Value of Risky Debt/Selling Put Option

CFA Level II Fixed Income
#1

Hi everyone,

Hope you’re all plugging away as hard as I am.

My question concerns the following: V(risky debt) = V(risk free debt) - V(put option on company)

Now, I realize that V(risky debt) < V(risk free debt) since there is no risk to the investment and I understand that the put option can be correctly priced using the BSM. The V(put option on company) is a reflection of the probability of default that investors bear the risk for should volatility increase or should market conditions worsen.

I’m having a hard time just understanding the theory behind how selling a put option would account for the difference in risky debt. I was hoping that somebody could put this in layman’s terms for me.

Thanks in advance.

#2

Magician?

#3

Suppose that you make a risky loan of $1 million to a company. Consider what you’ll receive for various values of the company’s assets when the loan matures; if the assets are worth:

  • $2 million, then you get $1 million
  • 1.5 million, then you get $1 million
  • $1.1 million, then you get $1 million
  • $1 million, then you get $1 million
  • $900,000, then you get $900,000
  • $500,000, then you get $500,000
  • $200,000, then you get $200,000

So the payoff is the same as $1,000,000 risk-free, plus a short position in a put option on the company’s assets with a $1 million strike.

#4

I think I might have just confused myself since this is quite clear but thank you for the visual explanation, Sir.

#5

You’re very welcome.