Under the Option chapter, the notes mentions that “the higher the risk free rate, the higher the Call Option Price”. However, under the Fixed Income Chapter “as an upward sloping yield curve becomes flatter, the Call Option Value increases” which means the “lower the interest rate, the higher the call option value will be”.
I thought these two relationship are exactly the opposite meaning. Can someone help explain these two relationships a little more? Thank you!
Are you sure this is correct? Can you give the exact source where you read this please? 2016 Book, chapter and page.
Trying to reasoning this I can tell the following: Suppose I buy today a call option on interest rates. If middle and long-term interest rates rise above the implied interest rates used to calculate the call price today, then the call becomes more valuable because I can borrow money at a cheaper rate than the market is currently offering (assume we are now at expiration time). This also means that the rate curve became more steeper, right? We can see the positive relationship between interest rates and price of call options on interest rates.
Deriving from above, if the curve become more flat, this means that the rates decreased so the call losses value. Will I exercise a higher borrowing interest rate than the currently rate the market is offering? Nope.
Please check again the source of the statement you quoted.
Hello, Thanks for replying this to me! I totally agree with your explnation. That is why I have been struggling with this. It is listed on Page 190 of the Kaplan Book 4 for the "Valuation and analysis: bonds with embedded option"chapter under the “Shape of the yiled curve” section’s last sentence.
OK i’m assuming we’re talking standard option (listed) on some underlying. Yes this is correct - think of the call option as deferring the purchase of the underlying (say stock), if interest rates are high then the call is more valuable to me because the cost of buying stock and financing the purchase is very costly. Likewise this is opposite for a put (deferred sale). Of course the less convoluted way to think about it is that the interest rate determines the forward price of the underlying.
I don’t know what this is. You might be referring to an embedded call option giving the issuer the right to redeem the bond? In which case lower rates will give it an incentive to re-finance its outstanding debt on more favourable terms.
Oh no man,
One thing is the price of a call option on interest rates and other thing is a bond with an embedded call option. The book is correct in the case of the embedded call.
Bond prices and interest rates are negatively related, this means that when interest rates get higher the bond price gets lower and viceversa. The value of an embedded call in a bond will also be negatively related to the interest rates.
Be careful what you compare. For example, a call in interest rates is totally different than a bond with an embedded call. The first one protects you from interest rates rise and the second one, from bond price rise.
I think you can rely in what my first post explained. I talked about call on interest rates, not bonds with embedded options.
Hope this helps.
This is great to know! Thanks a lot for all the explanations!!! I think I have to pay more attention next time to what I compare. I can finally sleep well tonight now. Thanks!
I’m happy to help 