Option payoff- debt holder

[Ernest Seow]

Dear all,
I was reading Fixed Income - Credit Analysis Models and is somewhat stuck.
In the reading, the author liken the holder of risky debt as taking the below 2 positions:-

1. investing in risk-free bond and;
2. writing a short put

I understand the payoff for the bond investor when the state of the world is good.
However, when the state of the world is poor i.e. value of company asset (say S) is lower than face value of the risk free debt (say X).
Question: Why is the short put portion’s payoff not X-S but only S? Given poor state of the world, long put will exercise the put and sell S to short put and in return, receive X.
Thank you.
Cheers,
Ernest

 

[oz001]

The bondholder’s total payoff in the worse case will be:
risk free bond (X) - loss on short put (X-S) = S
in other words, the bond is used to pay the put holder, in exchange for receiving the asset S.
The same result derives from put-call parity:
Bond + short put = asset + short call
In the down scenario, the short call is worthless.

 

[Ernest Seow]

oz001 wrote:
The bondholder’s total payoff in the worse case will be:
risk free bond (X) - loss on short put (X-S) = S
in other words, the bond is used to pay the put holder, in exchange for receiving the asset S.
The same result derives from put-call parity:
Bond + short put = asset + short call
In the down scenario, the short call is worthless.

Awesome, thanks for the explanation!

 

[Ernest Seow]

oz001 wrote:
The bondholder’s total payoff in the worse case will be:
risk free bond (X) - loss on short put (X-S) = S
in other words, the bond is used to pay the put holder, in exchange for receiving the asset S.
The same result derives from put-call parity:
Bond + short put = asset + short call
In the down scenario, the short call is worthless.

Awesome, thanks for the explanation!