond’s price will move around less with rates.

The proper way to think about bonds with embedded options is to think about who owns the options and to remember one important idea:

options have value

Thus, whoever owns the option has to pay for it.

Call options, prepay options, accelerated sinking fund options, and caps on floating-rate bonds all favor the bond issuer: the issuer owns these options. Therefore, the issuer has to pay for these options. They pay for them in one of two ways: they accept a lower price for the bond (than for an option-free bond), or they pay a higher coupon (than for an option-free bond).

Put options, conversion options, and floors on floating-rate bonds all favor the bondholder: the bondholder owns these options. Therefore, the bondholder has to pay for these options. They pay for them in one of two ways: they pay a higher price for the bond (than for an option-free bond), or they accept a lower coupon (than for an option-free bond).

thank you both! one follow up: im seeing a question that asks what happens to the value of put and call options when there is an increase in yield volatility. the answer is that the values of both will increase with greater yield volatility. I got this right but am a little confused because thinking about the formulas now makes me think that the value of the call should decreases with greater volatility. any thought?

My pleasure.

As the volatility of the (price of the) underlying increases, the value of all options (puts and calls) increases: the more volatile the underlying, the greater the chance that the option could be in the money, or further in the money.

However, because a callable bond is, in essence, a portfolio comprising a long (option-free) bond and a short call option, as the value of the call option *increases*, the value of the callable bond _ **decreases** _.

Hey, if we are talking about the relationship between the interest volatility and the value of an option,

remember the formulas:

**Value of the callable bond = value of the option-free bond – value of the call option**

**Value of the putable bond = value of the option-free bond + value of the put option**

Value of the **call option** and the **put option** will both increase with the increase in volatility.

However, as we could see in the formula, the interest volatility affects the callable and the puttable bond in the opposite ways. With an increase in interest volatility, the value of the call option will increase, which will cause the value of the callable bond to decrease (since you are substracting a bigger value). On the other hand, an increase in interest volatility will cause the value of the put option to increase, and make the value of the puttable bond to increase (since you are adding a bigger value).

Therefore, the interest volatility for the callable bond is when the volatility increases and the interest volatility of the puttable bond is when the volatility decreases because in each case, the value of the callable (puttable) bond will decrease.

Hope it clears your confusion!