Investments, tenth edition

  Option Pricing and the Crisis of 2008–2009 

 Merton  

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   shows how option pricing models can provide insight into the financial crisis of 

2008–2009. The key to understanding his argument is to remember that when banks lend 

to or buy the debt of firms with limited liability, they implicitly write a put option to the 

borrower (see Chapter 20, Section 20.5). If the borrower has sufficient assets to pay off 

the loan when it comes due, it will do so, and the lender will be fully repaid. But if the 

borrower has insufficient assets, it can declare bankruptcy and discharge its obligations by 

transferring ownership of the firm to its creditors. The borrower’s ability to satisfy the loan 

by transferring ownership is equivalent to the right to “sell” itself to the creditor for the 

face value of the loan. This arrangement is therefore just like a put option on the firm with 

exercise price equal to the stipulated loan repayment.

   

 Consider the payoff to the lender at loan maturity (time  T ) as a function of the value of 

the borrowing firm,  V  

 T 

 , when the loan, with face value  L,  comes due. If  V  

 T 

   $   L,   the  lender 

is paid off in full. But if  V  

 T 

   ,   L,  the lender gets the firm, which is worth less than the 

promised payment  L.  

 We can write the payoff in a way that emphasizes the implicit put option: 

 

  Payoff 5

b

L

V

T

5 L 2

b

0

L 2 V

T

    

if V

T

$ L

if V

T

, L

  

(21.4)  

Equation 21.4 shows that the payoff on the loan equals  L  (when the firm has sufficient 

assets to pay off the debt),  minus  the payoff of a put option on the value of the firm ( V  

 T 

 ) 

with an exercise price of  L.  Therefore, we may view risky lending as a combination of safe 

lending, with a guaranteed payoff of  L,  combined with a short position in a put option on 

the borrower. 

  

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 This material is based on a lecture given by Robert Merton at MIT in March 2009. You can find the lecture 

online at   http://mitworld.mit.edu/video/659   .