Investor Option Positions in Putable and Callable Bonds

Summary

The note addresses a confusion about comparing a bond putable at a specified date with a callable bond of a stated maturity, and whether put-call parity makes their values equivalent. Its answer focuses on the investor’s option position: the holder of a putable bond is long the put, while the holder of a callable bond is short the call because the issuer controls the call right.

That distinction matters for valuation and payoff comparison. Even if put and call prices happen to match for at-the-money options under particular conditions, being long a put is not the same position as being short a call. The response therefore challenges the claimed equivalence rather than resolving the exercise’s precise timing convention. It gives no option-pricing derivation or assumptions about rates, exercise dates, or bond cash flows, so its point is a warning to identify who owns each embedded option before applying parity.

Key ideas

• A putable bond gives its investor a long put position.
• A callable bond leaves its investor short the issuer’s call option.
• Equal put and call prices in a special case do not make the investor positions equivalent.
• Bond option comparisons must specify option ownership and exercise timing.

Tags

# Time to Put or Call a Bond


# Time to Put or Call a Bond












I was studying putable bond and callable bond on my own, there is an exercise question that was a little confusing to me:

I understand what the answer explains, but I am confused that, is a bond "that is putable at t=4" equal to a 4-year bond that is putable? Statement 1 says, (1) is a bond putable at t=4, I thought it meant the bond can only be put at or after t=4. Statement (2) is a 4 year bond that is callable. According to the answer, with put-call parity, the value of the bond in statement (2) is equal to that of a 4 year bond that is putable. However, does that mean the bond can be put any time within 4 years?

If so, how can the value of statement (1) and (2) be the same? Or is it that the time to put the bond does not matter when valuing a bond?

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/49638

Aren’t both statements incorrect? In a puttable bond, the investor is LONG the put. In a callable bond , the investor is SHORT the call. It may be true that put price = call price for ATM options, but being long a put is always better than being short a call.

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