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smalldoorboy
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Joined: January 15th, 2008, 7:10 am

Can I treat bonds as put options?

August 5th, 2008, 8:28 am

Hello, Since the payoff of buying bonds are quite similar to selling put options, can I use Black Scholes equation to price bonds? Are there any papers talking about this idea? Thank you very much.
 
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TheBridge
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Joined: November 22nd, 2005, 3:42 pm

Can I treat bonds as put options?

August 5th, 2008, 9:23 am

so the underlying process is the income of the country-company or whatever yes you can theoretically do that but i would not recommand this as the income is not know in a continuous way so what would be the volatility to be used in a BS framework ?
 
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Traden4Alpha
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Can I treat bonds as put options?

August 5th, 2008, 12:28 pm

You could say that a bond is a put on: 1) the difference of assets minus liabilities (with strike of 0); 2) the ratio of assets to liabilities (with strike of 1); or 3) the difference of log(assets) - log(liabilities) (with strike of 0). I suspect that forms #2 and #3 are superior to form #1. At the very least, these balance sheet variables are observable in the quarterly financial reports of companies. One might also be able to develop or find a model that relates continuous stock price to a continuous estimate of the difference of these balance sheet variables. After all, the difference of asset levels minus liability levels is equal to an integration of earnings (revenues minus costs) over time and the stock price represents, in theory, an NPV of expected (=integrated) earnings, too.Whether BS will work is another matter because the equity levels in a company aren't a random walk, but more of an integration of a random walk (the exception might be financial companies whose assets and liabilities follow a random walk in valuation). Also, companies that intentionally vary their levels of leverage may not fit this model that well.
 
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TraderJoe
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Can I treat bonds as put options?

August 5th, 2008, 2:03 pm

QuoteOriginally posted by: smalldoorboyHello, Since the payoff of buying bonds are quite similar to selling put options, can I use Black Scholes equation to price bonds? Are there any papers talking about this idea? Thank you very much.Can you be a little more specific? What type of bond - ZCB, coupon paying bond, fixed rate, floating rate, convertible? What type of put - European, American? What happens if the bond issuer defaults? Sorry if these questions sound trivial ...
 
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Traden4Alpha
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Can I treat bonds as put options?

August 5th, 2008, 2:53 pm

QuoteOriginally posted by: TraderJoeQuoteOriginally posted by: smalldoorboyHello, Since the payoff of buying bonds are quite similar to selling put options, can I use Black Scholes equation to price bonds? Are there any papers talking about this idea? Thank you very much.Can you be a little more specific? What type of bond - ZCB, coupon paying bond, fixed rate, floating rate, convertible? What type of put - European, American? What happens if the bond issuer defaults? Sorry if these questions sound trivial ...This model would best apply to bonds with a fixed payoff structure (i.e., not floating rate or convertibles) with the bond's payoff being the equivalent to premium earned by selling an OTM put. A default represents an exercise of the put option by the borrower to keep the lender's capital. One minus the recovery ratio represents how far ITM the long bond = short put option is. Because defaults can happen at anytime, but may be more prevalent on the maturity date (e.g., the borrower defaults when they find they can't roll the bond), the model would need to mix American and European elements.
Last edited by Traden4Alpha on August 4th, 2008, 10:00 pm, edited 1 time in total.
 
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SemiMartingale
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Can I treat bonds as put options?

August 6th, 2008, 11:53 am

I don't know if it is what your refer to, but for sufficient low values of K, you have the following approximation:Put(T,K) = K * (D(0,T) - B(0,T)) where D(0,T) is the discount factor.
 
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DavidJN
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Can I treat bonds as put options?

August 6th, 2008, 3:35 pm

See Robert Merton's "On the Pricing of Corporate Debt: the risk structure of interest rates", Journal of Finance, 1974
 
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smalldoorboy
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Can I treat bonds as put options?

August 11th, 2008, 2:54 am

Thanks everyone.It looks like the model by Merton only applies to a company with one discount bond outstanding. If a company issue several callalbe coupon bonds with different maturity dates, is there any model which can be applied?