interest rates and put/call prices

The material says that interest rates are directly related to call prices and inversely related. This would mean that an interest rate decrease would cause a decrease in a call price. However, a decrease in rates would lead to an increase in bond prices…if bond prices increased wouldn’t the call option be worth more?

All else equal, increase in bond price will cause a decrease in the call price.

This can be seen by put- call parity, or by the Black-Scholes Merton option pricing model (L2 topic).

For put call parity:

c+x/(1+r) = p+S

Also, say that the bond price goes up (and interest rates decrease), then the price of the call will go down.

This is because if the call is in the money (or at the money), and the call is exercised, the proceeds from the investment will now be reinvested. That is, reinvested at the now lower interest rate. So an investor will not be willing to pay as much for the call, and the call price will decrease.

It should be noted though, that for equity options, the interest rate is not a very big factor for changes in call prices unless the option is in-the-money.

“This is because if the call is in the money (or at the money), and the call is exercised, the proceeds from the investment will now be reinvested. That is, reinvested at the now lower interest rate. So an investor will not be willing to pay as much for the call, and the call price will decrease.”

Never thought about it this way. Since when calculating bonds we assume that the coupon payments are reinvested at the discount rate. This also explains why bonds are issued with a premium when the coupon rate is higher than the (YTM i.e. discount rate).

Thanks dwheats and correct me if I am wrong.

dwheats, you are therefore suggesting that a call option value is inversely related to its own price? It sounds so wrong (but makes sense arithmetically).

Not sure if I understand what you are saying. Please elaborate.

A call option value is positively related to the underlying asset because the payoff at any time is:

c = max(0,S-X)

By price do you mean the underlying assets?

By itsa own price do you mean the underlying assets price?

By its own price do you mean the underlying assets price?

^ I edited my comment above, I meant call price.

By its own price do you mean the underlying assets price?

If market rates are higher than the current YTM on a bond, the bond will subsequently trade at a discount to par (investors are less intrigued by lower rate offered the bond and it will push the price down).

If market rates are less than the current YTM on a bond, the bond will subsequently trade at a premium to par (investors are more intrighed by the higher rate offered on the bond and will push the price up).

I am looking at it from the issuer’s POV, maybe that is why I find it weird. As rates fall, bond prices increase, and the bond has a higher probability of being “redeemed”. Hence, the value of the call option, from the issuer’s POV, is higher when rates fall.

Could you enlighten me on the following dwheats?

“The price of the embedded call option will rise when interest rates decrease. This is because as rates decrease, the possibility that the bonds will be called increases, which adds value to the call option. As the price of the call option increases, the dollar price of the callable bond will decrease or be maintained at the call price.”

http://www.investopedia.com/exam-guide/cfa-level-1/fixed-income-investments/pricing-bonds.asp

This is different than what I was speaking of above. This has to do with a call option on the bond, not on an share of a company. Sorry if my above responses were directed at a wrong question.

The above exerpt is correct. This is because as the bond price increases, it increases the chance that the bond will be called (becuase the issuer can redeem the bond at a price below the market price). This increases the value of the embedded call option.

A decrease in ytm will increase the value of the bond, the bond coupon payments and face value are now disounted at a lower rate, thus increasing the value of the bond. An increase in the value of the bond will increase its intrinsic value if its in the money, thus increasing the value of the call option. Dwheats, I got this from the investopedia link above. What do you mean by market rates. I am assuming you mean the coupon rate? And pardon my spam above, I was trying out the quote feature and unintentionally ended up posting more unecessary comments.

• "If a bond’s coupon rate is above the yield required by the market, the bond will trade above its par value or at a premium. This will occur because investors will be willing to pay up on the bonds price to achieve the additional yield. As investors continue to buy the bond, the yield will decrease until it reaches market equilibrium. Remember that as yield decrease, bond prices rise."

By market rate I mean the yield to maturity on another bond trading in the market.

Ok we’re on the same page then! thanks.

Ohh ok cheers dwheats.