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Explanation:

Option-free bond price: 103.60
Bond with embedded option price: 102.80
Price difference: 103.60 - 102.80 = 0.80

This price difference represents the value of the embedded option. Since the bond with the embedded option is cheaper, the embedded option must be an option that benefits the issuer (not the investor).

If the embedded option were a put option (benefiting the investor), the bond would be more valuable, not less.
If the embedded option is a call option (benefiting the issuer), the bond is less valuable because the issuer can call it away.

The investor in the callable bond is effectively short a call option worth 0.80, as they have given the issuer the right to call the bond.

Explanation:

Option-free bond price: 103.60
Bond with embedded option price: 102.80
Price difference: 103.60 - 102.80 = 0.80

If the embedded option were a put option (benefiting the investor), the bond would be more valuable, not less.
If the embedded option is a call option (benefiting the issuer), the bond is less valuable because the issuer can call it away.

The investor in the callable bond is effectively short a call option worth 0.80, as they have given the issuer the right to call the bond.

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In an arbitrage-free framework, the price of an option-free bond is 103.60 and the price of an otherwise identical bond with an embedded option is 102.80. An investor in the bond with an embedded option is:

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Last updated: January 29, 2026 at 14:03

long a put worth 0.80.

20.0%

short a put worth 0.80.

20.0%

short a call worth 0.80.

60.0%